Time-optimal trajectory planning for autonomous parking of tractor-semitrailer vehicle based on piecewise Gauss pseudospectral method

For the autonomous parking problem of the tractor-semitrailer vehicle, a piecewise Gauss pseudospectral method is proposed as a trajectory planning scheme in this paper. Firstly, the trajectory planning problem is transformed into an optimal control problem by establishing a vehicle kinematics model for the low-velocity scene, the dynamic constraints including the physical constraints, the collision avoidance constraints, and the endpoint constraints. The optimal control problem are discretized into a nonlinear programming problem by piecewise Gauss pseudospectral method according to the movement area during parking process. The shortest time to complete parking is taken as the objective function. The Gauss pseudospectral method is further adopted to solve the nonlinear programming problem in the two parking stages. Three parallel parking conditions with different lengths of parking spaces and three vertical parking conditions with different widths of parking spaces are set for simulation verification based on Matlab/Simulink. The simulation results show that the proposed method can uniformly and effectively solve the trajectory planning problem of the tractor-semitrailer vehicle. Compared with the traditional pseudospectral method, a shorter parking time and a significantly higher convergence rate can be got with the method, which further indicates that the proposed method has good effectiveness and robustness.