An Optimization-based Trajectory Planning Method with Polynomial Curves

Trajectory planning is an essential module of autonomous vehicles, and its planning efficiency and robustness directly affect driving safety and ride comfort. The sampling-based polynomial curve trajectory planning method on Frenet Frame decouples the trajectory, which reduces the complexity of the problem-solving. However, the sampling method's limitations on the solution space, along with the collision detection, reduce the real-time performance and robustness. This paper proposes an efficient method that integrates optimization techniques with polynomial curve planning on Frenet Frame. The trajectory planning problem based on the polynomial curve is transformed into a quadratic programming problem. By taking the lateral and longitudinal distances between the ego vehicle and obstacles as part of the cost function, the optimization-based method avoids time-consuming collision detection. Active set method is employed to solve coefficients of the trajectory polynomial, thereby obtaining a safer and more comfortable trajectory. Simulation results illustrate that the proposed method outperforms the sampling-based polynomial curve trajectory planning method in terms of real-time performance and robustness.