Direct Trajectory Optimization Using a Variable Low-Order Adaptive Pseudospectral Method

A variable-order adaptive pseudospectral method is presented for solving optimal control problems. The method developed in this paper adjusts both the mesh spacing and the degree of the polynomial on each mesh interval until a specified error tolerance is satisfied. In regions of relatively high curvature, convergence is achieved by refining the mesh, while in regions of relatively low curvature, convergence is achieved by increasing the degree of the polynomial. An efficient iterative method is then described for accurately solving a general nonlinear optimal control problem. Using four examples, the adaptive pseudospectral method described in this paper is shown to be more efficient than either a global pseudospectral method or a fixed-order method.