Unified Modeling Approach of Kinematics, Dynamics and Control of a Free-Flying Space Robot Interacting with a Target Satellite

Author(s)
Murad Shibli

ABSTRACT

In this paper a unified control-oriented modeling approach is proposed to deal with the kinematics, linear and angular momentum, contact constraints and dynamics of a free-flying space robot interacting with a target satellite. This developed approach combines the dynamics of both systems in one structure along with holonomic and nonholonomic constraints in a single framework. Furthermore, this modeling allows consid-ering the generalized contact forces between the space robot end-effecter and the target satellite as internal forces rather than external forces. As a result of this approach, linear and angular momentum will form holonomic and nonholonomic constraints, respectively. Meanwhile, restricting the motion of the space robot end-effector on the surface of the target satellite will impose geometric constraints. The proposed momentum of the combined system under consideration is a generalization of the momentum model of a free-flying space robot. Based on this unified model, three reduced models are developed. The first reduced dynamics can be considered as a generalization of a free-flying robot without contact with a target satellite. In this re-duced model it is found that the Jacobian and inertia matrices can be considered as an extension of those of a free-flying space robot. Since control of the base attitude rather than its translation is preferred in certain cases, a second reduced model is obtained by eliminating the base linear motion dynamics. For the purpose of the controller development, a third reduced-order dynamical model is then obtained by finding a common solution of all constraints using the concept of orthogonal projection matrices. The objective of this approach is to design a controller to track motion trajectory while regulating the force interaction between the space robot and the target satellite. Many space missions can benefit from such a modeling system, for example, autonomous docking of satellites, rescuing satellites, and satellite servicing, where it is vital to limit the con-tact force during the robotic operation. Moreover, Inverse dynamics and adaptive inverse dynamics control-lers are designed to achieve the control objectives. Both controllers are found to be effective to meet the specifications and to overcome the un-actuation of the target satellite. Finally, simulation is demonstrated by to verify the analytical results.

In this paper a unified control-oriented modeling approach is proposed to deal with the kinematics, linear and angular momentum, contact constraints and dynamics of a free-flying space robot interacting with a target satellite. This developed approach combines the dynamics of both systems in one structure along with holonomic and nonholonomic constraints in a single framework. Furthermore, this modeling allows consid-ering the generalized contact forces between the space robot end-effecter and the target satellite as internal forces rather than external forces. As a result of this approach, linear and angular momentum will form holonomic and nonholonomic constraints, respectively. Meanwhile, restricting the motion of the space robot end-effector on the surface of the target satellite will impose geometric constraints. The proposed momentum of the combined system under consideration is a generalization of the momentum model of a free-flying space robot. Based on this unified model, three reduced models are developed. The first reduced dynamics can be considered as a generalization of a free-flying robot without contact with a target satellite. In this re-duced model it is found that the Jacobian and inertia matrices can be considered as an extension of those of a free-flying space robot. Since control of the base attitude rather than its translation is preferred in certain cases, a second reduced model is obtained by eliminating the base linear motion dynamics. For the purpose of the controller development, a third reduced-order dynamical model is then obtained by finding a common solution of all constraints using the concept of orthogonal projection matrices. The objective of this approach is to design a controller to track motion trajectory while regulating the force interaction between the space robot and the target satellite. Many space missions can benefit from such a modeling system, for example, autonomous docking of satellites, rescuing satellites, and satellite servicing, where it is vital to limit the con-tact force during the robotic operation. Moreover, Inverse dynamics and adaptive inverse dynamics control-lers are designed to achieve the control objectives. Both controllers are found to be effective to meet the specifications and to overcome the un-actuation of the target satellite. Finally, simulation is demonstrated by to verify the analytical results.

KEYWORDS

Free-Flying Space Robot, Target Satellite, Servicing Flying Robot, Adaptive Control, Inverse Dynamic Control, Hubble Telescope

Free-Flying Space Robot, Target Satellite, Servicing Flying Robot, Adaptive Control, Inverse Dynamic Control, Hubble Telescope

Cite this paper

nullM. Shibli, "Unified Modeling Approach of Kinematics, Dynamics and Control of a Free-Flying Space Robot Interacting with a Target Satellite,"*Intelligent Control and Automation*, Vol. 2 No. 1, 2011, pp. 8-23. doi: 10.4236/ica.2011.21002.

nullM. Shibli, "Unified Modeling Approach of Kinematics, Dynamics and Control of a Free-Flying Space Robot Interacting with a Target Satellite,"

References

[1] S. Dubowsky, E. E. Vance and M.A. Torres, “The Control of Space Manipulators Subject to Spacecraft Attitude Control Saturation Limits,” Proceeding of NASA Conference on Space Telerobotics, Pasadena,. 31 February-2 March, 1989, pp. 409-418.

[2] A. Ellery, “An Introduction to Space Robotics,” Springer, New York, 2000.

[3] W. Fehse, “Automated Ren-dezvous and Docking of Spacecraft,” Cambridge University Press, Cambridge, 2003. doi:10.1017/CBO9780511543388

[4] P. C. Hughes, “Space-craft Attitude Dynamics,” Wiley, New York, 1986.

[5] P. W. Likins, “Analytical Dynamics and Nonrigid Spacecraft Simula-tion,” JPL Technology Report, 32-1593, July 1974.

[6] W. W. Hooker and G. Margulies, “The Dynamical Attitude Equations for an N-Body Satellite,” Journal of Astronaunt Sciences, Vol. 12, No. 4, 1965, pp. 123-128.

[7] R. E. Roberson and J. Wit-tenburg, “A Dynamical Formalism for an Arbitrary Number of Rigid Bodies, with Reference to the Problem of Satellite Atti-tude Control,” Proceeding on International Federation Of Automatic Control Congress, London, 1966, London, 1968.

[8] J. Y. L. Ho, “Direct Path Method for Flexible Multibody Spacecraft Dynamics,” Journal of Spacecraft and Rockects, Vol. 14, 1997, pp. 102-110. doi:10.2514/3.571 67

[9] W. Hooker, “Equations of Motion for Interconnected Rigid and Elastic Bodies: A Derivation Independent of Angular Momen-tum,” Celestial Mechanics, Vol. 11, 1975, pp. 337-359. doi:10.1007/BF01228811

[10] Z. Vafa and S. Dubbowsky, “Minimization of Spacecraft Disturbances in Space Robotic Systems,” 11th Proceeding on AAS Guidance and Control, Advances in the Astronautical Sciences, San Diego, 1988, Vol. 66, pp. 91-108.

[11] Z. Vafa and S. Dubbowsky, “On the Dy-namics of Manipulators in Space using the Virtual Manipulator Approach,” IEEE Proceding on International Conference Ro-botics Automation, Raleigh, March 1987. pp. 579-585.

[12] Z. Vafa and S. Dubbowsky, “On the Dynamics of Manipulators in Space using the Virtual Manipulator, with Applications to Path Palnning,” Journal of Astronaut Scence, Special Issue on Space Robotics, Vol. 38, No. 4, 1990, pp. 441-472.

[13] Z. Vafa and S. Dubbowsky, “The Kinematics and Dynamics of Space Ma-nipulators: The Virtual Manipulator Approach,” International Journal of Robotics Research, Vol. 9, No. 4, 1990, pp. 3-21. doi:10.1177/02783649900 0900401

[14] Z. Vafa, “The Kine-matics, Dynamics and Control of Space Manipultors,” Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, 1987.

[15] K. Yoshida, “Achievements in Space Robotics,” IEEE Robotics & Automation Magazine, Vol. 16, No. 4, 2009, pp. 20-28. doi:10.1109/MRA.2009.934818

[16] M. Galicki, “An Adaptive Regulator of Robotic Manipulators in the Task Space,” IEEE Transactions on Automatic Control, Vol. 53, 2008, pp. 1058-1062.

[17] M. Stilman, “Global Manipulation Planning in Robot Joint Space With Task Constraints,” IEEE Transactions on Robotics, Vol. 26, No. 3, 2010, pp. 576-584. doi: 10.1109/TRO.2010. 2044949

[18] M. D. Carpenter, M. A. Peck, “Reducing Base Reactions With Gyroscopic Actuation of Space-Robotic Systems,” IEEE Transactions on Robotics, Vol. 25, No. 6, 2009, pp. 1262-1270. doi:10.1109/TRO.2009.2032953

[19] Y. Xu, and H.-Y. Shum, “Dynamic Control and Coupling of a Free-Flying Space Robot System,” Journal of Robotic Systems, Vol. 11, No. 7, 1994, pp. 573-589. doi:10.1002/rob.4620110702

[20] Hu, Y.-R. and Vukovich, “Dynamic Control of Free- floating Coordinated Space Robots,” Journal of Robotic Systems, Vol. 15, No. 4, 1998, pp. 217-230. doi:10.1002 /(SICI)1097-4563(199804)15:4<217:AID-ROB4>3.0.CO;2-S

[21] X.-S. Ge, et al., “Nonholonomic Motion Planning of Space Robotics Based on the Genetic Algorithm with Wavelet Ap-proximation,”: IEEE International Con- ference on Control and Automation, Guangzhou, 30 May -1 June, 2007, pp.1977 - 1980.

[22] M. Shibli, F. Aghili and C.-Y. Su, “Hybrid Inverse Dynamics Control of a Free-Flying Space Robot in Contact with a Target Satellite,” 1st IEEE International Symposium on Systems and Control in Aeronautics and Astronautics, Harbin, January 19-21, 2006, p. 6.

[23] X. F. Ge and J. T Jin, “Dy-namics Analyze of a Dual-Arm Space Robot System based on Kane's Method,” 2nd International Conference on Industrial Mechatronics and Automation, Wuhan, 30-31 May 2010, pp. 646-649.

[24] H. Y. Hang, et al., “Kinematical Simulation and Dynamic Analysis of the Free Float Space Robot,” 2nd Inter-national Conference on Computer Modeling and Simulation, Sanya, 22-24 January 2010, pp. 285-289.

[25] Z. F. Yu, Y. B. Yu, D. Y. Shang and F. N. Yu, “Yu Yongbo Shang Deyong Yu Fangna, “On Orbit Servicing Flexible Space Robots Dynamics and Control During Capturing Target,” International Confer-ence on Measuring Technology and Mechatronics Automation, Changsha, 13-14 March 2010, pp. 817-820. doi::10.1109/ICMTMA.2010.198

[26] S. Abiko, et al., “Adaptive Control for a Torque Controlled Free-Floating Space Robot with Kinematic and Dynamic Model Uncertainty,” IEEE/RSJ International Conference on Intelligent Robots and Systems, St. Louis, 10-15 Octomber 2009, pp. 2359-2364.

[27] D. F. Huang and C. Li, “Inverse Kinematic Control of Free-Floating Space Robot System based on a Mutual Mapping Neural Network,” 7th World Congress on Intelligent Control and Automation, Chongqing, 25-27 June 2008, pp. 8666-8670.

[28] H. T. Shui, et al., “Optimal Motion Planning for Free-Floating Space Robots Based on Null Space Ap-proach,” International Conference on Measuring Technology and Mechatronics Automation, Zhangjiajie, 11-12 April 2009, pp. 845-848.

[29] J. G. Wang, et al., “Modeling and Simula-tion of Robotic System for Servicing HUBBLE Space Tele-scope,” IEEE/RSJ International Conference on Intelligent Ro-bots and Systems, Beijing, Octomber 2006, pp. 1026-1031. doi: 10.1109/ IROS.200281804

[30] M. Shibli, F. Aghili and C.-Y. Su, “Modeling of a Free- Flying Space Robot in Contact with a Target Satellite,” IEEE CCA05 Conference on Control Appli-cations, Toronto, 28-31 August, 2005, pp. 559-564.

[31] J. I. Neimark and N. A. Fufaef, “Dynamics of Nonholonomic Sys-tems,” Translations of Mathematical Monographs, American Mathematical Society, Providence, Rhode Island, 1972.

[32] A. M. Lopsec, “Nichthholomome Systeme in Mehrdimensionalen Euklidischen Raumen,” Trudy Sem. Vektor. Tenzor Anal. 4, 302-317; Russian transl., ibid, 318-332, (1937).

[33] C. Lanczos, “The Variational Principle of Mechanics,” University of Toronto Press, Toronto, 1966.

[34] M. Shibli, C.-Y. Su and F. Aghili, “Adaptive Inverse Dynamics Control of a Free-flying Space Robot in Contact with a Target Satellite: A Hubble Space Telescope Case,” IEEE Canadian Conference on Electrical and Computer Engineering, Ottawa Congress Centre, Ottawa, 7-10 May 2006, pp. 1275-1278.

[35] H. Nijmeijer, et al., “Nonlin-ear Dynamical Control Systems,” Springer, Berlin, 1990.

[36] R. C. Hibbeller, “Dynamics,” Prentice Hall, New Jersey 2001.

[37] H. Goldstien, “Classical Mechanics,” 2nd edition, Addison-Wesley, New Jersey, 1980.

[38] A. Ben-Israel and N. E. T Greville, “Generalized Inverses: Theory and Application,” 2nd Edition, Springer, New York, 2003.

[39] M. Shibli, “Modeling and Control of a Free-Flying Space Robot Interacting with a Target Satellite,” Ph.D. Thesis, NASA Astrophysics Data System, 2009.

[1] S. Dubowsky, E. E. Vance and M.A. Torres, “The Control of Space Manipulators Subject to Spacecraft Attitude Control Saturation Limits,” Proceeding of NASA Conference on Space Telerobotics, Pasadena,. 31 February-2 March, 1989, pp. 409-418.

[2] A. Ellery, “An Introduction to Space Robotics,” Springer, New York, 2000.

[3] W. Fehse, “Automated Ren-dezvous and Docking of Spacecraft,” Cambridge University Press, Cambridge, 2003. doi:10.1017/CBO9780511543388

[4] P. C. Hughes, “Space-craft Attitude Dynamics,” Wiley, New York, 1986.

[5] P. W. Likins, “Analytical Dynamics and Nonrigid Spacecraft Simula-tion,” JPL Technology Report, 32-1593, July 1974.

[6] W. W. Hooker and G. Margulies, “The Dynamical Attitude Equations for an N-Body Satellite,” Journal of Astronaunt Sciences, Vol. 12, No. 4, 1965, pp. 123-128.

[7] R. E. Roberson and J. Wit-tenburg, “A Dynamical Formalism for an Arbitrary Number of Rigid Bodies, with Reference to the Problem of Satellite Atti-tude Control,” Proceeding on International Federation Of Automatic Control Congress, London, 1966, London, 1968.

[8] J. Y. L. Ho, “Direct Path Method for Flexible Multibody Spacecraft Dynamics,” Journal of Spacecraft and Rockects, Vol. 14, 1997, pp. 102-110. doi:10.2514/3.571 67

[9] W. Hooker, “Equations of Motion for Interconnected Rigid and Elastic Bodies: A Derivation Independent of Angular Momen-tum,” Celestial Mechanics, Vol. 11, 1975, pp. 337-359. doi:10.1007/BF01228811

[10] Z. Vafa and S. Dubbowsky, “Minimization of Spacecraft Disturbances in Space Robotic Systems,” 11th Proceeding on AAS Guidance and Control, Advances in the Astronautical Sciences, San Diego, 1988, Vol. 66, pp. 91-108.

[11] Z. Vafa and S. Dubbowsky, “On the Dy-namics of Manipulators in Space using the Virtual Manipulator Approach,” IEEE Proceding on International Conference Ro-botics Automation, Raleigh, March 1987. pp. 579-585.

[12] Z. Vafa and S. Dubbowsky, “On the Dynamics of Manipulators in Space using the Virtual Manipulator, with Applications to Path Palnning,” Journal of Astronaut Scence, Special Issue on Space Robotics, Vol. 38, No. 4, 1990, pp. 441-472.

[13] Z. Vafa and S. Dubbowsky, “The Kinematics and Dynamics of Space Ma-nipulators: The Virtual Manipulator Approach,” International Journal of Robotics Research, Vol. 9, No. 4, 1990, pp. 3-21. doi:10.1177/02783649900 0900401

[14] Z. Vafa, “The Kine-matics, Dynamics and Control of Space Manipultors,” Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, 1987.

[15] K. Yoshida, “Achievements in Space Robotics,” IEEE Robotics & Automation Magazine, Vol. 16, No. 4, 2009, pp. 20-28. doi:10.1109/MRA.2009.934818

[16] M. Galicki, “An Adaptive Regulator of Robotic Manipulators in the Task Space,” IEEE Transactions on Automatic Control, Vol. 53, 2008, pp. 1058-1062.

[17] M. Stilman, “Global Manipulation Planning in Robot Joint Space With Task Constraints,” IEEE Transactions on Robotics, Vol. 26, No. 3, 2010, pp. 576-584. doi: 10.1109/TRO.2010. 2044949

[18] M. D. Carpenter, M. A. Peck, “Reducing Base Reactions With Gyroscopic Actuation of Space-Robotic Systems,” IEEE Transactions on Robotics, Vol. 25, No. 6, 2009, pp. 1262-1270. doi:10.1109/TRO.2009.2032953

[19] Y. Xu, and H.-Y. Shum, “Dynamic Control and Coupling of a Free-Flying Space Robot System,” Journal of Robotic Systems, Vol. 11, No. 7, 1994, pp. 573-589. doi:10.1002/rob.4620110702

[20] Hu, Y.-R. and Vukovich, “Dynamic Control of Free- floating Coordinated Space Robots,” Journal of Robotic Systems, Vol. 15, No. 4, 1998, pp. 217-230. doi:10.1002 /(SICI)1097-4563(199804)15:4<217:AID-ROB4>3.0.CO;2-S

[21] X.-S. Ge, et al., “Nonholonomic Motion Planning of Space Robotics Based on the Genetic Algorithm with Wavelet Ap-proximation,”: IEEE International Con- ference on Control and Automation, Guangzhou, 30 May -1 June, 2007, pp.1977 - 1980.

[22] M. Shibli, F. Aghili and C.-Y. Su, “Hybrid Inverse Dynamics Control of a Free-Flying Space Robot in Contact with a Target Satellite,” 1st IEEE International Symposium on Systems and Control in Aeronautics and Astronautics, Harbin, January 19-21, 2006, p. 6.

[23] X. F. Ge and J. T Jin, “Dy-namics Analyze of a Dual-Arm Space Robot System based on Kane's Method,” 2nd International Conference on Industrial Mechatronics and Automation, Wuhan, 30-31 May 2010, pp. 646-649.

[24] H. Y. Hang, et al., “Kinematical Simulation and Dynamic Analysis of the Free Float Space Robot,” 2nd Inter-national Conference on Computer Modeling and Simulation, Sanya, 22-24 January 2010, pp. 285-289.

[25] Z. F. Yu, Y. B. Yu, D. Y. Shang and F. N. Yu, “Yu Yongbo Shang Deyong Yu Fangna, “On Orbit Servicing Flexible Space Robots Dynamics and Control During Capturing Target,” International Confer-ence on Measuring Technology and Mechatronics Automation, Changsha, 13-14 March 2010, pp. 817-820. doi::10.1109/ICMTMA.2010.198

[26] S. Abiko, et al., “Adaptive Control for a Torque Controlled Free-Floating Space Robot with Kinematic and Dynamic Model Uncertainty,” IEEE/RSJ International Conference on Intelligent Robots and Systems, St. Louis, 10-15 Octomber 2009, pp. 2359-2364.

[27] D. F. Huang and C. Li, “Inverse Kinematic Control of Free-Floating Space Robot System based on a Mutual Mapping Neural Network,” 7th World Congress on Intelligent Control and Automation, Chongqing, 25-27 June 2008, pp. 8666-8670.

[28] H. T. Shui, et al., “Optimal Motion Planning for Free-Floating Space Robots Based on Null Space Ap-proach,” International Conference on Measuring Technology and Mechatronics Automation, Zhangjiajie, 11-12 April 2009, pp. 845-848.

[29] J. G. Wang, et al., “Modeling and Simula-tion of Robotic System for Servicing HUBBLE Space Tele-scope,” IEEE/RSJ International Conference on Intelligent Ro-bots and Systems, Beijing, Octomber 2006, pp. 1026-1031. doi: 10.1109/ IROS.200281804

[30] M. Shibli, F. Aghili and C.-Y. Su, “Modeling of a Free- Flying Space Robot in Contact with a Target Satellite,” IEEE CCA05 Conference on Control Appli-cations, Toronto, 28-31 August, 2005, pp. 559-564.

[31] J. I. Neimark and N. A. Fufaef, “Dynamics of Nonholonomic Sys-tems,” Translations of Mathematical Monographs, American Mathematical Society, Providence, Rhode Island, 1972.

[32] A. M. Lopsec, “Nichthholomome Systeme in Mehrdimensionalen Euklidischen Raumen,” Trudy Sem. Vektor. Tenzor Anal. 4, 302-317; Russian transl., ibid, 318-332, (1937).

[33] C. Lanczos, “The Variational Principle of Mechanics,” University of Toronto Press, Toronto, 1966.

[34] M. Shibli, C.-Y. Su and F. Aghili, “Adaptive Inverse Dynamics Control of a Free-flying Space Robot in Contact with a Target Satellite: A Hubble Space Telescope Case,” IEEE Canadian Conference on Electrical and Computer Engineering, Ottawa Congress Centre, Ottawa, 7-10 May 2006, pp. 1275-1278.

[35] H. Nijmeijer, et al., “Nonlin-ear Dynamical Control Systems,” Springer, Berlin, 1990.

[36] R. C. Hibbeller, “Dynamics,” Prentice Hall, New Jersey 2001.

[37] H. Goldstien, “Classical Mechanics,” 2nd edition, Addison-Wesley, New Jersey, 1980.

[38] A. Ben-Israel and N. E. T Greville, “Generalized Inverses: Theory and Application,” 2nd Edition, Springer, New York, 2003.

[39] M. Shibli, “Modeling and Control of a Free-Flying Space Robot Interacting with a Target Satellite,” Ph.D. Thesis, NASA Astrophysics Data System, 2009.