Homotopic Optimization for Autonomous Vehicle Maneuvering

Optimization of vehicle maneuvers using dynamic models in constrained spaces is challenging. Homotopic optimization, which has shown success for vehicle maneuvers with kinematic models, is studied in the case where the vehicle model is governed by dynamic equations considering road-tire interactions. This method involves a sequence of optimization problems that start with a large free space. By iteration, this space is progressively made smaller until the target problem is reached. The method uses a homotopy index to iterate the sequence of optimizations, and the method is verified by solving challenging maneuvering problems with different road surfaces and entry velocities using a double-track vehicle dynamics model. The main takeaway is that homotopic optimization is also efficient for dynamic vehicle models at the limit of road-tire friction, and it demonstrates capabilities in solving demanding maneuvering problems compared with alternative methods like stepwise initialization and driver model-based initialization.