Time-Optimal Multistage Controllers for Nonlinear Continuous Processes

Abstract

The problem addressed is that of the online computational burden of gross-motion control laws for quick, strongly nonlinear systems like revolute robots. It will be demonstrated that a large amount of offline computation can be substituted for most of the online burden in cases of time optimization with constrained inputs if point-to-point specifications can be relaxed to cell-to-cell transitions. These cells result from a coarse discretization of likely swaths of state space into a set of nonuniform, contiguous volumes of relatively simple shapes. The cell boundaries approximate stream surfaces of the phase fluid and surfaces of equal transit times. Once the cells have been designed, the schedules of bang-coast-bang for the inputs are determined for all likely starting cells and terminating cells for various load conditions. The scheduling process is completed by treating all cells into which the trajectories might unexpectedly stray as additional starting cells. Then an efficient-to-compute control law can be based on the resulting table of optimal strategies.