The continuous inverse kinematic problem for mobile manipulators: a case study in the dynamic extension

The continuous inverse kinematic problem amounts to computing a configuration of a mobile manipulator capable of producing a prescribed trajectory in the taskspace. By adopting a control system representation of kinematics of the mobile manipulator this problem is made equivalent to the problem of exact or asymptotic output tracking that may be solved by the dynamic extension algorithm. We study the continuous inverse kinematic problem for a mobile manipulator comprising a 3 DOF RTR manipulator mounted on a kinematic car type mobile platform. Our main result is a continuous asymptotic inverse kinematics algorithm employing dynamic state feedback. The performance of this inversion algorithm has been examined in computer simulations.

[1]  Xiaoping Yun,et al.  Coordinating locomotion and manipulation of a mobile manipulator , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[2]  Arjan van der Schaft,et al.  Non-linear dynamical control systems , 1990 .

[3]  J. Descusse,et al.  Decoupling with Dynamic Compensation for Strong Invertible Affine Non Linear Systems , 1985 .

[4]  Homayoun Seraji,et al.  A Unified Approach to Motion Control of Mobile Manipulators , 1998, Int. J. Robotics Res..

[5]  Carlos Canudas de Wit,et al.  Theory of Robot Control , 1996 .

[6]  Krzysztof Tchoń,et al.  Kinematics of mobile manipulators : a control theoretic perspective , 2001 .

[7]  Robert Muszynski,et al.  Instantaneous kinematics and dexterity of mobile manipulators , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[8]  Xiaoping Yun,et al.  Unified analysis on mobility and manipulability of mobile manipulators , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[9]  Richard Colbaugh.  Adaptive stabilization of mobile manipulators , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[10]  H. Nijmeijer,et al.  Dynamic input-output decoupling of nonlinear control systems , 1988 .

[11]  Richard Colbaugh.  Adaptive stabilization of mobile manipulators , 1998, J. Field Robotics.