ABSTRACT
The main objective of this paper is to address motion planning for systems in which the dynamic equations describing the evolution of the system change in dif ferent regions of the state space. We adopt the con trol theory point of view and focus on the planning of open loop trajectories that can be used as nominal in puts for control Systems with changing dynamic be havior are characterized by: (a) equality and inequality constraints that partition the state space into regions (discrete states); and (b) trajectories that are governed by different dynamic equations as the system traverses different regions in the state space. The motion plan therefore consists of the sequence of regions (discrete states) as well as continuous trajectory (evolution of the continuous state) within each of the regions. Since the task may require that the system trajectories and the inputs are sufficiently smooth, we formulate the mo tion planning problem as an optimal control problem and achieve the smoothness by specifying an appropri ate cost function.
