Navigation Functions for Dynamical, Nonholonomically Constrained Mechanical Systems
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University of Michigan Ann Arbor United States
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In this review we explore the possibility of adapting first order hybridfeedback controllers for nonholonomically constrained systems to their dynamicalcounterparts. For specific instances of first order models of such systems, we havedeveloped gradient based hybrid controllers that use Navigation functions to reachpoint goals while avoiding obstacle sets along the way. Just as gradient controllersfor standard quasi-static mechanical systems give rise to generalized PD-stylecontrollers for dynamical versions of those standard systems, so we believe it willbe possible to construct similar lifts in the presence of non-holonomic constraintsnotwithstanding the necessary absence of point attractors.