Time–mesh Refinement in Optimal Control Problems for Nonholonomic Vehicles

Direct methods are becoming the most used technique to solve nonlinear optimal control problems. Regular time meshes having equidistant spacing are most frequently used. However, in some cases, these meshes cannot cope accurately with nonlinear behaviour unless a very large number of mesh nodes is used. One way to improve the solution involves adaptive mesh refinement algorithms which allow a non uniform node collocation. In the method presented in this paper, a time mesh refinement strategy based on the local error is developed. The technique was applied to solve two problems involving nonholonomic vehicles and it led to results with higher accuracy and yet with lower overall computational time when compared to a mesh having equidistant nodes.