Robust model-based trajectory planning for nonlinear systems

Model-based trajectory planning algorithms are capable of providing a high level of performance. However, they are often lacking in robustness, which severely limits their field of application. In this paper the method of parametric desensitization is applied to nonlinear models, providing a feasible solution to the problem of robust model-based trajectory planning for nonlinear plants with parametric uncertainties. By using an indirect variational solution method, the necessary optimality conditions deriving from Pontryagin's minimum principle are imposed, and lead to a differential two-point boundary value problem; numerical solution of the latter is accomplished by means of collocation techniques. The method is applied to two test cases: a nonlinear spring-mass system and a flexible link manipulator with Coulombian friction. Results show that the technique developed in this paper can significantly improve the robustness of the resulting trajectory to parametric model mismatches in comparison with the conventional method.