An application of sequential convex programming to time optimal trajectory planning for a car motion

This paper proposes an iterative method for solving non-convex optimization problems which we call sequential convex programming (SCP) and an application of our method to time trajectory planning problem for a car motion. Firstly, we introduce a formulation of the motion of a car along a reference trajectory as an optimal control problem. We use a special convexity based formulation path employing coordinates and a change of variables technique. Secondly, we use a direct transcription to transform this optimal control problem into a large scale optimization problem which is ¿nearly¿ convex. Then, SCP method is applied to solve the resulting problem. Finally, numerical results and comparison with sequential quadratic programming (SQP) and interior point (IP) methods are reported.