Neighboring Extremal Method Using Gauss Pseudospectral Collocation Scheme for Trajectory Optimization

This paper proposes a trajectory optimization method that combines the Gauss pseudospectral collocation scheme and the neighboring extremal method, which can be applied to optimal control problem with terminal constraints and arbitrary performance index. This method firstly builds the neighboring extremal perturbation equations through the first order condition around normal optimal solution. Secondly, Gauss pseudospectral collocation scheme is used to transform the perturbation equations into a set of linear algebraic equations. Then analytical solution can be derived to eliminate errors and ensure the optimality. Several simulations have been carried out to verify the performance of the proposed method. Results show that it has a better performance than the traditional methods. In comparison with the classic backward sweep method, it provides the similar results with faster computational efficiency. Comparative simulation results with GPOPS-II further verify the optimality of the proposed method.