Real-Time Generation of Time-Optimal Commands for Rest-to-Rest Motion of Flexible Systems

This brief presents an analysis of the time-optimal control for rest-to-rest motion of flexible structures with lightly damped modes. For such systems, the switch command timings are shown to be periodic, and the repeat time of the solution set is derived as a function of the natural mode frequencies. Based on this result, we formulate a new approach for the quick generation of time-optimal commands for any given reference move where a finite set of these periodic solutions are computed offline, and are later used to derive time-optimal profiles by solving a much reduced subset of original problem in real-time. This provides large computational benefit over existing schemes, which require expensive computations where nonconvex and nonlinear parametric optimization problems are solved for every reference move. The proposed approach is compared with existing input shaping-based schemes in terms of computational requirement and system performance. Extensions are provided for systems with multiple flexible modes, and with different limits on maximum acceleration and deceleration.