Time optimal trajectory planning with feedforward and friction compensation

The problem of time-optimal trajectory design for high performance point-to-point positioning system under state and control constraints is considered. The proposed solution takes into account Coulomb and viscous friction. A particular structure for the trajectory is postulated, and conditions for its optimality are proven using the Pontryagin Maximum Principle. The explicit solution for the co-states is found. It is shown that one of the co-states contain jumps, together with two singular arcs. Results for a real-life implementation on a nano-positioning X-Y stage are shown.