Robust trajectory optimization using polynomial chaos and convex optimization

Abstract The polynomial chaos (PC) theory and direct collocation method have been integrated to solve a lot of robust trajectory optimization problems. However, the computational cost and memory consumption increase significantly with the increase of the dimension of uncertain factors, and the nonlinearity of dynamic equations. To address this issue, a novel robust trajectory optimization procedure combining PC with the convex optimization technique is proposed in this paper. With the proposed procedure, the trajectory optimization can be implemented with high accuracy and efficiency, by taking advantage of the high accuracy of PC in addressing UP for highly nonlinear dynamics and the high efficiency of convex optimization in solving optimal control. The proposed robust trajectory optimization procedure is applied to two examples and compared with the existing method employing PC and the pseudospectral method. The results show that the proposed procedure can obtain highly accurate results similar to the existing method. Moreover, with the increase of random dimension, the optimal trajectory can still be generated very efficiently without significant increase of computational cost. These results demonstrates the effectiveness of the proposed procedure.