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Nonholonomic System Theory

This chapter deals with the analysis of problems that involve differential constraints. One fundamental result is the Frobenius theorem, which allows one to determine whether the state transition equation represents a system is actually nonholonomic. In some cases, it may be possible to integrate the state transition equation, resulting in a problem that can be described without differential models. Another result is Chow's theorem, which indicates whether a system is controllable. Intuitively, this means that the differential constraints can be completely overcome by generating arbitrarily short maneuvers. The car-like robot enjoys the controllability property, which enables it to move itself sideways by performing parallel parking maneuvers.