Control of Mechanical Systems With Rolling Constraints: Application to Dynamic Control of Mobile Robots

There are many examples of mechanical systems which require rolling contacts between two or more rigid bodies. Rolling contacts engender nonholonomic constraints in an otherwise holonomic system. In this paper, we develop a unified approach to the control of mechanical systems subject to both holonomic and nonholonomic constraints. We first present a state space realization of a constrained system and show that it is not input-state linearizable. We then discuss the input-output linearization and zero dynamics of the system. This approach is applied to the dynamic control of mobile robots. Two types of control algorithms for mobile robots are investigated: (a) trajectory tracking, and (b) path following. In each case, a smooth nonlinear feedback is obtained to achieve asymptotical input-output stability, and Lagrange stability of the overall system. Simulation results are presented to demonstrate the effectiveness of the control algorithms and to compare the performance of trajectory tracking and path following algorithms. Disciplines Mechanical Engineering Comments University of Pennsylvania Department of Computer and Information Science Technical Report No. MSCIS-92-44. This technical report is available at ScholarlyCommons: https://repository.upenn.edu/cis_reports/504 Control of Mechanical Systems with Rolling Constraints: Application to Dynamic Control of Mobile Robots MS-CIS-92-44 GRASP LAB 320 Nilanjan Sarkar Xiaoping Yun Vijay Kuillar University of Pennsylvania School of Engineering and Applied Science Computer and Information Science Department

[1]  L. Dubins.  On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents , 1957 .

[2]  Leopold Alexander Pars,et al.  A Treatise on Analytical Dynamics , 1981 .

[3]  Tsuneo Yoshikawa,et al.  Dynamic hybrid position/force control of robot manipulators--Description of hand constraints and calculation of joint driving force , 1986, IEEE Journal on Robotics and Automation.

[4]  Jean-Paul Laumond,et al.  Finding Collision-Free Smooth Trajectories for a Non-Holonomic Mobile Robot , 1987, IJCAI.

[5]  David J. Montana,et al.  The Kinematics of Contact and Grasp , 1988, Int. J. Robotics Res..

[6]  James J. Clark,et al.  Control of visual attention in mobile robots , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[7]  Kenneth J. Waldron,et al.  Actively Coordinated Vehicle Systems , 1989 .

[8]  A. Bloch,et al.  Controllability and stabilizability properties of a nonholonomic control system , 1990, 29th IEEE Conference on Decision and Control.

[9]  L. Shepp,et al.  OPTIMAL PATHS FOR A CAR THAT GOES BOTH FORWARDS AND BACKWARDS , 1990 .

[10]  Claude Samson,et al.  Feedback control of a nonholonomic wheeled cart in Cartesian space , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[11]  Yoram Koren,et al.  Potential field methods and their inherent limitations for mobile robot navigation , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[12]  Lifia Imag-Cnw.  Smooth trajectory planning for a car in a structured world , 1991 .

[13]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[14]  Vijay Kumar,et al.  Control of contact conditions for manipulation with multiple robotic systems , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[15]  G. Campion,et al.  Controllability and State Feedback Stabilizability of Nonholonomic Mechanical Systems , 1991 .

[16]  Vladimir J. Lumelsky,et al.  Motion planning for a hospital transport robot , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[17]  Sanjiv Singh,et al.  Obstacle detection for high speed autonomous navigation , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[18]  Nilanjan Sarkar,et al.  Control of Multiple Arm Systems With Rolling Constraints , 1991 .

[19]  Georges Bastin,et al.  Modelling and control of non-holonomic wheeled mobile robots , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[20]  Carlos Canudas de Wit,et al.  Path following of a 2-DOF wheeled mobile robot under path and input torque constraints , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.