Abstract
This paper focuses on the dynamics and optimal reorientation of a free-floating space robot system in the presence of initial state uncertainties. A control strategy combining optimal motion planning and feedback control is presented based on the dynamic model of the system. In the design of the optimal motion planning, Legendre pseudospectral method (LPM) is used to transform the optimal reorientation problem into a nonlinear programming problem. Then, sequential quadratic programming algorithm is employed to solve the nonlinear programming problem and off-line generate the optimal reference trajectory of the system. In the design of feedback control, the state equation is linearized around the reference trajectory obtained by LPM. The tracking control problem is converted into a two-point boundary value problem based on Pontryagin’s maximum principle. Then LPM is used to discretize the two-point boundary value problem and transform it into a set of linear algebraic equations. This process does not require any integration calculations and has good performance in real time. Numerical simulations indicate that the control strategy is effective with good robustness.
Similar content being viewed by others
References
Xu W, Liang B, Xu Y (2011) Survey of modeling, planning, and ground verfication of space robotic systems. Acta Astronaut 68(11–12):1629–1649
Flores-Abad A, Ma O, Pham K, Ulrich S (2014) A review of space robotics technologies for on-orbit serving. Prog Aerosp Sci 68:1–26
Papadopoulos E, Dubowsky S (1991) On the nature of control algorithms for free-floating space manipulators. IEEE Trans Robot Autom 7(6):750–758
Nakamura Y, Mukherjee R (1991) Nonholonomic path planning of space robots via a bidirectional approach. IEEE Trans Robot Autom 7(4):500–514
Coverstone-Carroll VL, Wilkey NM (1995) Optimal control of a satellite-robot system using direct collocation with non-linear programming. Acta Astronaut 36(3):149–162
Yamada K, Yoshikawa S (1997) Feedback control of space robot attitude by cyclic arm motion. J Guid Control Dyn 20(4):715–720
Xu W, Liu Y, Liang B, Xu Y, Li C, Qiang W (2008) Non-holonomic path planning of a free-floating soace robotic system using genetic algorithms. Adv Robot 22(4):451–476
Xu W, Li C, Liang B, Xu Y, Liu Y, Qiang W (2009) Target berthing and base reorientation of free-floating space robotic system after capturing. Acta Astronaut 64(2–3):109–126
Sabatini M, Monti R, Gasbarri P, Palmerini GB (2013) Deployable space manipulator commanded by means of visual-based guidance and navigation. Acta Astronaut 83:27–43
Sabatini M, Monti R, Gasbarri P, Palmerini GB (2013) Adaptive and robust algorithms and tests for visual-based navigation of a space robotic manipulator. Acta Astronaut 83:65–84
Ulrich S, Sasiadek JZ, Barkana I (2012) Modeling and direct adaptive control of a flexible-joint manipulator. J Guid Control Dyn 35(1):25–39
Ulrich S, Sasiadek JZ, Barkana I (2014) Nonlinear adaptive output feedback control of flexible-joint space manipulators with joint stiffness uncertainties. J Guid Control Dyn 37(6):1961–1975
Yu X, Chen L (2015) Modeling and observer-based augmented adaptive control of flexible-joint free-floating space manipulators. Acta Astronaut 108:146–155
Yu X, Chen L (2015) Singular perturbation adaptive control and vibration suppression of free-flying flexible space manipulators. Proc Inst Mech Eng Part C J Mech Eng Sci 229(11):1989–1997
Sun J, Tian Q, Hu H (2016) Structural optimization of flexible components in a flexible multibody system modeled via ANCF. Mech Mach Theory 104:59–80
Liu X, Li H, Chen Y, Cai G (2015) Dynamics and control of space robot considering joint friction. Acta Astronaut 111:1–18
Liu X, Li H, Wang J, Cai G (2015) Dynamics analysis of flexible space robot with joint friction. Aerosp Sci Technol 47:164–176
Alepuz JP, Emami MR, Pomares J (2016) Direct image-based visual servoing of free-floating space manipulators. Aerosp Sci Technol 55:1–9
Zhang B, Liang B, Wang X, Li G, Chen Z, Zhu X (2016) Manipulability measure of dual-arm space robot and its application to design an optimal configuration. Acta Astronaut 128:322–329
Rybus T, Seweryn K, Sasiadek JZ (2017) Control system for free-floating space manipulator based on nonlinear model predictive control (NMPC). J Intell Robot Syst 85(3–4):491–509
Tortopidis I, Papadopoulos E (2007) On point-to-point motion planning for underactuated space manipulator systems. Robot Auton Syst 55(2):122–131
Boning P, Dubowsky S (2011) A kinematic approach to determining the optimal actuator sensor architecture for space robots. Int J Robot Res 30(9):1194–1204
Sabatini M, Gasbarri P, Monti R, Palmerini GB (2012) Vibration control of a flexible space manipulator during on orbit operations. Acta Astronaut 73:109–121
Liu X, Baoyin H, Ma X (2013) Optimal path planning of redundant free-floating revolute-jointed space manipulators with seven links. Multibody Syst Dyn 29(1):41–56
Jarzebowska E, Pietrak K (2014) Constrained mechanical systems modeling and control: a free-floating space manipulator case as a multi-constrained system. Robot Auton Syst 62(10):1353–1360
Nanos K, Papadopoulos E (2015) Avoiding dynamic singularities in Cartesian motions of free-floating space manipulators. IEEE Trans Aerosp Electron Syst 51(3):2305–2318
Fahroo F, Ross IM (2001) Costate estimation by a Legendre pseudospectral method. J Guid Control Dyn 24(2):270–277
Gong Q, Kang W, Ross IM (2006) A pseudospectral method for the optimal control of constrained feedback linearizable systems. IEEE Trans Autom Control 51(7):1115–1129
Fahroo F, Ross IM (2008) Pseudospectral methods for infinite-horizon nonlinear optimal control problems. J Guid Control Dyn 31(4):927–936
Garg D, Patterson M, Hager WW, Rao AV, Benson DA, Huntington GT (2010) A unified framework for the numerical solution of optimal control problems using pseudospectral methods. Automatica 46(11):1843–1851
Yan H, Ross IM, Alfriend KT (2007) Pseudospectral feedback control for three-axis magnetic attitude stabilization in elliptic orbits. J Guid Control Dyn 30(4):1107–1115
Ross IM, Sekhavat P, Fleming A, Gong Q (2008) Pseudospectral feedback control: Foundations, examples and experimental results for a new approach. J Guid Control Dyn 31(2):307–321
Tian B, Zong Q (2011) Optimal guidance for reentry vehicles based on indirect Legendre pseudospectral method. Acta Astronaut 68(7–8):1176–1184
Zhou H, Rahman T, Wang D, Chen W (2013) Onboard pseudospectral guidance for re-entry vehicle. Proc Inst Mech Eng Part G: J Aerosp Eng 228(11):1925–1936
Yang L, Zhou H, Chen W (2014) Application of linear Gauss pseudospectral method in model predictive control. Acta Astronaut 96:175–187
Tian B, Fan W, Su R, Zong Q (2015) Real-time trajectory and attitude coordination control for reusable launch vehicle in reentry phase. IEEE Trans Ind Electron 62(3):1639–1650
Shabana AA (2005) Dynamics of multibody systems, 3rd edn. Cambridge University Press, Cambridge
Gill PE, Murray W, Saunders MA (2005) SNOPT: an SQP algorithm for large-scale constrainted optimization. SIAM Rev 47(1):99–131
Bryson AE, Ho YC (1975) Applied optimal control. Hemisphere Publishing, New York
Acknowledgements
The authors are grateful for the financial support from the National Natural Science Foundation of China (Grant Nos. 11732005 and 11472058).
Author information
Authors and Affiliations
Corresponding author
Additional information
Technical Editor: André Cavalieri.
Appendix
Appendix
The expressions of \(\varvec{J}_i\;(i=0,1,2,3)\) in Eq. (63) are
where \(\varvec{R}_i\) is the coordinate transformation matrix of \(B_i\) with respect to the reference frame. \(\varvec{R}_{i,j}\) is the coordinate transformation matrix of \(B_j\) with respect to the body-fixed frame of \(B_i\). The expressions of \(\varvec{k}_{ij}\) are
Rights and permissions
About this article
Cite this article
Yao, Q., Ge, X. Optimal reorientation of a free-floating space robot subject to initial state uncertainties. J Braz. Soc. Mech. Sci. Eng. 40, 146 (2018). https://doi.org/10.1007/s40430-018-1064-1
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s40430-018-1064-1