An Adaptive Backstepping Control for a Free-Floating Space Manipulator Using a Linearly Parametrized Dynamic Model
Publication: Journal of Aerospace Engineering
Volume 37, Issue 2
Abstract
A manipulator mounted on a free-floating satellite will be a key technology in active debris removal and on-orbit servicing missions. Such a system is characterized by a dynamic coupling between the manipulator and the satellite. Thus, there is a need for model-based control systems that take the satellite’s motion into account. As it is assumed that the satellite is uncontrolled during the manipulator’s operations, the satellite-manipulator system is nonholonomic, which makes a stability analysis complex. In addition, it is difficult to precisely identify mass and inertia of the system. To overcome these problems, a backstepping adaptive control system is proposed. Stability is proved using Lyapunov theory. There are three main novelties of the approach: (1) the backstepping algorithm is used for operational space control of a free-floating space manipulator; (2) adaptation laws are derived directly, using the full linearly parametrized dynamic model, with conserved, but nonzero initial momentum and angular momentum; and (3) satellite velocity measurements are used as the desired trajectory in order to allow application of the backstepping algorithm for the full dynamic model with nonzero initial momentum and angular momentum. Control quality is validated using Monte Carlo simulations. Our results are compared with a control scheme based on the kinematic Jacobian with satellite velocity feedback. Our adaptive control system not only performs better in terms of control quality, but also ensures asymptotic stability.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The authors would like to thank Dr. Tomasz Barciński from the Centrum Badań Kosmicznych Polskiej Akademii Nauk (CBK PAN) for his helpful suggestions.
References
Abiko, S., and G. Hirzinger. 2007. “An adaptive control for a free-floating space robot by using inverted chain approach.” In Proc., 2007 IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, 2236–2241. New York: IEEE. https://doi.org/10.1109/IROS.2007.4399007.
Abiko, S., and G. Hirzinger. 2009. “Adaptive control for a torque controlled free-floating space robot with kinematic and dynamic model uncertainty.” In Proc., 2009 IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, 2359–2364. New York: IEEE. https://doi.org/10.1109/IROS.2009.5354601.
Abiko, S., and K. Yoshida. 2010. “Adaptive reaction control for space robotic applications with dynamic model uncertainty.” Adv. Rob. 24 (Jun): 1099–1126. https://doi.org/10.1163/016918610X501264.
Alder, L. J., and S. M. Rock. 1993. “Adaptive control of a flexible-link robotic manipulator with unknown payload dynamics.” In Proc., American Control Conf., 2088–2092. New York: IEEE. https://doi.org/10.23919/ACC.1993.4793249.
Angeles, J. 2002. Fundamentals of robotic mechanical systems: Theory methods, and algorithms. 2nd ed. Berlin: Springer.
Basmadji, F. L., G. Chmaj, T. Rybus, and K. Seweryn. 2019. “Microgravity testbed for the development of space robot control systems and the demonstration of orbital maneuvers.” In Proc., SPIE: Photonics Applications in Astronomy, Communications, Industry and High-Energy Physics Experiments, 71–96. Bellingham, WA: Society of Photo-Optical Instrumentation Engineers. https://doi.org/10.1117/12.2537981.
Basmadji, F. L., K. Seweryn, and J. Z. Sąsiadek. 2020. “Space robot motion planning in the presence of nonconserved linear and angular momenta.” Multibody Syst. Dyn. 50 (6): 71–96. https://doi.org/10.1007/s11044-020-09753-x.
Bjerkeng, M., and K. Y. Pettersen. 2012. “Nonholonomic reorientation of free-flying space robots using parallelogram actuation in joint space.” In Proc., 2012 IEEE Int. Conf. on Robotics and Automation, 4974–4979. New York: IEEE. https://doi.org/10.1109/ICRA.2012.6224820.
Cavenago, F., A. M. Giordano, and M. Massari. 2018. “Contact force observer for space robots.” In Proc., IEEE Conf. on Decision and Control (CDC), 1525–1536. New York: IEEE. https://doi.org/10.1109/CDC40024.2019.9029285.
Christidi-Loumpasefski, O. O., K. Nanos, and E. Papadopoulos. 2017. “On parameter estimation of space manipulator systems using the angular momentum conservation.” In Proc., 2017 IEEE Int. Conf. on Robotics and Automation (ICRA), 5453–5458. New York: IEEE. https://doi.org/10.1109/ICRA.2017.7989641.
Dubovsky, S., and E. Papadopoulos. 1993. “The kinematics, dynamics, and control of free-flying and free-floating space robotic systems.” IEEE Trans. Rob. Autom. 9 (5): 531–534. https://doi.org/10.1109/70.258046.
Ehrenwald, L., and M. Guelman. 1998. “Integrated adaptive control of space manipulators.” J. Guide Control Dyn. 21 (1): 156–163. https://doi.org/10.2514/2.4212.
Ellery, A. 2019. “Tutorial review on space manipulators for space debris mitigation.” Robotics 8 (2): 34. https://doi.org/10.3390/robotics8020034.
Gu, Y.-L., and T. Xu. 1993. “A normal form augmentation approach to adaptive control of space robot systems.” In Proc., IEEE Int. Conf. on Robotics and Automations, 275–294. New York: IEEE. https://doi.org/10.1109/ROBOT.1993.291872.
Hu, Q., L. Xu, and A. Zhang. 2012. “Adaptive backstepping trajectory tracking control of robot manipulator.” J. Franklin Inst. 349 (5): 1087–1105. https://doi.org/10.1016/j.jfranklin.2012.01.001.
Huang, P., D. Wang, Z. Meng, F. Zhang, and J. Guo. 2016. “Adaptive postcapture backstepping control for tumbling tethered space robot-target combination.” J. Guide Control Dyn. 39 (1): 150–156. https://doi.org/10.2514/1.G001309.
Jia, Y. H., Q. Hu, and S. J. Xu. 2014. “Dynamics and adaptive control of a dual-arm space robot with closed-loop constraints and uncertain inertial parameters.” Acta Mech. Sin. 30 (1): 112–124. https://doi.org/10.1007/s10409-014-0005-1.
Kharabian, B., A. Tajik, M. Yaghoubi, B. Oveisi, and S. Rahmani. 2015. “Multiple model adaptive control in uncertain dynamic model of space manipulator.” Int. J. Adv. Mech. Autom. Eng. 2 (1): 7–11. https://doi.org/10.15242/IJAMAE.IAE0715205.
Kokotovic, P. V. 1992. “The joy of feedback: Nonlinear and adaptive.” IEEE Control Syst. Mag. 12 (3): 7–17. https://doi.org/10.1109/37.165507.
Kubo, Y., and J. Kawaguchi. 2022. “A new Coriolis matrix factorization.” J. GuidePass Control Dyn. 45 (7): 1299–1309. https://doi.org/10.2514/1.G006511.
Li, C. 2002. “Adaptive and robust composite control of coordinated motion of space robot system with prismatic joint.” In Proc., 4th World Congress on Intelligent Control and Automation, 1255–1259. New York: IEEE. https://doi.org/10.1109/WCICA.2002.1020783.
Liang, B., Y. Xu, and M. Bergerman. 1998. “Mapping a space manipulator to a dynamically equivalent manipulator.” ASME J. Dyn. Syst. Meas. Control 120 (1): 1–7. https://doi.org/10.1115/1.2801316.
Liu, F., Q. Li, L. Liang, and T. Hou. 2015. “Adaptive backstepping sliding mode control of space manipulators’ trajectory tracking in different gravity environments.” [In Chinese.] Chin. High Technol. Lett. 25 (4): 384–392. https://doi.org/10.3772/j.issn.1002-0470.2015.04.008.
Liu, Q., S. Shi, M. Jin, S. Fan, and H. Liu. 2022. “Minimum disturbance control based on synchronous and adaptive acceleration planning of dual-arm space robot to capture a rotating target.” Ind. Rob. Int. J. Rob. Res. Appl. 49 (6): 1116–1132. https://doi.org/10.1108/IR-12-2021-0291.
Liu, S., C. Ma, C. Luo, and X. Wang. 2010. “Adaptive control of free-floating space robot with disturbance based on robust fuzzy compensator.” In Proc., 2010 2nd Int. Conf. on Intelligent Human-Machine Systems and Cybernetics, 23–28. New York: IEEE. https://doi.org/10.1109/IHMSC.2010.13.
Lu, X., and Y. Jia. 2019. “Adaptive coordinated control of uncertain free-floating space manipulators with prescribed control performance.” Nonlinear Dyn. 97 (2): 1541–1566. https://doi.org/10.1007/s11071-019-05071-w.
Mark, C. P., and S. Kamath. 2019. “Review of active space debris removal methods.” Space Policy 47 (12): 194–206. https://doi.org/10.1016/j.spacepol.2018.12.005.
Murtaza, A., S. J. H. Pirzada, T. Xu, and L. Jianwei. 2020. “Orbital debris threat for space sustainability and way forward.” IEEE Access 8 (Jun): 61000–61019. https://doi.org/10.1109/ACCESS.2020.2979505.
Nuño, E., R. Ortega, and L. Basañez. 2010. “An adaptive controller for nonlinear teleoperators.” Automatica 46 (Sep): 155–159. https://doi.org/10.1016/j.automatica.2009.10.026.
Palma, P., K. Seweryn, and T. Rybus. 2022. “Impedance control using selected compliant prismatic joint in a free-floating space manipulator.” Aerospace 9 (8): 406. https://doi.org/10.3390/aerospace9080406.
Papadopoulos, E., F. Aghili, O. Ma, and R. Lampariello. 2022. “Robotic manipulation and capture in space.” Front. Rob. AI 2022 (1): 9. https://doi.org/10.3389/frobt.2022.849288.
Parlaktuna, O., and M. Ozkan. 2004a. “Adaptive control of free-floating space manipulators using dynamically equivalent manipulator model.” Rob. Autom. Syst. 46 (11): 185–193. https://doi.org/10.1016/j.robot.2003.11.007.
Parlaktuna, O., and M. Ozkan. 2004b. “Adaptive control of free-floating space robots in cartesian coordinates.” Adv. Rob. 18 (9): 943–959. https://doi.org/10.1163/1568553042225732.
Pazelli, T. F. P. A. T., R. S. Inoue, A. A. G. Siqueira, and M. H. Terra. 2008. “Mixed model based/fuzzy adaptive robust controller with H–∞ criterion applied to free-floating space manipulators.” In Proc., Int. Symp. on Artificial Intelligence, Robotics and Automation in Space. Los Angeles: European Space Agency.
Pazelli, T. F. P. A. T., M. H. Terra, and A. A. G. Siqueira. 2011. “Experimental investigation on adaptive robust controller designs applied to a free-floating space manipulator.” Control Eng. Pract. 19 (Jun): 395–408. https://doi.org/10.1016/j.conengprac.2010.12.011.
Rank, R., Q. Mühlbauer, W. Naumann, and K. Landzettel. 2011. “The DEOS automation and robotics payload.” In Proc., 11th ESA Workshop on Advanced Space Technologies for Robotics and Automation (ASTRA 2011). Noodwijk, Netherlands: ESTEC.
Ratajczak, J., and K. Tchoń. 2020. “Normal forms and singularities of non-holonomic robotic systems.” Syst. Control Lett. 138 (Jun): 104661. https://doi.org/10.1016/j.sysconle.2020.104661.
Rybus, T., T. Barciński, J. Lisowski, and K. Seweryn. 2015. “Analyses of a free-floating manipulator control scheme based on the fixed-base Jacobian with spacecraft velocity feedback.” In Aerospace robotics II. GeoPlanet: Earth and planetary sciences, 59–69. Berlin: Springer. https://doi.org/10.1007/978-3-319-13853-4_6.
Rybus, T., J. Prokopczuk, M. Wojtunik, K. Aleksiejuk, and J. Musiał. 2022. “Application of bidirectional rapidly exploring random trees (BiRRT) algorithm for collision-free trajectory planning of free-floating space manipulator.” Robotica 40 (12): 4326–4357. https://doi.org/10.1017/S0263574722000935.
Rybus, T., and K. Seweryn. 2013. “Trajectory planning and simulations of the manipulator mounted on a free-floating satellite.” In Aerospace robotics I. GeoPlanet: Earth and planetary sciences, 61–73. Berlin: Springer. https://doi.org/10.1007/978-3-642-34020-8_6.
Rybus, T., K. Seweryn, and J. Z. Sąsiadek. 2017. “Control system for free-floating space manipulator based on nonlinear model predictive control (NMPC).” J. Intell. Rob. Syst. 85 (3): 491–509. https://doi.org/10.1007/s10846-016-0396-2.
Sabatini, M., P. Gasbarri, and G. B. Palmerini. 2017. “Coordinated control of a space manipulator tested by means of an air bearing free floating platform.” Acta Astronaut. 139 (8): 296–305. https://doi.org/10.1016/j.actaastro.2017.07.015.
Sakha, M. S., H. Kharrati, and F. Mehdifar. 2021. “Adaptive control of free-floating manipulator in presence of stochastic input disturbances and unknown dynamical parameters.” J. Vib. Control 2021 (1): 10775463211010525. https://doi.org/10.1177/10775463211010525.
Sąsiadek, J. Z. 1994. “Space robotics and manipulators—The past and the future.” Control Eng. Pract. 2 (3): 491–497. https://doi.org/10.1016/0967-0661(94)90787-0.
Schaub, H., and J. L. Junkins. 2002. Analytical mechanics of aerospace systems. Reston, VA: American Institute of Aeronautics and Astronautics.
Seweryn, K., et al. 2017. “The prototype of space manipulator WMS LEMUR dedicated to capture tumbling satellites in on-orbit environment.” In Proc., 11th Int. Workshop on Robot Motion and Control (RoMoCo), 15–22. Wasowo Palace, Poland. https://doi.org/10.1109/RoMoCo.2017.8003887.
Seweryn, K., F. L. Basmadji, and T. Rybus. 2022. “Space robot performance during tangent capture of an uncontrolled target satellite.” J. Astronaut. Sci. 69 (4): 1017–1047. https://doi.org/10.1007/s40295-022-00330-2.
Shan, M., J. Guo, and E. Gill. 2016. “Review and comparison of active space debris capturing and removal methods.” Prog. Aerosp. Sci. 80 (Jun): 18–32. https://doi.org/10.1016/j.paerosci.2015.11.001.
Siciliano B., L. Sciavicco, L. Villani, and G. Oriolo. 2009. “Robotics: Modelling, planning and control.” In Advanced textbooks in control and signal processing, 469–522. London: Springer.
Soltanpour, M. R., and S. E. Shafiei. 2009. “Robust backstepping control of robot manipulator in task space with uncertainties in kinematics and dynamics.” Elektronika Elektrotechnika 8 (96): 47–50.
Taira, Y., and S. Sagara. 2005. “A design of digital adaptive control systems for space robot manipulators using a transpose of the generalized Jacobian matrix.” Artif. Life Rob. 9 (1): 41–45. https://doi.org/10.1007/s10015-004-0333-5.
Taveira, T. F. P. A., A. A. G. Siqueira, and M. H. Terra. 2006. “Adaptive nonlinear H–∞ controllers applied to a free-floating space manipulator.” In Proc., 2006 IEEE Int. Conf. on Control Applications, 1476–1481. New York: IEEE. https://doi.org/10.1109/CACSD-CCA-ISIC.2006.4776859.
Ulrich, S., J. Z. Sąsiadek, and I. Barkana. 2012. “Modeling and direct adaptive control of a flexible-joint manipulator.” J. Guide Control Dyn. 35 (1): 25–39. https://doi.org/10.2514/1.54083.
Umetani, Y., and K. Yoshida. 1989. “Resolved motion rate control of space manipulators with generalized Jacobiam matrix.” IEEE Trans. Rob. Autom. 5 (3): 303–314. https://doi.org/10.1109/70.34766.
Virgili-Llop, J., J. V. Drew, R. Zappula II, and M. Romano. 2017. “Laboratory experiments of resident space object capture by a spacecraft-manipulator system.” Aerosp. Sci. Technol. 71 (15): 530–545. https://doi.org/10.1016/j.ast.2017.09.043.
Walker, M. W., and L.-B. Wee. 1991. “Adaptive control of space based robot manipulators.” IEEE Trans. Rob. Autom. 7 (6): 828–835. https://doi.org/10.1109/70.105391.
Wang, H. 2011. “On adaptive inverse dynamics for free-floating space manipulators.” Rob. Autom. Syst. 59 (Aug): 782–788. https://doi.org/10.1016/j.robot.2011.05.013.
Wang, H., and Y. Xie. 2009a. “Passivity based adaptive Jacobian tracking for free-floating space manipulators without using spacecraft acceleration.” Automatica 45 (Jun): 1510–1517. https://doi.org/10.1016/j.automatica.2009.02.013.
Wang, H., and Y. Xie. 2009b. “Stability analysis of adaptive Jacobian controller for free-floating space manipulators.” In Proc., 48th IEEE Conf. on Decision and Control and 28th Chinese Control Conf., 8174–8179. New York: IEEE. https://doi.org/10.1109/CDC.2009.5399602.
Wang, H., and Y. Xie. 2012a. “Prediction error based adaptive Jacobian tracking for free-floating space manipulators.” IEEE Trans. Aerosp. Electron. Syst. 48 (4): 3207–3221. https://doi.org/10.1109/TAES.2012.6324694.
Wang, H., and Y. Xie. 2012b. “On the recursive adaptive control for free-floating space manipulators.” J. Intell. Rob. Syst. 66 (4): 443–461. https://doi.org/10.1007/s10846-011-9632-y.
Wee, L.-B., M. W. Walker, and N. H. McClamroch. 1997. “An articulated-body model for a free-flying robot and its use for adaptive motion control.” IEEE Trans. Rob. Autom. 13 (2): 264–277. https://doi.org/10.1109/70.563648.
Xu, S., H. Wang, D. Zhang, and B. Yang. 2013. “Adaptive reactionless motion control for free-floating space manipulators with uncertain kinematics and dynamics.” In Proc., 3rd IFAC Int. Conf. on Intelligent Control and Automation Science, 646–653. Chengdu, China: International Federation of Automatic Control. https://doi.org/10.3182/20130902-3-CN-3020.00145.
Xu, S., H. Wang, D. Zhang, and B. Yang. 2016. “Adaptive zero reaction motion control for free-floating space manipulators.” IEEE Trans. Aerosp. Electron. Syst. 52 (3): 1067–1076. https://doi.org/10.1109/TAES.2016.130715.
Xu, Y., and T. Kanade. 1992. Space robotics: Dynamics and control. New York: Springer.
Xu, Y., and H. Y. Shum. 1991. Dynamic control of a space robot system with no thrust jets controlled base. Pittsburgh: Carnegie-Mellon Univ.
Xu, Y., H. Y. Shum, T. Kanade, and J. J. Lee. 1994. “Parametrization and adaptive control of space robot systems.” IEEE Trans. Aerosp. Electron. Syst. 30 (2): 435–451. https://doi.org/10.1109/7.272266.
Yang, G., Y. Liu, M. Jin, and H. Liu. 2019. “A robust and adaptive control method for flexible-joint manipulator capturing a tumbling satellite.” IEEE Access 7 (2): 159971–159985. https://doi.org/10.1109/ACCESS.2019.2950674.
Yao, Q. 2021. “Adaptive trajectory tracking control of a free-flying space manipulator with guaranteed prescribed performance and actuator saturation.” Acta Astronaut. 185 (Aug): 283–298. https://doi.org/10.1016/j.actaastro.2021.05.016.
Yoshida, K., and Y. Umetani. 1990. “Control of space free-flying robot.” In Proc., 29th IEEE Conf. on Decision and Control, 97–102. New York: IEEE. https://doi.org/10.1109/CDC.1990.203553.
Zhan, B., M. Jin, G. Yang, and Z. Zhao. 2022. “A novel collision-free detumbling strategy for a space robot with a 7-DOF manipulator in postcapturing phase.” J. Aerosp. Eng. 35 (3): 04022008. https://doi.org/10.1061/(asce)as.1943-5525.0001388.
Zhang, F., Y. Fu, J. Qu, and S. Wang. 2015. “Robust adaptive control of a free-floating space robot system in cartesian space.” Int. J. Adv. Rob. Syst. 12 (11): 157. https://doi.org/10.5772/61743.
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Journal of Aerospace Engineering
Volume 37 • Issue 2 • March 2024
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© 2023 American Society of Civil Engineers.
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Received: May 26, 2023
Accepted: Sep 19, 2023
Published online: Dec 11, 2023
Published in print: Mar 1, 2024
Discussion open until: May 11, 2024
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