A radial basis function method for direct trajectory optimization

This paper presents a radial basis function (RBF) method to directly solve an optimal control problem with state and control constraints. The proposed method transcribes the optimal control problem into a nonlinear programming (NLP) problem via RBF parameterization of states and controls along with unequal discretization at shifted Legendre-Gauss-Lobatto (LGL) nodes. The advantage of the method is its flexibility to choose among various RBF functions for parameterization. In fact, regardless of the number of nodes and how they are selected, any RBF with invertible Gram matrix (coefficient matrix) can be arbitrarily chosen for the unique approximation of states and controls. Numerical results are provided to verify the efficiency of the method.