This paper presents a new nonholonomy criteria and reveals the physical interpretation of holonomoic and nonholonomic constraints acting on a free-flying space robot with or without interaction with a free Flying/Floating target object. The analysis in this paper interprets the physical interpretation behind such constraints, and clarifies geometric and kinematic conditions that generate such constraints. Moreover, a new criterion of finding the holonomy/nonholonomy of constraints impose on a free-flying space robot with or without interaction with a floating object is presented as well. The proposed criteria are applicable in case of zero or non-zero initial momentum conditions. Such nonholonomy criteria are proposed by utilizing the concept of orthogonal projection matrices and singular value decomposition (SVD). Using this methodology will also enable us to verify online whether the constraints are violated in case of real-time applications and to take a correction action or switch the controllers. This criterion is still yet valid even the interaction with floating object is lost. Applications of the proposed criteria can be dedicated to in-orbit servicing robotic satellite to capture malfunctioned spacecrafts and satellites, docking space of NASA and Russian shuttles with International Space Station (ISA), building in-orbit stations, space rescue missions and asteroids dust sampling. Finally, simulation results are presented to demonstrate the effectiveness of the proposed criterion.
Z. Vafa and S. Dubbowsky, “The Kinematics and Dynamics of Space Manipulators: The Virtual Manipulator Approach,” International Journal of Robotics Research, Vol. 9, No. 4, 1990, pp. 3-21.
S. Dubowsky and E. Papadopoulos, “The Kinematic, Dynamics, and Control of Free-Flying and Free-Flaoting Space Robotic Systems,” IEEE Transactions on Robotics and Automation, Vol. 9, No. 5, 1993, pp. 531-543.
X.-S. Ge, H. Li and Q.-Z. Zhang, “Nonholonomic Motion Planning of Space Robotics Based on the Genetic Algorithm with Wavelet Approximation,” IEEE International Conference on Control and Automation, Guangzhou, 30 May-1 June 2007, pp. 1977-1980.
T. Yoshikawa, “Dynamics Hybrid Position/Force Control of Robot Manipulators-Description of Hand Constraints and Calculation of Joint Driving Force,” IEEE Journal of Robotics and Automation, Vol. 3, No. 5, 1987, pp. 386-392.
A. De Luca and G. Oriolo, “Modeling and Control of Nonholonomic Mechanical Systems,” In: J. Angeles and A. Kecskemethy, Eds., Kinematics and Dynamics of Multi-Body Systems, CISM Courses and Lectures, Vol. 360, Springer-Verlag, Wien, 1995, pp. 277-342.
A. M. Lopsec, “Nichthholomome Systeme in Mehrdimensionalen Euklidischen Raumen,” Trudy Seminara po Vektornomu i Tenzornomu Analizu, Vol. 4, 1937, pp. 302-317. A. M Bloch, M. Reyhanoglu and N. H. McClamroch, “Control and Stabilization of Nonholonomic Dynamic Systems,” IEEE Transactions on Automatic Control, Vol. 37, No. 11, 1992, pp. 1746-1757. doi:10.1109/9.173144
J. G. Wang, R. Mukherji, M. Ficocelli, A. Ogilvie, M. Liu and C. Rice, “Modeling and Simulation of Robotic System for Servicing Hubble Space Telescope,” IEEE/RSJ International Conference on Intelligent Robots and Systems, Beijing, October 2006, pp. 1026-1031.
H. T. Shui, J. W. Wang and H. X. Ma, “Optimal Motion Planning for Free-Floating Space Robots Based on Null Space Approach,” International Conference on Measuring Technology and Mechatronics Automation, Zhangjiajie, 11-12 April 2009, pp. 845-848.
M. Shibli, “Unified Modeling Approach of Kinematics, Dynamics, and Control of a Free-Flying Space Robot Interacting with a Target Satellite,” Journal of Intelligent Control and Automation, Vol. 2, No. 1, 2011, pp. 8-23.
M. Shibli, C.-Y. Su and F. Aghili, “Online Nonholonomy Criterion of a Free-Flying Space Robot with/without Interaction with a Target Satellite,” 36th International Symposium on Robotics, IEEE Robotics and Automation, Tokyo, 28 November-1 December, 2005.