Efficient mixed-integer nonlinear programming for optimal motion planning of non-holonomic autonomous vehicles

In recent years, different approaches of motion planning have been proposed for autonomous vehicles. In order to keep convex formulations, the planning problem is always decoupled into a lateral and longitudinal component, which often leads to infeasible trajectories. In this paper, we present a method which takes vehicles orientation and the curvature of trajectory into consideration using mixed-integer nonlinear programming method. We design constraints with the orientation of the vehicle computed in a discrete manner for collision free, and at the same time constrain the maximum curvature of the trajectory. These constraints are specially designed to ensure the convexity of the planning space and the trajectory converges to a global optimum. In the end, we demonstrate the feasibility of the method in this paper through simulations of lane changing scenario.