Optimal Kinematic-based Trajectory Planning and Tracking Control of Autonomous Ground Vehicle Using the Variational Approach

Abstract

In this paper, a novel kinematic-based optimal trajectory planning formulation for an autonomous vehicle is presented. In this new formulation, the quadratic errors of position, velocity, and acceleration are minimized subject to the rear wheel car-like vehicle nonlinear kinematic model. Minimizing the error of velocity and acceleration in addition to the error of position, allows us to obtain both optimal vehicle trajectory and control law. The Variational approach is used to minimize the cost function. Then, optimal trajectory and control inputs are numerically calculated by solving a set of two-point boundary value (TPBV) nonlinear differential equations. Finally, the proposed method is evaluated in two scenarios of lane changing and multi-curvature road which verify the success of the proposed method in generating an optimal trajectory and control inputs.