Control of mechanical systems with rolling contacts: Applications to robotics

Nilanjan Sarkar, University of Pennsylvania


The problems of modeling and control of mechanical dynamic systems subject to rolling contacts are investigated. There are two important theoretical contributions in this dissertation. First, contact kinematic relationships up to second order are developed for two rigid bodies in point contact. These equations relate gross rigid body motion to the changes in the positions of the points of contact. Second, a unified approach to the control of mechanical systems subject to both holonomic and nonholonomic constraints is proposed. The basic approach is to extend the state-space to include, in the addition to the generalized coordinates and velocities, contact coordinates which describe the displacements of the contact points and their derivatives. This redundant state-space formulation provides a convenient way to specify output equations to control contact motion. The control problem is formulated as an affine nonlinear problem and a differential-geometric, control-theoretic approach is used to decouple and linearize such systems. It is shown that such a system, even though not input-state linearizable, is input-output linearizable. Further, the zero dynamics of such a system is shown to be Lagrange stable. The proposed methodology is applied to three different robotic systems: (a) wheeled mobile robots, (b) two arms manipulating an object with rolling contact between each arm and the object, and (c) a single robot arm maintaining controlled contact against a moving environment. In each case, a nonlinear controller is designed to achieve the desired performances. For mobile robots, a new control algorithm called dynamic path following is proposed and shown to be quite effective and robust. In the context of two arm manipulation, grasp adaptation through the control of contact motion is demonstrated. Maintaining rolling contact with a moving surface is formulated as an acatastatic system. The proposed scheme involves simultaneously controlling interaction forces as well as the relative (rolling) motion. In all cases, computer simulations results are presented to demonstrate the efficacy of the control schemes.

Subject Area

Mechanical engineering|Mechanics|Computer science

Recommended Citation

Sarkar, Nilanjan, "Control of mechanical systems with rolling contacts: Applications to robotics" (1993). Dissertations available from ProQuest. AAI9413904.