Efficient waypoint tracking hybrid controllers for double integrators using classical time optimal control

Abstract

Motivated by applications from the domain of modular reconfigurable systems, we show how the classical closed form time optimal control, which exploits the special structure of double integrator systems (i.e. ones with point-mass Newton’s Law dynamics) can be used to design waypoint tracking controllers. We present two methods, one which will track general way point specs, and another which will track waypoints that lie on convex or concave trajectories. Both approaches are based on appropriate setting or switching of the state a reference generator with the same point mass dynamics. The techniques we present admit very compact and simple implementations, suitable for use in low cost micro controllers and DSP processors used in modular reconfigurable systems.