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Dynamics of Nonholonomic Mechanical Systems

Nonholonomic mechanical systems pose a challenge to roboticists. Indeed, different from holonomic systems, a paradigm of which is the standard industrial manipulator, their nonholonomic counterparts require, for the description of their configurations, a number of variables greater than their mobility. As a consequence, some of the state variables of these systems are neither controllable nor observable. This kind of systems is studied here with the purpose of devising novel mechanical designs and control strategies that will make the operation of rolling robots more reliable and efficient. In the process of this study, we came across a new class of nonholonomic mechanical systems that leads to mathematical models resembling holonomic systems because of their simplicity. We term these systems quasiholonomic. In order to fully characterize quasiholonomic systems, we undertook an in-depth review of nonholonomic systems that led to the concept of holonomy matrix, to supplement the classical results based on the Frobenius Theorem.

Currently we are investigating mechanical design criteria under which a given robotic topology can lead to a quasiholonomic system. Our aim in this project is to design rolling robots with omnidirectional wheels that will be capable of either quasiholonomic or fully holonomic motions with suitable control schemes. A major issue in this investigation is the loss of holonomy, or quasiholonomy, due to disturbances from the environment. We will thus have a plant to control which is capable of undergoing topological changes, when switching from holonomic mode to nonholonomic (or quasiholonomic) mode, and vice versa. (Figure 6.16)

 S. Ostrovskaya, J. Angeles

Figure 6.16: Rolling robot with three ball-wheels: (a) top view; (b) cross section

Annual Report

Mon Jun 26 21:22:20 GMT 2000