Efficient Trajectory Planning for Autonomous Vehicles Using Quadratic Programming With Weak Duality

Highly autonomous driving technology is expected to improve driving safety and convenience, and collision avoidance technology is essential for fully autonomous driving. Planning a collision-free trajectory that includes velocity and path is one of the most challenging objectives. Optimization-based trajectory planners have been proposed in many previous studies because they offer a high degree of freedom and can handle various situations. However, most previous trajectory planners used nonlinear programming due to the nonlinearity or non-convexity of the optimization problem. These methods come with a high computational load. The trajectory planner requires the real-time ability to cope with dynamically changing environments. This article focuses on the trajectory planning of autonomous vehicles through quadratic programming (QP), which requires a low computational load. To achieve this, we introduce the longitudinal-lateral decomposition method. In addition, collision-free constraints are expressed as linear constraints through proposed ingenious dual functions. The proposed weak duality optimization problem has a QP form and optimized trajectory and obstacle avoidance timing through only one QP problem. This study verified that the proposed trajectory planner could plan smooth collision-free maneuvers for several driving situations by simulations.