Research on lie group dynamics modeling and trajectory-tracking optimal control of intelligent ground vehicle

Abstract Aiming at the multi-objective integrated coordination problem of trajectory tracking control accuracy and vehicle stability, a Lie-group-based dynamics modeling and trajectory-tracking optimal control method of intelligent ground vehicle is proposed in this paper. Based on the theory of Lie group and Lie algebra, the kinematic relationship of intelligent ground vehicle was established, and the integral variational dynamic equation expression was established using the variational method and Lagrange principle. A vehicle performance index function that balances energy optimization and efficiency optimization was established by combining the two-degree-of-freedom dynamic equation and stability constraints of intelligent ground vehicle. On this basis, an optimal control method for trajectory tracking of intelligent ground vehicle is proposed based on Legendre interpolation polynomial discretization method and Gauss pseudospectral method. The comparative results show that the proposed optimal control method can balance vehicle motion control accuracy, real-time performance, and optimization solution efficiency, thereby ensuring the lateral stability control effect of vehicle while achieving trajectory tracking accuracy.