Balancing Accuracy and Efficiency: Fast Motion Planning Based on Nonlinear Model Predictive Control

Nonlinear Model Predictive Control (NMPC) is an effective method for the motion planning of automated vehicles. With the working conditions become more nonlinear and complicated, it is necessary to design an efficient NMPC method while guarantee the control accuracy simultaneously. This work presents a fast NMPC method aiming for balancing accuracy and efficiency in multiple obstacle vehicles situations. Given the high nonlinearity of vehicle dynamics, Lagrange interpolation is adopted to discretize vehicle dynamics function and objective function to ensure accuracy with less discretization points. The interpolation order is chosen adaptively based on the numerical analysis of the distribution characteristics of discretization error. Moreover, a hybrid strategy is presented to construct the constraints for obstacle avoidance by combing the elliptic and linear time-varying ones together to make a good balance between the control accuracy and solving efficiency. The acceleration effect and performance of the motion planning algorithm designed by NMPC are validated by comparative numerical analysis in multiple obstacle vehicles scenarios.