Progressive Smoothing for Motion Planning in Real-Time NMPC

Nonlinear model predictive control (NMPC) is a popular strategy for solving motion planning problems appearing in autonomous driving applications that include collision avoidance constraints. Non-smooth obstacle shapes, such as rectangles, introduce additional local minima in the underlying optimization problem. Using smooth over-approximations, e.g., ellipsoidal shapes, limits the performance due to their conservativeness. We propose to vary the smoothness and the related over-approximation by a homotopy. Instead of varying the smoothness in consecutive sequential quadratic programming iterations, we use formulations that decrease the smooth over-approximation from the end towards the beginning of the prediction horizon. Thus, the real-time iteration scheme applies to the proposed NMPC formulation, i.e., only one quadratic program needs to be solved at each time step. Different formulations are compared in simulation experiments and shown to successfully improve performance without increasing the computational burden.