Mixed-integer optimization-based planning for autonomous racing with obstacles and rewards

Trajectory planning with the consideration of obstacles is a classical task in autonomous driving and robotics applications. This paper introduces a novel solution approach for the subclass of autonomous racing problems which is additionally capable of dealing with reward objects. This special type of objects is representing particular regions in state space, whose optional reaching is somehow beneficial (e.g. results in bonus points during a race). First, a homotopy class is selected which represents the left/right and catch/ignore decisions related to obstacle avoidance and reward collection, respectively. For this purpose, a linear mixed-integer problem is posed such that an approximated combinatorial problem is solved and repetitive switching decisions between solver calls are avoided. Secondly, an optimal control problem (OCP) based on a single-track vehicle model is solved within this homotopy class. In the corresponding nonlinear program, homotopy iterations are performed on the race track boundaries which correspond to the previously chosen homotopy class. This leads to an improved convergence of the solver compared to the direct approach. The mixed-integer method's effectiveness is demonstrated within a real-world test scenario during the autonomous racing competition Roborace. Furthermore, its combination with the OCP as well as the performance gain resulting from the homotopy iterations are shown in simulation.