Optimal Motion Planning of Four-Wheeled Trailer System

To solve the problem of optimal motion planning of four-wheeled trailer systems(FWTSs) with control constraints, a symplectic numerical method for optimal control subject to index-2 differential-algebraic equations(DAEs) with inequality constraints is developed. In the proposed method, the optimal control problem is firstly converted into a mixed nonlinear complementary problem(MNCP) with the help of variation principle and generation function theory. Then, the mixed nonlinear complementary problem is converted into equivalent nonsmooth equations. Finally, the nonsmooth equations are solved by nonsmooth Newton method. The proposed method satisfies the first-order necessary conditions and matrices involved are sparse, it is beneficial to save memory and heighten efficiency. Numerical simulations demonstrate that the proposed method is effective for motion planning of four-wheeled trailer system.