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

This paper is a response to requests from several respected colleagues in academia for a careful writeup of the classical time-optimal control based hybrid controllers that we have been using for material transport control in our modular reconfigurable manufacturing systems application. Specifically, we show how classical closed form time optimal control, which exploits the special structure of double integrator systems (ie ones with point-mass Newton¿s Law dynamics) can be used to design hybrid controllers for waypoint tracking. While double integrator dynamics are very simple, they are extremely prevalent in many domains, beyond manufacturing systems, eg, transportation, disk drives, robotics, and aerospace. 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 (switching) of the state of a reference generator with the same point mass dynamics in a two-degree-of-freedom controller topology. The techniques we present admit very compact implementations, suitable for use in low cost micro controllers and DSP chips used in modular reconfigurable embedded systems applications. Since these controllers were to be integrated with a discrete planner, as part of the control software of a large complex new research platform, every effort was made to keep the controllers as simple as possible. Our controllers can be viewed as examples of basic hybrid controllers that are being used successfully in practice, and can be used as benchmarks by controls researchers for more sophisticated hybrid control design methods.