Verified email at sharif.edu
Sharif University of Technology
1- PhD. in Aerospace Engineering , University of Kansas , 1989, USA.
2- M.S. in Aerospace Engineering, University of Kansas, 1984, USA.
3- B.S. in Aerospace Engineering, University of Kansas, 1982, USA.
4- B.S. in Civil Engineering, University of Kansas, 1982, USA.
5- FAA Private Pilot License, 1981, USA.
• Aerospace Flight Dynamics and Control,
• Stochastic Optimal Control and Nonlinear Filtering,
• Spacecraft Orbit and Attitude determination and Control,
• Motion Planning and Trajectory Optimization,
• Aeroelastic/Statistical Analysis/Simulation of Dynamic Systems,
• Reliability Based and Multidisciplinary Design Optimization.
Amir Shakouri, Seid H. Pourtakdoust, and Mohammad Sayanjali
Advances in Space Research, ISSN: 02731177, eISSN: 18791948, Pages: 992-1000, Published: 15 August 2020 Elsevier BV
Abstract This paper proposes a solution for multiple-impulse orbital maneuvers near circular orbits for special cases where orbital observations are not globally available and the spacecraft is being observed through a limited window from a ground or a space-based station. The current study is particularly useful for small private launching companies with limited access to global observations around the Earth and/or for orbital maneuvers around other planets for which the orbital observations are limited to the in situ equipment. An appropriate cost function is introduced for the sake of minimizing the total control/impulse effort as well as the orbital uncertainty. It is subsequently proved that for a circle-to-circle maneuver, the optimization problem is quasi-convex with respect to the design variables. For near circular trajectories the same cost function is minimized via a gradient based optimization algorithm in order to provide a sub-optimal solution that is efficient both with respect to energy effort and orbital uncertainty. As a relevant case study, a four-impulse orbital maneuver between circular orbits under Mars gravitation is simulated and analyzed to demonstrate the effectiveness of the proposed algorithm.
N. Raouf, A. Davar, and Seid H. Pourtakdoust
Mechanics Based Design of Structures and Machines, ISSN: 15397734, eISSN: 15397742, Published: 2020 Informa UK Limited
Sasan Amani, Seid H. Pourtakdoust, and Farshad Pazooki
Mechanics Based Design of Structures and Machines, ISSN: 15397734, eISSN: 15397742, Published: 2020 Informa UK Limited
S. Saraygord Afshari, Seid H. Pourtakdoust, B.J. Crawford, R. Seethaler, and A.S. Milani
Composite Structures, ISSN: 02638223, Published: 2020 Elsevier BV
Amir Shakouri, Maryam Kiani, and Seid H. Pourtakdoust
IEEE Transactions on Aerospace and Electronic Systems, ISSN: 00189251, eISSN: 15579603, Pages: 2128-2137, Published: October 2019 Institute of Electrical and Electronics Engineers (IEEE)
A novel trajectory design methodology is proposed in the current work to minimize the state uncertainty in the crucial mission of spacecraft rendezvous. The trajectory is shaped under constraints utilizing a multiple-impulse approach. State uncertainty is characterized in terms of covariance, and the impulse time as the only effective parameter in uncertainty propagation is selected to minimize the trace of the covariance matrix. Furthermore, the impulse location is also adopted as the other design parameter to satisfy various translational constraints of the space mission. Efficiency and viability of the proposed idea have been investigated through some scenarios that include constraints on final time, control effort, and maximum thruster limit addition to considering safe corridors. The obtained results show that proper selection of the impulse time and impulse position fulfills a successful feasible rendezvous mission with minimum uncertainty.
Amir Shakouri, Maryam Kiani, and Seid H. Pourtakdoust
Acta Astronautica, ISSN: 00945765, Volume: 161, Pages: 200-208, Published: August 2019 Elsevier BV
Abstract A new shape-based geometric method (SBGM) is proposed for generation of multi-impulse transfer trajectories between arbitrary coplanar oblique orbits via a heuristic algorithm. The key advantage of the proposed SBGM includes a significant reduction in the number of design variables for an N-impulse orbital maneuver leading to a lower computational effort and energy requirement. The SBGM generates a smooth transfer trajectory by joining a number of confocal elliptic arcs such that the intersections share common tangent directions. It is proven that the well-known classic Hohmann transfer and its bi-elliptic counterpart between circular orbits are special cases of the proposed SBGM. The performance and efficiency of the proposed approach is evaluated via computer simulations whose results are compared with those of optimal Lambert maneuver and traditional methods. The results demonstrate a good compatibility and superiority of the proposed SBGM in terms of required energy effort and computational efficiency.
Forough Nasihati Gourabi, Maryam Kiani, and Seid H. Pourtakdoust
Aerospace Science and Technology, ISSN: 12709638, Pages: 671-682, Published: March 2019 Elsevier BV
Abstract Orbit estimation (OE) is a required significant task in almost all space missions. Accordingly, a wide variety of sensors and estimation algorithms have been developed within the last few decades to this aim. However, the current study proposes a novel autonomous OE method that is purely based on temperature data of six orthogonal surfaces of a three-axis stabilized satellite as it orbits around the Earth. While the utility of satellite surface temperature data has been recently investigated for satellite attitude estimation (AE) assuming its navigational information, the present paper is focused on OE via only temperature data that has not been attended to in the related literature. To this end, it is assumed that satellite surfaces are equipped with small plates that are thermally isolated from the internal heat sources so that their temperature changes mainly arise from environmental radiation emanated mainly from the Sun and the Earth. In this sense, a thermal model is developed and demonstrated to show how the satellite surface temperatures and their time rates are the only ingredients needed, as measurement quantities, for the proposed OE method to produce the satellite navigational data in terms of its position and velocity vectors. In addition, the effect of sensor configuration on state observability and estimation accuracy is investigated while the unscented Kalman filter (UKF) is exploited in the estimation process. Performance and viability of the proposed temperature-based OE are verified through Monte Carlo simulations and a comprehensive sensitivity analysis over orbital parameters, satellite initial conditions, sensor accuracy and attitude error.
N. Raouf, Seid H. Pourtakdoust, and S. Samiei Paghaleh
Journal of Failure Analysis and Prevention, ISSN: 15477029, Pages: 1635-1642, Published: 1 December 2018 Springer Science and Business Media LLC
Structural and system reliability of a typical jet vane (JV) thrust vector control (TVC) subsystem subjected to stochastic loadings is investigated. Jet vane TVC (JVTVC) is used in many aerospace liquid and solid propulsion systems. For the purpose of this work, JVTVC structural reliability of a solid rocket propulsion system is computed using an explicit closed-form limit state function. The JV structure is influenced by the internal ballistic loads emanating out of the solid rocket propulsion internal ballistic, whose performance is modeled via a one-dimensional uniform flow assumption at the engine steady operating condition. Subsequently, JV structural reliability is predicted using the methods of mean value first-order second-moment as well as the first- and second-order reliability methods. The reliability results of the analytical methods are compared with Monte Carlo simulation for verification purposes. Finally, a comprehensive sensitivity analysis is performed to identify the key JVTVC and solid rocket propulsion design parameters affecting the TVC total system reliability. The parameters considered for sensitivity analysis include the JV geometric and structural properties as well as the solid rocket propulsion ballistic and geometric features. It turned out that the vane support arm radius and the vane area are the most important strength and load design variables, respectively, that impact the JVTVC failure reliability.
A. Labibian, S.H. Pourtakdoust, A. Alikhani, and H. Fourati
Aerospace Science and Technology, ISSN: 12709638, Volume: 82-83, Pages: 479-486, Published: November 2018 Elsevier BV
This paper is focused on the development and verification of a heat attitude model (HAM) for satellite attitude determination. Within this context, the Sun and the Earth are considered as the main external sources of radiation that could effect the satellite surface temperature changes. Assuming that the satellite orbital position (navigational data) is known, the proposed HAM provides the satellite surface temperature with acceptable accuracy and also relates the net heat flux (NHF) of three orthogonal satellite surfaces to its attitude via the inertial to satellite transformation matrix. The proposed HAM simulation results are verified through comparison with commercial thermal analysis tools. The proposed HAM has been successfully utilized in some researches for attitude estimation, and further studies for practical implementations are still ongoing.
ajad Saraygord Afshari and Seid H. Pourtakdoust
Aviation, ISSN: 16487788, eISSN: 18224180, Pages: 45-54, Published: 16 October 2018 Vilnius Gediminas Technical University
Reliability evaluation is a key factor in serviceability and safety analysis of air vehicles. Structural health monitoring methods have grown to a degree of maturity in many industries. However, there is a challenging interest to tie in SHM with reliability assessment. In this respect, consideration of stochastic structural dynamics with SHM data and random loadings opens a new chapter in failure prevention. The current study focuses on the stochastic behavior of structures as a way to relate SHM data with reliability. In this respect, uncertain factors such as atmospheric turbulence, structural parameters, and sensor outputs are considered in the process of reliability assessment. Firstly, an experimental evaluation is conducted using a simple cantilevered beam. Subsequently, system identification is weaved in with a probability density evolution equation for calculating the reliability of a wing structural component. Numerical simulations demonstrate that structural reliability of a typical WSC can be effectively evaluated. The proposed scheme paves the way for new SHM research topics such as online life prediction and reliability based failure prevention.
A Hassanpour and Seid H Pourtakdoust
Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, ISSN: 09544100, eISSN: 20413025, Volume: 232, Pages: 2034-2047, Published: 1 September 2018 SAGE Publications
Microburst is considered an extreme powerful hazard for aircrafts, especially during takeoff, approach and landing phases of flight. Current airborne piloting practices involve taking alternative routes, if early detection of microburst wind shear (MBW) for its effective avoidance is possible. In this respect, design and analysis of precision automatic flight path control systems for microburst penetration are of outmost importance whose success can significantly reduce crash risks and thus enhance the flight safety. The current study is focused on the design and analysis of a three-dimensional model predictive controller for a wide body transport type aircraft encountering MBW in approach to landing phase of flight. This task is performed utilizing the full nonlinear six degrees of freedom aircraft equations of motion and the most complete 3D model of the MBW and its gradients. The results are promising for online applications as the proposed model predictive controller-based controller has effectively guided and kept the aircraft on the approach glide path with negligible deviations against aircraft initial lateral displacements, sharp edge gust disturbance as well as the MBW.
S. Saraygord Afshari and Seid H. Pourtakdoust
Structural Control and Health Monitoring, ISSN: 15452255, eISSN: 15452263, Published: August 2018 Wiley
H. Zare, Seid H. Pourtakdoust, and A. Bighashdel
Aeronautical Journal, ISSN: 00019240, Volume: 122, Issue: 1254, Pages: 1176-1198, Published: 1 August 2018 Cambridge University Press (CUP)
ABSTRACTThe effect of inertial forces on the Structural Dynamics (SD) behaviour of Elastic Flapping Wings (EFWs) is investigated. In this regard, an analytical modal-based SD solution of EFW undergoing a prescribed rigid body motion is initially derived. The formulated initial-value problem is solved analytically to study the EFW structural responses, and sensitivity with respect to EFWs’ key parameters. As a case study, a rectangular wing undergoing a prescribed sinusoidal motion is simulated. The analytical solution is derived for the first time and helps towards a conceptual understanding of the overall EFW's SD behaviour and its analysis required in their designs. Specifically, the EFW transient and steady response in on-off servo condition is also attended.
Hadi Zare, Seid H. Pourtakdoust and Ariyan Bighashdel
Advances in Aircraft and Spacecraft Science, ISSN: 2287528X, eISSN: 22875271, Pages: 335-348, Published: 1 May 2018 Techno Press
A. Bighashdel, H. Zare, Seid H. Pourtakdoust, and Ali A. Sheikhy
IEEE Sensors Journal, ISSN: 1530437X, Pages: 3572-3579, Published: 1 May 2018 Institute of Electrical and Electronics Engineers (IEEE)
Strain gauge balances (SGBs) are efficient and accurate means of static force measurement. However, due to their inherent elastic characteristics, they lack desired performance when used in dynamic loading conditions. In this paper, a novel technique is presented that remedies their inherent weakness in measuring dynamic periodic forces. The proposed method produces a correction factor to compensate the measured loading in dynamic situations. For this purpose, first an analytical investigation is performed to determine the structural dynamic behavior of a typical SGB system via the modal approach. This analytical investigation leads to identification of the structural interference effects that occurs on the SGB output in dynamic scenarios and renders the desired validated dynamic correction factor for periodic loading correction. The proposed methodology allows for extraction of the true SGB signal and/or loading out of the complex erroneous SGB output. As a case study, a periodic loading is measured via two different balances and the results are compared with and without taking into account the correction factor. The result of this investigation demonstrates that the introduced correction factor plays a crucial role in dynamic force estimation, especially when the loading frequency approaches the natural frequencies of the balancing system structure.
Maryam Kiani, Aylin Barzegar, and Seid H. Pourtakdoust
Acta Astronautica, ISSN: 00945765, Volume: 144, Pages: 271-282, Published: March 2018 Elsevier BV
Abstract Gaussian approximation filters have increasingly been developed to enhance the accuracy of attitude estimation in space missions. The effective employment of these algorithms demands accurate knowledge of system dynamics and measurement models, as well as their noise characteristics, which are usually unavailable or unreliable. An innovation-based adaptive filtering approach has been adopted as a solution to this problem; however, it exhibits two major challenges, namely appropriate window size selection and guaranteed assurance of positive definiteness for the estimated noise covariance matrices. The current work presents two novel techniques based on relative entropy and confidence level concepts in order to address the abovementioned drawbacks. The proposed adaptation techniques are applied to two nonlinear state estimation algorithms of the extended Kalman filter and cubature Kalman filter for attitude estimation of a low earth orbit satellite equipped with three-axis magnetometers and Sun sensors. The effectiveness of the proposed adaptation scheme is demonstrated by means of comprehensive sensitivity analysis on the system and environmental parameters by using extensive independent Monte Carlo simulations.
Seid Miad Zandavi and Seid H. Pourtakdoust
Structural and Multidisciplinary Optimization, ISSN: 1615147X, eISSN: 16151488, Pages: 705-720, Published: 1 February 2018 Springer Science and Business Media LLC
This paper presents design of a typical Guided Flying Vehicle (GFV) using the multidisciplinary design optimization (MDO). The main objectives of this multi-disciplinary design are maximizing the payload’s weight as well as minimizing the miss distance. The main disciplines considered for this design include aerodynamics, dynamic, guidance, control, structure, weight and balance. This design of GFV is applied to three and six Degree of Freedom (DOF) to show comparison of simulation results. The hybrid scheme of optimization algorithm is based on Nelder-Mead Simplex optimization algorithm and Nondominated Sorting Genetic Algorithm II (NSGA II), called Simplex-NSGA II. This scheme is implemented for finding an optimal solution through the MDO. The Simplex-NSGA II method is a heuristic optimization algorithm that applies to multi-objective functions and the results are then compared with the most famous algorithms, like Nondominated Sorting Genetic Algorithm II (NSGA II) and Multi-Objective Particle Swarm Optimization (MOPSO). Simulation results demonstrate the superior performance of the Simplex-NSGA II over NSGA II and MOPSO. Also, it is used in this study in order to achieve an optimal solution using MDO in both 3DOF and 6DOF simulations of GFV to reach desirable performance index.
A. Labibian, A. Alikhani, and Seid H. Pourtakdoust
Aerospace Science and Technology, ISSN: 12709638, Pages: 317-327, Published: November 2017 Elsevier BV
Abstract This paper presents a novel heat based measurement model for attitude determination (AD) using temperature data via two filtering techniques. Within the space environment, the Sun and Earth are considered as the major sources of external radiation that affect satellite surface temperature. In order to perform the required AD task, the satellite surface temperatures are related to its attitude via a proposed heat model (HM), assuming that the satellite navigational data is available. The proposed HM relates the net heat flux of three satellite orthogonal surfaces to its attitude. Filtering implementation of the proposed HM using the Unscented Kalman Filter (UKF) for AD is the key contribution of this paper, while the results are compared with those of the Extended Kalman Filter (EKF) for performance assessment. The results demonstrate the positive applicability of the proposed HM for AD via filtering, while performance evaluation of both filtering techniques is performed using a Monte Carlo simulation. In addition, threshold boundaries for the satellite initial attitude and rates error for which the proposed HM is able to produce acceptable AD results are outlined. The study is completed with a pertinent conclusion and future research directives.
Mojtaba Sharifi, Seid H. Pourtakdoust, and Mohamad Parnianpour
Optimal Control Applications and Methods, ISSN: 01432087, eISSN: 10991514, Pages: 167-183, Published: 1 March 2017 Wiley
Sajad Saraygord Afshari and Seid H. Pourtakdoust
Proceedings of SPIE - The International Society for Optical Engineering, ISSN: 0277786X, eISSN: 1996756X, Volume: 10168, Published: 2017 SPIE
Many modern industrialized systems such as aircrafts, rotating turbines, satellite booms, etc. cannot perform their desired tasks accurately if their uninhibited structural vibrations are not controlled properly. Structural health monitoring and online reliability calculations are emerging new means to handle system imposed uncertainties. As stochastic forcing are unavoidable, in most engineering systems, it is often needed to take them into the account for the control design process. In this research, smart material technology is utilized for structural health monitoring and control in order to keep the system in a reliable performance range. In this regard, a reliability-based cost function is assigned for both controller gain optimization as well as sensor placement. The proposed scheme is implemented and verified for a wing section. Comparison of results for the frequency responses is considered to show potential applicability of the presented technique.
N. Raouf and Seid H. Pourtakdoust
Journal of Spacecraft and Rockets, ISSN: 00224650, eISSN: 15336794, Pages: 306-314, Published: 2017 American Institute of Aeronautics and Astronautics (AIAA)
Time-varying structural reliability of a multistage solid-propellant launch vehicle subjected to deterministic and stochastic loads is investigated. The study is of practical importance because the launch vehicle’s structure is influenced by a combination of external aerodynamics as well as inertial and internal ballistic loads emanating from the solid rocket motors. In addition, as launch-vehicle flight conditions change during flight, the vehicle will be subjected to time-varying loads. In this sense, the environmental, aerodynamic, and internal pressure fluctuations can be interpreted as stochastic forces affecting the launch-vehicle structural reliability. To account for temporal variations of the total loads experienced by the launch vehicle, its time-dependent structural reliability is formulated via a stress limit state function. The first-order reliability method is used to estimate the launch-vehicle cumulative failure probability as a function of flight time. The results are verified using the m...
Multisensor Attitude Estimation: Fundamental Concepts and Applications, Pages: 181-198, Published: 3 November 2016 CRC Press
A. Labibian, Seid. H. Pourtakdoust, M. Kiani, Ali Akbar Sheikhi, and A. Alikhani
Sensors and Actuators, A: Physical, ISSN: 09244247, Volume: 250, Pages: 114-122, Published: 15 October 2016 Elsevier BV
Abstract Attitude Determination (AD) is one of the key requirements of many current and emerging remote sensing missions. As such AD has been traditionally accomplished through a variety of algorithms and measurement models pertinent to sensing mechanisms. The current paper addresses conceptual validation and utility of a novel radiation based heat (measurement) model for space application. The proposed new Heat Attitude (HA) model utilizes temperature data to relate the Satellite Surfaces’ (SS) Net Heat Flux (NHF) to attitude assuming that the satellite navigational data are available. As Sun and the Earth are considered the main external sources of radiation, their effects are modeled for the SS temperature changes via a novel measurement model and sensing mechanism. In this respect and in order to experimentally validate the capability of the proposed HA model, a Cubic Laboratory Satellite (CLS) with three orthogonal copper coated surface plates is constructed. Next, Non-Contact Thermopiles (NCT) are installed to measure the SS radiative temperatures in a vacuum chamber equipped with a Sun simulator. Subsequently, the CLS is tested under static and dynamic scenarios where the temperature data are used for error analysis and model validation via an Extended Kaman Filter (EKF). Comparison of the CLS true and HA model EKF estimated attitudes demonstrate a good accuracy. In this sense, the proposed novel HA model is promising and paves the way for a new low cost alternative approach for space AD applications.
Seid H. Pourtakdoust and Jalal Karimi
Advanced UAV Aerodynamics, Flight Stability and Control: Novel Concepts, Theory and Applications, Pages: 577-611, Published: 30 August 2016 John Wiley & Sons, Ltd
Seid H. Pourtakdoust and Maryam Kiani
Advanced UAV Aerodynamics, Flight Stability and Control: Novel Concepts, Theory and Applications, Pages: 613-644, Published: 30 August 2016 John Wiley & Sons, Ltd
H. Shahrabi and Seid H. Pourtakd
Journal of Systems Engineering and Electronics, ISSN: 16711793, Pages: 634-648, Published: 22 June 2016 Journal of Systems Engineering and Electronics
N. Raouf, Seid H. Pourtakdoust, B. Ashouri Amin Abadi, and A. Rajabi-Ghanavieh
Journal of Spacecraft and Rockets, ISSN: 00224650, eISSN: 15336794, Pages: 389-392, Published: 2016 American Institute of Aeronautics and Astronautics (AIAA)
M. Kiani and Seid H. Pourtakdoust
Aerospace Science and Technology, ISSN: 12709638, Pages: 159-167, Published: 27 July 2015 Elsevier BV
Orbit determination (OD) problem utilizing onboard sensors is a key requirement for many current and future space missions. Though there exists ample research and work on this subject, a novel algorithm is presented in this paper for the nonlinear problem of OD. In this regard, initially a new cubature–quadrature particle filter (CQPF) that uses the square-root cubature–quadrature Kalman filter (SR-CQKF) to generate the importance proposal distribution is developed. The developed CQPF scheme avoids the limitation of the standard particle filter (PF) concerning new measurements. Subsequently, CQPF is enhanced to take advantage of the relative entropy (Kullback–Leibler Distance) criterion to adaptively select the number of particles thus enhancing the efficiency and accuracy of the newly proposed adaptive CQPF (ACQPF). The current study also applies ACQPF for the OD of a low Earth orbit (LEO) satellite equipped with a three-axis magnetometer (TAM) sensor pack that provides noisy geomagnetic field measurements. The results and performance of the proposed filter are compared with a variety of Gaussian approximation filters as well as different versions of PF via a Monte Carlo simulation. It is demonstrated that the proposed ACQPF outperforms the comparative estimators in terms of the root mean square of the estimation error. Moreover, a sensitivity analysis on the orbital elements, plants' and the estimators' parameters is conducted to verify the feasibility and robustness of the ACQPF over a wider acceptable range of operating system and environment.
Maryam Kiani, Seid H. Pourtakdoust, and Ali Akbar Sheikhy
Measurement: Journal of the International Measurement Confederation, ISSN: 02632241, Pages: 180-190, Published: 11 June 2015 Elsevier BV
Abstract Three-axis magnetometers (TAMs) have been widely utilized as the cornerstone of integrated navigation (IN) and attitude determination (AD) in many aerospace systems. However, accurate navigation and AD demands for precise calibration of TAM. For this purpose, a complete TAM calibration process is presented in the current research to compensate all of the key errors. In this regard, a hyper least square (HyperLS) estimator is extended for accurate and consistent ellipsoid fitting problem of TAM calibration. Subsequently, the calibrated TAM is utilized for real time attitude determination via nonlinear colored noise filters of extended Kalman filter, simplex unscented Kalman filter (SUKF) and cubature Kalman filter. Effectiveness of the proposed calibration scheme is investigated through implementation on a Honeywell HMC5883L magnetometer. Comparative study of the results with those of well-known methods of strict ellipsoid and the three-step algorithm demonstrates the suitability of the HyperLS and SUKF in terms of accessible estimation accuracy.
M. Kiani and Seid H. Pourtakdoust
Applied Soft Computing Journal, ISSN: 15684946, Pages: 1-17, Published: 22 May 2015 Elsevier BV
Abstract New heuristic filters are proposed for state estimation of nonlinear dynamic systems based on particle swarm optimization (PSO) and differential evolution (DE). The methodology converts state estimation problem into dynamic optimization to find the best estimate recursively. In the proposed strategy the particle number is adaptively set based on the weighted variance of the particles. To have a filter with minimal parameter settings, PSO with exponential distribution (PSO-E) is selected in conjunction with jDE to self-adapt the other control parameters. The performance of the proposed adaptive evolutionary algorithms i.e. adaptive PSO-E, adaptive DE and adaptive jDE is studied through a comparative study on a suite of well-known uni- and multi-modal benchmark functions. The results indicate an improved performance of the adaptive algorithms relative to original simple versions. Further, the performance of the proposed heuristic filters generally called adaptive particle swarm filters (APSF) or adaptive differential evolution filters (ADEF) are evaluated using different linear (nonlinear)/Gaussian (non-Gaussian) test systems. Comparison of the results to those of the extended Kalman filter, unscented Kalman filter, and particle filter indicate that the adopted strategy fulfills the essential requirements of accuracy for nonlinear state estimation.
Maryam Kiani and Seid H. Pourtakdoust
Advances in Space Research, ISSN: 02731177, eISSN: 18791948, Pages: 1028-1037, Published: 15 February 2015 Elsevier BV
Abstract Accurate orbit determination (OD) is vital for every space mission. This paper proposes a novel heuristic filter based on adaptive sample-size Gaussian swarm optimization (AGSF). The proposed estimator considers the OD as a stochastic dynamic optimization problem that utilizes a swarm of particles in order to find the best estimation at every time step. One of the key contributions of this paper is the adaptation of the swarm size using a weighted variance approach. The proposed strategy is simulated for a low Earth orbit (LEO) OD problem utilizing geomagnetic field measurements at 700 km altitude. The performance of the proposed AGSF is verified using Monte Carlo simulation whose results are compared with other advanced sample based nonlinear filters. It is demonstrated that the adopted filter achieves about 2.5 km accuracy in position estimation that fulfills the essential requirements of accuracy and convergence time for OD problem.
N Raouf and Seid H Pourtakdoust
Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, ISSN: 09544100, eISSN: 20413025, Volume: 229, Pages: 1785-1797, Published: 21 August 2015 SAGE Publications
This paper focuses on multi-objective reliability optimization of a two-stage launch vehicle using a hybridized Genetic Algorithm-Particle Swarm Optimization with provisions of relative weighting between the objectives. In this respect, the launch vehicle key subsystems as well as their functions are initially introduced. Subsequently, the system reliability block diagram is constructed using the launch vehicle working order of the subsystems augmented with the requirements for a robust fault/failure tolerant design and performance. Next, based on the proposed reliability block diagram arrangement a bi-objective optimization is formulated to maximize the system reliability while minimizing the launch vehicle cost with design variables being the component reliability, system redundancy level, and the type of components. To examine the validity of the proposed algorithm, a benchmark problem in reliability-redundancy optimization is also investigated through the proposed scheme. Benchmark simulation results indicate that neither genetic algorithm nor the particle swarm optimization alone can produce sufficiently accurate optimal results, but their hybrid combination is more efficient and achieves the desired level of accuracy. Thus the proposed hybrid genetic algorithm-particle swarm optimization is applied to the problem of launch vehicle multi-objective reliability optimization that has resulted in a convex Pareto front, out of which many design points could be selected for implementation. Finally, a Monte Carlo simulation is performed against the subsystem reliability uncertainty in order to analyze the effect of uncertainty on the total launch vehicle reliability and cost.
J Karimi and Seid H Pourtakdoust
Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, ISSN: 09544100, eISSN: 20413025, Volume: 229, Pages: 1043-1056, Published: 18 May 2015 SAGE Publications
A major issue required to enhance the autonomy level of unmanned vehicles is real-time motion planning. In this context, optimal trajectories need to be generated online considering the vehicle’s dynamic potentials and constraints. However, autonomous air vehicles often need to plan and execute their missions with varying objectives that may even be dictated in flight. Therefore, the current study introduces and focuses on the new concept of variable-objective motion planning. In this regard, a new dynamic multi-objective heuristic optimization algorithm is developed for path and motion planning of autonomous air vehicles in presence of deterministic terrain obstacles as well as random threats. Effectiveness of the proposed algorithm is demonstrated via several simulated scenarios and verified against past research. The results are promising and indicative of a good potential of the proposed algorithm in producing optimal real-time optimal feasible trajectories with multi-variable objectives.
M. Sayanjali and Seid H. Pourtakdoust
Acta Astronautica, ISSN: 00945765, Volume: 110, Pages: 115-128, Published: May 2015 Elsevier BV
Abstract This paper investigates the problem of optimal transfer trajectory design towards the L2 centered Halo orbit of the Sun–Earth three body system, where the initial launch is to start from a low Earth parking orbit (LEO). The proposed optimal transfer trajectory consists of an active part with low-thrust propulsion and a passive coasting part with no thrust or fuel consumption. In this respect a pseudo-stable manifold (SM) is initially determined through backward time integration of the bicircular four body (BCFB) equations of motion, whose initial states are obtained via stable manifolds of the restricted three body problem (R3BP). The optimal transfer trajectories are extracted via a hybrid direct–indirect optimization formulation applied on both R3BP as well as the BCFB models for comparative purposes. The optimal transfer trajectories are designed and analyzed for different Halo injection points (HOI), different Moon׳s final anomaly (FMA) and also for different locations of the burn-out conditions.
Kourosh Darvish, Seid H. Pourtakdoust, and Nima Assadian
Aerospace Science and Technology, ISSN: 12709638, Pages: 12-24, Published: April 2015 Elsevier BV
The problem of spacecraft formation control and reconfiguration for halo orbit around the second libration point (L2) of the Sun–Earth Three Body (TB) system is investigated. Station keeping, reconfiguration and precision formation control of spacecrafts on halo orbits are performed via the use of the nonlinear Integral Sliding Mode (ISM) method as well as the optimal closed loop Linear Quadratic Regulator (LQR) approach. In this regard the nonlinear relative dynamics of deputy–chief spacecrafts are derived within the concept of the three body problem. The behavior of the two controllers are compared for different tasks of the formation mission in order to determine the more preferred strategy that fulfills the desired response behavior. In addition the controllers are evaluated for robustness in terms of their compensation against the major source of environmental disturbance, namely the Moon's gravity perturbation.
Mohammad Samani and Seid H. Pourtakdoust
Journal of Theoretical and Applied Mechanics (Poland), ISSN: 14292955, Pages: 1115-1124, Published: 2014 Polish Society of Theoretical and Applied Mechanics
In this paper, selection and analysis of an atmospheric two stage separation system is discussed. The main purpose of this system is to test a supersonic parachute projectile, where a stage separation occurs after the burn out. Subsequently, the parachute is ejected from the payload after a minimum elapsed time. The separation times, for the supersonic parachute ejection, as well as the time needed for a safe clearing distance between the two stages are two critical issues in the separation process. In this respect, the knowledge of the relative position between the two stages is necessary to assure a safe distance and in order to adjust the required system parameters. In addition, as the nature of the parameters involved in the separation process is not deterministic, it would be useful to utilize the concept of random variables in the dynamic modeling of the separation process. In this paper, the modeling and simulation of the separation process is initially performed and partially verified. Subsequently, an approximate statistical method is utilized to acquire some probabilistic information about the relative distances at the two critical times. According to the simulation results, the relative distance between the two stages falls in a safe region. Finally, Monte Carlo simulation is also performed for comparison and verification of the statistical results that indicated a small and acceptable deviation between the two approaches. Thus, it can be concluded that the simpler approximate statistical approach is also valid for uncertainty analysis and can provide valuable knowledge needed in the preliminary design phase of the separation system.
Scientia Iranica, ISSN: 10263098, eISSN: 23453605, Pages: 1451-1460, Published: 2014
Maryam Kiani and Seid H. Pourtakdoust
Acta Astronautica, ISSN: 00945765, Volume: 105, Pages: 109-116, Published: December 2014 Elsevier BV
Abstract A novel algorithm is presented in this study for estimation of spacecraft׳s attitudes and angular rates from vector observations. In this regard, a new cubature–quadrature particle filter (CQPF) is initially developed that uses the Square-Root Cubature–Quadrature Kalman Filter (SR-CQKF) to generate the importance proposal distribution. The developed CQPF scheme avoids the basic limitation of particle filter (PF) with regards to counting the new measurements. Subsequently, CQPF is enhanced to adjust the sample size at every time step utilizing the idea of confidence intervals, thus improving the efficiency and accuracy of the newly proposed adaptive CQPF (ACQPF). In addition, application of the q-method for filter initialization has intensified the computation burden as well. The current study also applies ACQPF to the problem of attitude estimation of a low Earth orbit (LEO) satellite. For this purpose, the undertaken satellite is equipped with a three-axis magnetometer (TAM) as well as a sun sensor pack that provide noisy geomagnetic field data and Sun direction measurements, respectively. The results and performance of the proposed filter are investigated and compared with those of the extended Kalman filter (EKF) and the standard particle filter (PF) utilizing a Monte Carlo simulation. The comparison demonstrates the viability and the accuracy of the proposed nonlinear estimator.
Seid H. Pourtakdoust and M. Sayanjali
Nonlinear Dynamics, ISSN: 0924090X, Pages: 955-972, Published: April 2014 Springer Science and Business Media LLC
In this paper, the gravitational effect of a fourth body on the resonance orbit defined in the restricted three-body problem (RTBP) is considered. In this regard, Resonance Hamiltonian of the RTBP and the Hamiltonian associated with the fourth gravitational body that perturbs the resonance orbit are computed. The Melnikov approach is utilized as a mean for the detection of chaos in resonance orbit under the influence of the fourth gravitation body. In addition, the numerical simulation of RTBP and bicircular four-body model, time–frequency analysis (TFA), and fast Lyapunov indicator (FLI) are performed to verify the results of the Melnikov approach. The results indicate that for the (2:1) resonance orbit, the Melnikov integral computed over outer loop of separatrix does not cross the zero line, and consequently chaos is unexpected. On the other hand, the Melnikov integral computed over the inner sepratrix loop crosses the zero line indicating a potential for chaos. Similarly, it is shown that inclusion of the fourth body gravitation leads the (3:1) as well as the (4:1) resonance orbits to chaos. Additionally, simulation results indicate that for some initial conditions on the separatrix, the fourth body effect bounds the amplitude of the resonance orbits while diffusing its corresponding trajectory in the bounded phase space. TFA and the FLI verify similar results.
M Kiani and Seid H Pourtakdoust
Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, ISSN: 09544100, eISSN: 20413025, Volume: 228, Pages: 801-819, Published: May 2014 SAGE Publications
Concurrent orbit and attitude determination (COAD) plays a key role in reducing the cost of navigation and control subsystem for small satellites. This article is devoted to the problem of the COAD of satellites. A measurement package consisting of three axis magnetometer (TAM) and a sun sensor is shown to be sufficient to estimate the attitude and orbit information. To this end, an autonomous gyro-less COAD algorithm is proposed and implemented through the centralized data fusion of the TAM and the sun sensor. The set of nonlinear-coupled roto-translation dynamics of the satellite is used with a modified unscented Kalman filter (MUKF) to estimate the full satellite states. The MUKF is specially proposed to substantially cut the run time by minimizing the number of required sigma points. The results indicate that the adopted strategy fulfills the essential requirements of accuracy and the speed of state estimation. Local observability is demonstrated and an extensive Monte Carlo simulation has shown desirable stability characteristics for the proposed algorithm. Additionally, a sensitivity analysis on the orbital elements and sensor characteristics is performed to verify the feasibility and utility of the MUKF over a wider acceptable range of sensory and operating environments.
Journal of Theoretical and Applied Mechanics (Poland), ISSN: 14292955, Pages: 47-60, Published: 2014
J. Karimi and Seid H. Pourtakdoust
Aerospace Science and Technology, ISSN: 12709638, Pages: 60-71, Published: April 2013 Elsevier BV
Abstract Motion planning is a key factor in enhancing the autonomy level of unmanned flying vehicles. A new dynamic hybrid algorithm is developed to solve the motion planning problem in real-time using a heuristic optimization approach. The proposed algorithm effectively combines desired features such as rapid convergence to an optimal path with reduced computational effort. In addition to the terrain obstacles, the proposed algorithm is able to avoid random threats that may arise sporadically in the terrain. Using the maneuver automaton concept, nonlinear dynamic model and performance constraints are also considered in the process of motion planning to further ensure feasible trajectories. Evaluation of the proposed algorithm against several simulated scenarios has effectively demonstrated its potential for generating optimal contour-matching trajectories that succeed in avoiding stochastic obstacles.
J Karimi and Seid H Pourtakdoust
Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, ISSN: 09544100, eISSN: 20413025, Volume: 227, Pages: 3-18, Published: January 2013 SAGE Publications
Motion planning and trajectory control are two basic challenges of unmanned vehicles. In motion planning problem, feasible trajectories are developed while nonlinear dynamic model and performance constraints of the vehicle under utility are considered. In this study, motion planning is performed via an enhanced particle swarm optimization algorithm. The resulting offline generated trajectories are tracked using a nonlinear trajectory control system methodology. The Lyapunov-based constrained backstepping approach and command filters are utilized in designing the trajectory control system. Command filters smoothen the input signals and provide their derivatives. Evaluation of the proposed integrated approach in several simulated scenarios has effectively demonstrated the potential of both algorithms in generating optimal contour matching trajectories as well as excellent tracking capability of the trajectory control system.
Maryam Kiani and Seid H. Pourtakdoust
Applied Mechanics and Materials, ISSN: 16609336, eISSN: 16627482, Volume: 225, Pages: 417-422, Published: 2012 Trans Tech Publications, Ltd.
This paper deals with attitude determination, parameter identification and reference sensor calibration simultaneously. A LEO satellite’s attitude, inertia tensor as well as calibration of Three-Axis-Magnetometer (TAM) are estimated during a maneuver designed to satisfy persistency of excitation condition. For this purpose, kinematic and kinetic state equations of spacecraft motion are augmented for the determination of inertia tensor and TAM calibration parameters including scale factors, misalignments and biases along three body axes. Attitude determination is a nonlinear estimation problem. Unscented Kalman Filter (UKF) as an advanced nonlinear estimation algorithm with good performance can be used to estimate satellite attitude but its computational cost is considerably larger than the widespread, low accuracy, Extended Kalman Filter (EKF). Reduced Sigma Points Filters provide good solutions and also decrease run time of UKF. However, in contrast to nonlinear problem of attitude determination, parameter identification and sensor calibration have linear dynamics. Therefore, a new Marginal UKF (MUKF) is proposed that combines the utility of Kalman Filter with Modified UKF (MMUKF). The proposed MMUKF utilizes only 14 sigma points to achieve the complete 25-dimensional state vector estimation. Additionally, a Monte Carlo simulation has demonstrated a good accuracy for concurrent estimation of attitude, inertia tensor as well as TAM calibration parameters in significantly less time with respect to sole utilization of the UKF.
H. Shahrabi, Seid H. Pourtakdoust, M. Abolghasemi, and M. Tivay
Systems Engineering, ISSN: 10981241, eISSN: 15206858, Pages: 307-320, Published: September 2012 Wiley
In keeping with the continuing effort toward the development of a domestic space research and development program in recent years, the Omid National Satellite (ONS) is the first domestically manufactured satellite from the Islamic Republic of Iran. As a technology demonstration, it was launched and utilized successfully in February 2009. Despite the simple mission of the ONS, because it was the first full-scale successful space deployment experience for the country, the domestic manufacturing capabilities for satellite and launch technologies were boosted. More importantly, the country's domestic platform for future space projects was established. Considering the important role of systems engineering (SE) in the localization of the Iranian space industry, this paper aims to present the ONS space program in terms of its SE management , conceptual design, subsystem descriptions with technical specifications, integration, testing, and development. The operational in-orbit aspects will also be described. The project generated a high level of hope and a sense of achievement among the many skilled national engineers who worked on the project. The specific and general lessons learned that are emphasized in this paper will be incorporated into the country's future space programs and will be used to support the development of the next generation of small satellites. © 2012 Wiley Periodicals, Inc. Syst Eng © 2012 Wiley Periodicals, Inc.
J. Karimi, H. Nobahari, and S.H. Pourtakdoust
Applied Soft Computing Journal, ISSN: 15684946, Pages: 1158-1167, Published: March 2012 Elsevier BV
A new hybrid approach for dynamic optimization problems with continuous search spaces is presented. The proposed approach hybridizes efficient features of the particle swarm optimization in tracking dynamic changes with a new evolutionary procedure. In the proposed dynamic hybrid PSO (DHPSO) algorithm, the swarm size is varied in a self-regulatory manner. Inspired from the microbial life, the particles can reproduce infants and the old ones die. The infants are especially reproduced by high potential particles and located near the local optimum points, using the quadratic interpolation method. The algorithm is adapted to perform in continuous search spaces, utilizing continuous movement of the particles and using Euclidian norm to define the neighborhood in the reproduction procedure. The performance of the new proposed approach is tested against various benchmark problems and compared with those of some other heuristic optimization algorithms. In this regard, different types of dynamic environments including periodic, linear and random changes are taken with different performance metrics such as real-time error, offline performance and offline error. The results indicate a desirable better efficiency of the new algorithm over the existing ones.
S.H. Pourtakdoust and S. Karimain Aliabadi
Scientia Iranica, ISSN: 10263098, Pages: 472-482, Published: June 2012 Elsevier BV
Abstract To evaluate the propulsion system capabilities of a Flapping Micro Air Vehicle (FMAV), a new aeroelastic model of a typical flexible FMAV is developed, utilizing the Euler–Bernoulli torsion beam and quasi steady aerodynamic model. The new model accounts for all existing complex interactions between the mass, inertia, elastic properties, aerodynamic loading, flapping amplitude and frequency of the FMAV, as well as the effects of several geometric and design parameters. To validate the proposed theoretical model, a typical FMAV, as well as an instrumented test stand for the online measurement of forces, flapping angle and power consumption, has been constructed. The experimental results are initially utilized to validate the flight dynamic model, and several appropriate conclusions are drawn. The model is subsequently used to demonstrate the flapping propulsion characteristics of the FMAV via simulation. Using dimensionless parameters, a set of new aeroelastic coordinates are introduced. In this reduced design space, new generalized performance curves have been deduced. The results indicate that by proper adjustment of the wing stiffness parameter, as a function of reduced frequency, the FMAV will attain its optimum propulsive efficiency. This fact raises additional ideas of utilizing intelligent variable stiffness materials and/or an active morphing technology for the sustained flight of FMAVs.
Seid H. Pourtakdoust, M. Kiani, and A. Hassanpour
Aerospace Science and Technology, ISSN: 12709638, Pages: 567-576, Published: October 2011 Elsevier BV
Abstract Microburst wind shear is a potential hazard for aviation safety, especially in some crucial phases of flight like take-off and landing. Optimal trajectories could be useful for suitable retrieval of transport aircrafts encountering microburst. These types of trajectories are investigated in this paper for landing phase in two scenarios of escape and landing utilizing the most recent realistic analytical model of the microburst. In this regard, a set of complete six degrees of freedom aircraftʼs equations of motion is taken in a variation formulation of this problem. This approach is particularly useful for determination of optimal escape or approach trajectories constrained with respect to physical controls as well as some crucial motion states. The set of resulting necessary conditions for optimality is solved numerically and analyzed with respect to a series of microburst characteristics as well as some typical aircraft initial engagement scenarios like the flight condition and the throttle setting. The results are promising in the sense that for the most typical microbursts, optimal trajectories and controls could be feasible with available control limits, thus allowing for a safe passage or landing of transport planes through microburst.
Rouzbeh Moradi, Seid H. Pourtakdoust, and Reza Kamyar
ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis, ESDA2010, Pages: 299-309, Published: 2010 ASMEDC
Spacecraft rendezvous and docking are two processes in which a chaser pursues and meets a leader spacecraft in order to perform several mission based tasks. Although in some preliminary design analysis, these two operations may be pursued independently there could be circumstances in which the spacecraft trajectory and attitudes are coupled and interdependent. The present study is based on the presumption that the often independent translational and rotational motions of the spacecraft are coupled as a result of thrust misalignment. So the thrusters not only contribute to the rendezvous translational motion, but also affect the docking reorientation maneuver through their disturbing effects. In this regard, the coupled spacecraft rendezvous and docking (RvD) maneuver is treated as a multi-objective optimization problem. Multi-objective ant colony optimization (ACOR) and Genetic algorithm (GA) as new variants of multi objective metaheuristics that have proven to be successful in handling non convex and multi minima problems are utilized to determine the required pareto front. Three design points are selected such that a wide range of mission based operations are covered and the results are compared. It is shown that, despite the presence of the disturbing effects due to the thruster misalignment, the required control commands are reasonable. For a comparative analysis, two different schemes are also utilized to obtain the closed loop control form for the RvD problem under study and their results are compared.
Iranian Journal of Science and Technology, Transaction B: Engineering, ISSN: 10286284, Pages: 197-213, Published: April 2010
Nima Assadian and Seid H. Pourtakdoust
Advances in Space Research, ISSN: 02731177, Pages: 398-409, Published: 1 February 2010 Elsevier BV
In this paper, optimal trajectories of a spacecraft traveling from Earth to Moon using impulsive maneuvers (ΔV maneuvers) are investigated. The total flight time and the summation of impulsive maneuvers ΔV are the objective functions to be minimized. The main celestial bodies influencing the motion of the spacecraft in this journey are Sun, Earth and Moon. Therefore, a three-dimensional restricted four-body problem (R4BP) model is utilized to represent the motion of the spacecraft in the gravitational field of these celestial bodies. The total ΔV of the maneuvers is minimized by eliminating the ΔV required for capturing the spacecraft by Moon. In this regard, only a mid-course impulsive maneuver is utilized for Moon ballistic capture. To achieve such trajectories, the optimization problem is parameterized with respect to the orbital elements of the ballistic capture orbits around Moon, the arrival date and a mid-course maneuver time. The equations of motion are solved backward in time with three impulsive maneuvers up to a specified low Earth parking orbit. The results show high potential and capability of this type of parameterization in finding several Pareto-optimal trajectories. Using the non-dominated sorting genetic algorithm with crowding distance sorting (NSGA-II) for the resulting multiobjective optimization problem, several trajectories are discovered. The resulting trajectories of the presented scheme permit alternative trade-off studies by designers incorporating higher level information and mission priorities.
Nima Assadian and Seid H. Pourtakdoust
Acta Astronautica, ISSN: 00945765, Issue: 1-2, Pages: 45-58, Published: January 2010 Elsevier BV
Abstract In this study the effect of the Sun on the Lagrange points of the Earth–Moon system is investigated. A restricted four-body problem (R4BP) is introduced to take into account the effect of the Sun, Earth and Moon on the motion of an infinitesimal particle. The motion of the Earth–Moon-barycenter (EMB) around the Sun is considered to be elliptic in the ecliptic plane. Similarly, the motion of the Moon around the Earth is presumed to be elliptic, but out of the ecliptic plane. In this way, a spatial R4BP with non-coplanar motion of primaries is derived, which is named as BiElliptic problem (BEP). Transforming the equations of motion to a coordinate system originated at the EMB that rotates with the variable angular velocity of the Moon around the Earth, allows for the investigation of the effect of the Sun on the Lagrange points of the Earth–Moon circular restricted three-body system. The results reveal that the L1 and L2 points are replaced with nearby complex quasi-periodic orbits with considerable deviation from the Earth–Moon line of axes. These orbits are highly unstable and were found with the aid of a new algorithm developed for this purpose. The L3 quasi-equilibrium is greatly displaced, such that its trace approaches those of L4 and L5 with considerable overlaps. Also, for some specific time intervals two additional quasi-equilibrium points are detected for the real Sun–Earth–Moon BEP. In addition, a parametric study is also performed to detect the conditions for which the structure of the quasi-equilibria changes.
Ali Heydari, Seid H. Pourtakdoust, and Hamed Heydari
Proceedings of the IEEE International Conference on Control Applications, Pages: 456-460, Published: 2009 IEEE
A fuzzy controller has been suggested for attitude control of magnetic actuated satellites in order to calculate the desired mechanical torque based on the attitude error including error in the angles and their rates. The problem of selecting proper magnetic dipole based on the known desired mechanical torque has been investigated, two different methods for the purpose has been suggested and the performance of the attained fuzzy magnetic attitude controllers has been shown under two different simulated conditions.
H Ghanbarpour Asl, S H Pourtakdoust, and M Samani
Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, ISSN: 09544100, Volume: 223, Pages: 729-739, Published: 1 September 2009 SAGE Publications
Abstract A new algorithm for complete pre-flight calibration of triple magnetometers is developed. The traditional approach for calibrating these sensors are based on a cumbersome procedure called ‘swing’ that involves levelling and rotating the vehicle containing the magnetometers through a series of known headings. Application of such a procedure is difficult and costly. Recently, new approaches have been developed to calibrate magnetometers without the need of attitude information. Such methods are used mostly for the calibration of biases and scale factors. Additionally in situations where misalignment errors are also to be estimated, they are usually modelled as errors of a non-orthogonal frame relative to an orthogonal frame creating six additional unknown parameters to be estimated. The presented approach in this article utilizes a three-step algorithm to fully calibrate triple magnetometers without the need of attitude information through a batch least-square non-linear estimator. Since misalignment parameters are not all identifiable through attitude-independent techniques, the measurement equation is initially factorized such that the non-observable parameters are removed. This would allow identification of three parameters through attitude-independent techniques, while identification of the other three that require horizon information is carried out using a secondary procedure. In step one of the proposed scheme, the non-linear observation equation is transformed, via two non-linear functions, to a linear space with respect to the unknown parameters and the new unknown parameters are estimated with batch least-square estimator. In the second step, the first non-linear function is solved for nine parameters that have non-linear relationships with respect to the desired biases, scale factors, and misalignments. Subsequently, the second non-linear function is solved giving the main unknown calibration parameters in a non-physical frame. Finally, in the third step, to find the required transformation matrix between the magnetometer platform frame, the magnetometer is rotated in a horizontal plane about x, y, and z platform axis, respectively. Assuming that the vertical component of the geomagnetic field is known, the calibration parameters are next determined with respect to the platform frame utilizing the rotation matrix. The proposed three-step algorithm does not need any initial condition or iterations for convergence and more importantly does not require any attitude information for the estimation of misalignments. The algorithm is simulated to validate the performance of the estimator using experimental data gathered from a magnetometer triad. Results show relative superiority when compared with those of the two-step algorithm with heading errors of the order of 0.5 to 1 degrees.
S.H. Pourtakdoust, F. Pazooki, and M. Fakhri Noushabadi
Aircraft Engineering and Aerospace Technology, ISSN: 00022667, Pages: 212-220, Published: 2009 Emerald
Purpose – The purpose of this paper is to devise a new approach to synthesize closed‐loop feedback guidance law for online thrust‐insensitive optimal trajectory generation utilizing neural networks.Design/methodology/approach – The proposed methodology utilizes an open‐loop variational formulation that initially determines optimal launch/ascent trajectories for various scenarios of known uncertainties in the thrust profile of typical solid propellant engines. These open‐loop optimized trajectories will then provide the knowledge base needed for the subsequent training of a neural network. The trained network could eventually produce thrust‐insensitive closed‐loop optimal guidance laws and trajectories in flight.Findings – The proposed neuro‐optimal guidance scheme is effective for online closed‐loop optimal path planning through some measurable and computable engine and flight parameters.Originality/value – Determination of closed‐loop optimal guidance law for non‐linear dynamic systems with uncertainties...
Ali Shahvarpour, Hossein Pourtakdoust, Gholam Reza Vossoughi, Jung Yong Kim, and Mohamad Parnianpour
2008 International Conference on Control, Automation and Systems, ICCAS 2008, Pages: 548-553, Published: 2008 IEEE
Modeling the spine behavior plays a key role in understanding mechanisms leading to spinal disorders and injuries. The goal of this article is to develop a new model to obtain 3D spine movement patterns. High degrees of freedom of the system, a great many of muscles involved in the spine movements and its unstable intrinsic behavior make the control problem more difficult. New theories in computational motor control suggest optimal control as a useful tool for modeling Central Nervous System (CNS) to provide appropriate control signals while it computes the neural interactions with biological sensors. Therefore, CNS is modeled as an optimal controller. Our simulations illustrate the movement behavior and muscles force patterns which may be used to relate to the risk of injury in both joints and muscles.
Ali Heydari and Seid H. Pourtakdoust
2008 Mediterranean Conference on Control and Automation - Conference Proceedings, MED'08, Pages: 23-28, Published: 2008 IEEE
The problem of time optimal magnetic attitude control is treated and an open loop solution is first obtained using a variational approach. In order to close the control loop, a neural network with time varying weights is proposed as a feedback optimal controller applicable to the time varying nonlinear system. The good robustness and low real-time computational burden of the proposed neuro-controller makes the controller more useful compared to the other control methods.
S.H. Jalali‐Naini and S.H. Pourtakdoust
Aircraft Engineering and Aerospace Technology, ISSN: 00022667, Pages: 262-273, Published: 2008 Emerald
Purpose – The purpose of this paper is to develop a novel solution for the predicted error and introduces a systematic method to develop optimal and explicit guidance strategies for different missions.Design/methodology/approach – The predicted error is derived from its basic definition through analytical dynamics. The relations are developed for two classes of systems. First, for systems in which the acceleration commands are truncated at a specified time. Second, for systems in which the corrective maneuvers are cut off at a specified time. The predicted error differential equation is obtained in a way that allows for derivation of several optimal and explicit guidance schemes.Findings – The effect of tangential acceleration in conjunction with autopilot dynamics can be realized in guidance gain and the predicted error. The differential equation of velocity‐to‐be‐gained is obtained assuming the gravitational acceleration to be given as a vectorial function of time. The relations for different velocity p...
Seid Hossein Pourtakdoust and Seyed Hossein Mortazavi
AIAA Atmospheric Flight Mechanics Conference and Exhibit, Published: 2008 American Institute of Aeronautics and Astronautics
S.H. Pourtakdoust and H. Ghanbarpour Asl
Aircraft Engineering and Aerospace Technology, ISSN: 00022667, Pages: 485-493, Published: 2007 Emerald
Purpose – This paper aims to develop an adaptive unscented Kalman filter (AUKF) formulation for orientation estimation of aircraft and UAV utilizing low‐cost attitude and heading reference systems (AHRS).Design/methodology/approach – A recursive least‐square algorithm with exponential age weighting in time is utilized for estimation of the unknown inputs. The proposed AUKF tunes its measurement covariance to yield optimal performance. Owing to nonlinear nature of the dynamic model as well as the measurement equations, an unscented Kalman filter (UKF) is chosen against the extended Kalman filter, due to its better performance characteristics. The unscented transformation of the UKF is shown to equivalently capture the effect of nonlinearities up to second order without the need for explicit calculations of the Jacobians.Findings – In most conventional AHRS filters, severe problems can occur once the system suddenly experiences additional acceleration, resulting in erroneous orientation angles. On the contr...
H. Nobahari and S. H. Pourtakdoust
Aeronautical Journal, ISSN: 00019240, Volume: 111, Issue: 1124, Pages: 621-636, Published: October 2007 Cambridge University Press (CUP)
Abstract The well-known ant colony optimisation (ACO) meta-heuristic is applied to optimise the parameters of a new fuzzy command to line-of-sight (CLOS) guidance law. The new guidance scheme includes two phases, a midcourse and a terminal phase. In the first phase, a lead strategy is utilised which reduces the acceleration demands. A proportional derivative (PD) fuzzy sliding mode controller is used as the main tracking controller of the first phase. Moreover, a supervisory controller is coupled with the main tracking controller to guarantee the missile flight within the beam. In the terminal phase, a pure CLOS guidance law without lead angle is utilised. For this phase, a new hybrid fuzzy proportional-integral-derivative (PID) fuzzy sliding mode controller is proposed as a high precision tracking controller. The parameters of the proposed controllers for the first and the second phases are optimised using ACO. In this regard, the recently developed continuous ant colony system (CACS) algorithm is extended to multi-objective optimisation problems and utilised to optimise the parameters of the pre-constructed fuzzy controllers. The performance of the resulting guidance law is evaluated at different engagement scenarios and compared with the well-known feedback linearisation method. The comparison is also made in the presence of measurement noise.
ICAS-Secretariat - 25th Congress of the International Council of the Aeronautical Sciences 2006, Pages: 698-706, Published: 2006
Hadi Nobahari, Aria Alasty, and Seid H. Pourtakdoust
Aircraft Engineering and Aerospace Technology, ISSN: 00022667, Pages: 395-406, Published: 2006 Emerald
Purpose – The purpose of this paper is to propose a supervisory command‐to‐line‐of‐sight guidance law with lead angle which keeps the missile flight within the tracking beam.Design/methodology/approach – A nonlinear supervisory controller is designed and coupled with the main sliding mode controller in the form of an additional control signal. The supervisory control signal is activated when the beam angle constraint goes to be violated. Initially a supervisory controller is designed using nonlinear control theory. Subsequently the main tracking controller is designed using sliding mode approach which forces the missile to fly along the desired line‐of‐sight. The stability of the supervisory controller coupled with the main controller is proved in the Lyapunov sense.Findings – There exists a major drawback with the lead angle method of guidance, which is a high probability of flying out of the beam. The proposed supervisory controller has successfully overcome this deficiency. Thus, a better performance h...
Seyed Ahmad Fazelzadeh, Seid Hossein Pourtakdoust, and Nima Assadian
Aerospace Science and Technology, ISSN: 12709638, Pages: 192-198, Published: April 2006 Elsevier BV
Abstract Stochastic behavior of panels in supersonic flow is investigated to assess the significance of including the damping caused by the strains resulting from axial extension of the panel. The governing equations of motion are based on the Von Karman's large deflection equation and are considered with Kelvin's model of structural damping. The panel under study is two dimensional and simply supported for which the first order piston theory is used to account for the unsteady aerodynamic loading. Transformation of the governing partial differential equation to a set of ordinary differential equations is performed through the Galerkin averaging technique. The statistical response moment equations are generated for two modes using the Fokker–Planck equation with a Gaussian closure scheme. The response moments history and their steady state values are considered. Comparison with previous studies shows that the new nonlinear damping term developed through modeling has a significant effect on the response moments. This is verified through analysis of the effects of external pressure and in-plane force spectral density, air-to-structure mass ratio and structural damping ratio on the mean square value of modal amplitudes.
ICAS-Secretariat - 25th Congress of the International Council of the Aeronautical Sciences 2006, Pages: 3265-3274, Published: 2006
Hadi Nobahari and Seid H. Pourtakdoust
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN: 03029743, eISSN: 16113349, Volume: 3777 LNCS, Pages: 95-106, Published: 2005 Springer Berlin Heidelberg
The well-known ant colony optimization meta-heuristic is applied to design a new command to line-of-sight guidance law. In this regard, the lately developed continuous ant colony system is used to optimize the parameters of a pre-constructed fuzzy sliding mode controller. The performance of the resulting guidance law is evaluated at different engagement scenarios.
Collection of Technical Papers - AIAA Atmospheric Flight Mechanics Conference, Pages: 387-402, Published: 2005
Collection of Technical Papers - AIAA Guidance, Navigation, and Control Conference, Pages: 3083-3095, Published: 2005
S.H. Pourtakdoust, N. Rahbar, and A.B. Novinzadeh
Aircraft Engineering and Aerospace Technology, ISSN: 00022667, Pages: 376-383, Published: 2005 Emerald
Purpose – To devise a new technique to synthesise optimal feedback control law for non‐linear dynamic systems through fuzzy logic.Design/methodology/approach – The proposed methodology utilizes the open‐loop optimal control solutions (OCSs) of the non‐linear systems for the training of the fuzzy system in the process of developing closed‐loop fuzzy logic guidance (FLG). This is achieved through defining a set of non‐dimensionalised variables related to the system states.Findings – FLG is capable of generating closed‐loop control law for the non‐linear problem investigated. Since the proposed fuzzy structure is independent of the system equations, the approach is potentially applicable to other non‐linear system. Introduction of the non‐dimensional variables in place of the regular states has effectively increased the fuzzy training performance and greatly reduced the number of fuzzy rule bases required to produce accurate solutions for other untrained scenarios.Originality/value – There exist many complex...
S. H. Pourtakdoust and S. A. Fazelzadeh
Journal of Thermal Stresses, ISSN: 01495739, Pages: 147-169, Published: February 2005 Informa UK Limited
ABSTRACT This paper addresses the problem of aerothermoelastic behavior of a flat skin panel with wall shear stress effect in high supersonic flow. A fully coupled high-supersonic skin panel model that accounts for all thermal–fluid–structure interactions is developed. The governing equations are based on the von Karman large deflection of isotropic flat plates. Viscous and inviscid aerothermoelastic loading mechanisms between the fluid and structure are considered. The lumped-capacity assumption and Duhamel superposition principle are used for heat communication analysis. In addition, the effects of viscous flow shear stress, static pressure differential over the external surface, and constant axial loading in the panel middle surface have also been included in the governing equations. Using the Galerkin approach, the resulting system of differential equations is solved through the Runge–Kutta–Fehlberg integration method. Divergence and flutter bifurcation boundaries are determined for various nondimensi...
Seyed Hamid Jalali-Naini and S.H. Pourtakdoust
Collection of Technical Papers - AIAA Guidance, Navigation, and Control Conference, Pages: 4560-4576, Published: 2005 American Institute of Aeronautics and Astronautics
S.H. Pourtakdoust and N. Assadian
Journal of Sound and Vibration, ISSN: 0022460X, Volume: 272, Issue: 1-2, Pages: 287-299, Published: 22 April 2004 Elsevier BV
Abstract In this paper the effect of thrust on the bending behaviour of flexible missiles is investigated. For this purpose, the governing equations of motion of a flexible guided missile are derived following the Lagrangian approach. The missile is idealized as a non-uniform beam where the bending elastic deflections are modelled using the method of modal substitution. The vehicle (time varying) bending modeshapes and natural frequencies are determined by modelling variable mass and stiffness distributions with thrust and mass burning effects accounted for. To solve this problem the missile is divided into several segments of uniform stiffness, density and axial force distribution. This approach produces a non-linear transcendental equation, which requires an iterative scheme to numerically determine the magnitude of the eigenvalues. Since inertial measuring units (IMU) also sense the local body vibrations, the mass and stiffness non-uniformities plus the thrust action on elastic missiles can potentially influence their measurements and thus must be properly accounted for in an aeroelastic simulation. It is noted that the thrust force reduces the vehicle natural frequency while mass consumption increases it. Thus the modal natural frequencies can either decrease or increase in time. Also the critical buckling thrust, which dynamically causes a zero natural frequency, is obtained and therefore the thrust instability limitations are determined through simulation. With proper modelling of the IMU vibrations effects and engine/thrust fluctuations, the influence of body vibrations on the missile dynamics and controls are investigated with axial thrust effect.
Seid H. Pourtakdoust and Hadi Nobahari
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN: 03029743, eISSN: 16113349, Volume: 3172 LNCS, Pages: 294-301, Published: 2004 Springer Berlin Heidelberg
A new method for global minimization of continuous functions has been proposed based on Ant Colony Optimization. In contrast with the previous researches on continuous ant-based methods, the proposed scheme is purely pheromone-based. The algorithm has been applied to several standard test functions and the results are compared with those of two other meta-heuristics. The overall results are compatible, in good agreement and in some cases even better than the two other methods. In addition the proposed algorithm is much simpler, which is mainly due to its simpler structure. Also it has fewer control parameters, which makes the parameter settings process easier than many other methods.
Scientia Iranica, ISSN: 10263098, Issue: 1-2, Pages: 26-36, Published: Spring 2004
44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Published: 2003
S. H. Pourtakdoust and S. A. Fazelzadeh
Nonlinear Dynamics, ISSN: 0924090X, Pages: 387-404, Published: June 2003 Springer Science and Business Media LLC
In this paper chaotic behavior of nonlinear viscoelastic panels in asupersonic flow is investigated. The governing equations, based on vonKàarmàn's large deflection theory of isotropic flat plates, areconsidered with viscoelastic structural damping of Kelvin's modelincluded. Quasi-steady aerodynamic panel loadings are determined usingpiston theory. The effect of constant axial loading in the panel middlesurface and static pressure differential have also been included in thegoverning equation. The panel nonlinear partial differential equation istransformed into a set of nonlinear ordinary differential equationsthrough a Galerkin approach. The resulting system of equations is solvedthrough the fourth and fifth-order Runge–Kutta–Fehlberg (RKF-45)integration method. Static (divergence) and Hopf (flutter) bifurcationboundaries are presented for various levels of viscoelastic structuraldamping. Despite the deterministic nature of the system of equations,the dynamic panel response can become random-like. Chaotic analysis isperformed using several conventional criteria. Results are indicative ofthe important influence of structural damping on the domain of chaoticregion.
Amirreza Rahmani, Mir-Abbas Jalali, and Seid Pourtakdoust
AIAA Guidance, Navigation, and Control Conference and Exhibit, Published: 2003 American Institute of Aeronautics and Astronautics
Three-dimensional orbits in the vicinity of the collinear libration points of the Sun-Earth/Moon barycenter system are currently being considered for use with a number of missions planed for 2000 and beyond. Since such libration point trajectories are, in general, unstable, spacecraft moving on these paths must use some form of trajectory control to remain close to their nominal orbit. In this paper, circular restricted three body problem is reviewed and a numerical method to control spacecrafts on periodic halo orbits around L1 and L2 collinear points of the Sun-Earth/Moon barycenter system is investigated. The control approach is based on the optimal control theory and implements variation of extremals technique to solve the resulting two point boundary value problem. The reference trajectory, halo orbit, is supposed to be given in the form of the Fourier series.
Seyed Fazelzadeh, Seid Pourtakdoust, and Nima Assadian
Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, ISSN: 02734508, Pages: 4219-4225, Published: 2003 American Institute of Aeronautics and Astronautics
Stochastic behavior of viscoelastic panels in supersonic flow under random aerodynamic pressure and inplane forces is investigated. The governing equations of motion are based on the Von Karman’s large deflection equation and are considered with Kelvin’s model of viscoelastic structural damping. The panel under study is two dimensional and simply supported for which the first order piston theory is used to account for the unsteady aerodynamic loading. Transformation of the governing partial differential equation to a set of ordinary differential equations is performed through the Galerkin averaging technique. The statistical response moment equations are generated for two modes using the Fokker-Planck equation with a Gaussian closure scheme. The response moments history and their steady state values are considered. Comparison with previous studies shows that the new nonlinear damping term developed through modeling has a significant effect on the response moments. This is verified through analysis of the effects of external pressure and in-plane force spectral density, air-to-structure mass ratio and structural damping ratio on the mean square value of modal amplitudes.
Seid Pourtakdoust, M. Jalali, R. Ghorbani, and A. Zahedi
AIAA Guidance, Navigation, and Control Conference and Exhibit, Published: 2002 American Institute of Aeronautics and Astronautics
Due to inherent potential of General Regression Neural Network(GRNN) to approximate nonlinear functions, it can be implemented as a nonlinear state-feedback controller. In this paper the methodology of direct collocation and nonlinear programming is utilized in combination with GRNN to determine the optimal control of dynamical systems. Application of this method to the design of an optimal controller for a chaotic flexible beam as a non-autonomous, nonlinear system is investigated.
Advances in the Astronautical Sciences, ISSN: 00653438, Volume: 95 PART 2, Pages: 583-593, Published: 1997
M. A. Jalali and S. H. Pourtakdoust
Celestial Mechanics and Dynamical Astronomy, ISSN: 09232958, Pages: 151-162, Published: 1997 Springer Science and Business Media LLC
Regular solutions at the 3/2 commensurability are investigated forSitnikov’s problem. Utilizing a rotating coordinate system and theaveraging method, approximate analytical equations are obtained for thePoincare sections by means of Jacobian elliptic functions and 3πperiodicsolutions are generated explicitly. It is revealed that the system exhibitsheteroclinic orbits to saddle points. It is also shown that chaotic regionemerging from the destroyed invariant tori, can easily be seen for certaineccentricities. The procedure of the current study provides reliable answersfor the long-time behavior of the system near resonances.
Advances in the Astronautical Sciences, ISSN: 00653438, Volume: 93 PART 1, Pages: 779-786, Published: 1996
M. A. Jalali, B. Mehri, and S. H. Pourtakdoust
Celestial Mechanics & Dynamical Astronomy, ISSN: 09232958, eISSN: 15729478, Issue: 3-4, Pages: 271-287, Published: September 1995 Springer Science and Business Media LLC
Existence of periodic orbits inside elliptical galaxies has been investigated. Necessary conditions for regular, small amplitude periodic motion around the center of galaxy have been derived using implicit functions and solved by approximating through Taylor's series. The solution procedure requires to obtain functions of partial derivatives of dependent variables with respect to initial conditions. Derivation of these functions can be accomplished through solving a set of ordinary differential equations by proper choices of associated initial conditions. The results obtained show complete agreement with those obtained through the application of Poincaré-Lindstedt's method.
Seid Pourtakdoust and Mir Jalali
1995 Guidance, Navigation, and Control Conference, Pages: 1395-1404, Published: 1995 American Institute of Aeronautics and Astronautics
Several optimal three-dimensional orbital transfer problems are solved for thrust-limited spacecrafts using collocation and nonlinear programming techniques. The solutions for full nonlinear equations of motion are obtained where the integrals of the free Keplerian motion in three dimensions are utilized for coasting arcs. In order to limit the solution space, interior-point constraints are used which proved to be beneficial in finding the optimal results by making initial estimates more sensible. The application of this methodology to the design of several three dimensional optimal trajectories is also investigated. The results indicate that the method is suitable for any 3D transfer between non- coplanar and non-coaxial orbits.
American Society of Mechanical Engineers, Petroleum Division (Publication) PD, Pages: 53-58, Published: 1994
Flight Simulation Technologies Conference and Exhibit, 1990, Pages: 643-654, Published: 1990
1. Shakouri A., Kiani M., Pourtakdoust Seid H., “A New Shape -Based Multiple-Impulse Strategy for Coplanar Orbital Maneuvers”, Acta Astronautica, Volume 161, pp. 200-208, https://doi.org/10.1016/j.actaastro.2019.05.004, Elsevier, 11th, May 2019.
2. Nasihati Gourabi F., Kiani M., Pourtakdoust Seid H., “Autonomous temperature-based orbit estimation”, Aerospace Science and Technology, No. 86, pp. 671-682, https://doi.org/10.1016/j.ast.2019.01.056, Elsevier, January 2019.
3. Shakouri A., Kiani M., Pourtakdoust Seid H., “Covariance-Based Multiple-Impulse Rendezvous Design”, accepted for publication in IEEE Transactions on Aerospace and Electronic Systems, DOI 10.1109/TAES.2018.2882939, IEEE, November 2018.
4. Raouf N., Pourtakdoust Seid H., S. Samiei Paghaleh, “Reliability and Failure analysis of jet vane TVC system”, Journal of Failure Analysis and Prevention, Volume 18, Issue 6,pp. 1635-1642,Springer, October 2018.
5. Labibian A., Pourtakdoust Seid H., A. Alikhani, H. Fourati, “Development of a Radiation Based Heat Model for Satellite Attitude Determination”, Aerospace Science and Technology, No. 82-83, pp. 479-486, Doi.org/10.1016/j.ast.2018.09.031, Elsevier, September 27th , 2018.
6. Afshari S. S. , Pourtakdoust Seid H., “Probability Density Evolution For Time-Varying Reliability Assessment Of Wing Structures”, Aviation Journal, ISSN: 1648-7788 /, Volume 22, Issue 2,pp. 52-61, Doi.org/10.3846/aviation.2018.6010, May 2018.
7. Afshari S. S. , Pourtakdoust Seid H., “Utility of Probability Density Evolution Method for Experimental Reliability Based Active Vibration Control”, Structural Control & Health Monitoring, DOI: 10.1002/stc.2199, Wiley, April 2018.
8. Bighashdel A., Zare H., Pourtakdoust Seid H., “An Analytical Approach in Dynamic Calibration of Strain Gauge Balances for Aerodynamic Measurements”, IEEE Sensors Journal , DOI 10.1109/JSEN.2018.2815762, March 2018.
9. Zare H., Bighashdel A., Pourtakdoust Seid H., “Analytical Structural Behavior Of Elastic Flapping Wings Under The Actuator Effect”, The Aeronautical Journal ,Vol. 122, Issue 1254, pp. 1176-1198, Royal Aeronautical Society, U.K , August 2018.
1- Implementation of satellite attitude determination process via nonlinear filtering of thermal data. Patent No. 90141, Intellectual Property Center, Tehran-Iran, October 2016.
2- Development of a 3 DOF Dynamic Force/Moment Measurement System for Flapping Robots. Patent No. 94817, Intellectual Property Center, Tehran-Iran, January 2018.
3- Advanced UAV aerodynamics, flight stability and control: Novel concepts, theory and applications. John Wiley & Sons Inc, December 2016.ISBN-10: 1118928687, ISBN-13: 978-1118928684.
Chapter 17: Constrained Motion Planning and Trajectory Optimization for Unmanned Aerial Vehicles.
Chapter 18: Autonomous Space Navigation Utilizing Nonlinear Filters with MEMS Technology.
4- Recent Advances in Multisensor Attitude Estimation: Fundamental Concepts and Applications.
CRC Press- Taylor and Francis Group, August 2016. ISBN 9781498745710
Chapter 11: Recent Advances in Nonlinear Attitude Estimation Algorithms.