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: http://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