Efficient Solution of Mixed-Integer MPC Problems for Obstacle Avoidance Using Hybrid Zonotopes

Model predictive control (MPC) is a powerful approach for autonomous vehicle motion planning. MPC can account for both the vehicle dynamics and obstacle avoidance constraints by iteratively solving constrained optimization problems. Due to the non-convexities associated with obstacle avoidance constraints, these optimization problems often take the form of mixed-integer programs, which are challenging to solve online in embedded applications. This paper presents a mixed-integer quadratic program (MIQP) solution strategy for obstacle avoidance MPC formulations based on a hybrid zonotope set representation of the obstacle avoidance constraints. The structure of the hybrid zonotope constraints is exploited within both a branch-and-bound mixed-integer solver and an interior point method QP solver. For applications such as automated driving, where the obstacle-free space can be represented using an occupancy grid, the QP solution time is not strongly affected by the complexity of the obstacle map. For the examples considered in this paper, using 5 and 10 step MPC horizons, the proposed MIQP solver with hybrid zonotope constraints found the optimal solution 2-6 times faster on average than general-purpose commercial solvers and up to 13 times faster than MIQP formulations using H-rep constraints.