An algorithm for solving the equilibrium points of high-dimensional nonlinear vehicle dynamic system based on a combination of genetic algorithm, sequential quadratic programming method, and continuation method

Abstract

The paper proposes an algorithm that combines Genetic Algorithm, Sequential Quadratic Programming, and Continuation Method to solve the equilibrium points of a multi-degree-of-freedom vehicle nonlinear system. The algorithm’s effectiveness is demonstrated by applying it to search for equilibrium points of a 5-degree-of-freedom (5DOF) nonlinear vehicle model, which considers both longitudinal and lateral motion. The dynamic equilibrium points of front-wheel-drive, rear-wheel-drive, and all-wheel-drive vehicles with different front-wheel steering angle inputs are calculated. Taking the front-wheel-drive system as an example, the system equilibrium points are further analyzed using phase space analysis and eigenvalue analysis for verification. In addition, the impact of the driving effect on the equilibrium points bifurcation is investigated. The results show that compared with the Genetic Algorithm alone and the combination method of Genetic Algorithm and Sequential Quadratic Programming, the proposed algorithm can effectively and accurately solve the equilibrium points of the 5DOF vehicle model. The study also reveals that the driving effect significantly influences the vehicle equilibrium point bifurcation.