Optimal trajectory planning for nonlinear systems: robust and constrained solution

This paper presents a solution to the problem of generating constrained robust trajectory planning for nonlinear plants. By using an indirect variational solution method, the necessary optimality conditions deriving from the Pontryagin’s minimum principle are imposed, and lead to a differential Two-Point Boundary Value Problem (TPBVP); numerical solution of the latter is accomplished by means of collocation techniques. The robustness to parametric mismatches is obtained trough the use of sensitivity functions, while a hard constraint on actuator effort is obtained using a smoothing technique. Numerical results shows that the robustness can be greatly improved, and that the inclusion of constraints on actuator effort does not affect it.