Optimal Constrained Planning for Complex Mechatronic Systems

This thesis focuses on the challenging problem of the optimal planning for mechatronic systems. The goal is to find strategies which maximize or minimize some cost criteria defined over a given constrained problem. The planning for mobile or industrial robots is a general framework under which several different open research issues can be found. Motion planning, in fact, involves the solution of a variety of optimality problems which range from the optimal path design to the optimal trajectory planning. Since, obviously, this is a very wide research field the scope of our analysis has been limited to three main contributions which represents the novelties proposed in this thesis. Initially, the optimal path generation problem is solved in the case of planar paths for mobile robots by using a new and powerful planning primitive recently proposed in the literature. Subsequently, the optimal path tracking problem is handled by a new control scheme able to online optimal scale any designed trajectory, which can be phisically unfeasible for the controlled system, in order to fulfill given kinematic and/or dynamic constraints. Finally, the problem of the generation of optimal controls for the minimum-time state transitions of nonlinear systems is presented and an innovative differential method is devised.