Sequential Convex Programming Methods for Real-time Optimal Trajectory Planning in Autonomous Vehicle Racing

Optimization problems for trajectory planning in autonomous vehicle racing are characterized by their nonlinearity and nonconvexity. Instead of solving these optimization problems, usually a convex approximation is solved instead to achieve a high update rate. We present a real-time-capable model predictive control (MPC) trajectory planner based on a nonlinear single-track vehicle model and Pacejka's magic tire formula for autonomous vehicle racing. After formulating the general nonconvex trajectory optimization problem, we form a convex approximation using sequential convex programming (SCP). The state of the art convexifies track constraints using sequential linearization (SL), which is a method of relaxing the constraints. Solutions to the relaxed optimization problem are not guaranteed to be feasible in the nonconvex optimization problem. We propose sequential convex restriction (SCR) as a method to convexify track constraints. SCR guarantees that resulting solutions are feasible in the nonconvex optimization problem. We show recursive feasibility of solutions to the restricted optimization problem. The MPC is evaluated on a scaled version of the Hockenheimring racing track in simulation. The results show that an MPC using SCR yields faster lap times than an MPC using SL, while still being real-time capable.