Autonomous vehicle (AV) motion planning problems often involve non-convex constraints, which present a major barrier to applying model predictive control (MPC) in real time on embedded hardware. This paper presents an approach for efficiently solving mixed-integer MPC motion planning problems using a hybrid zonotope representation of the obstacle-free space. The MPC optimization problem is formulated as a multi-stage mixed-integer quadratic program (MIQP) using a hybrid zonotope representation of the non-convex constraints. Risk-aware planning is supported by assigning costs to different regions of the obstacle-free space within the MPC cost function. A multi-stage MIQP solver is presented that exploits the structure of the hybrid zonotope constraints. For some hybrid zonotope representations, it is shown that the convex relaxation is tight, i.e., equal to the convex hull. In conjunction with logical constraints derived from the AV motion planning context, this property is leveraged to generate tight quadratic program (QP) sub-problems within a branch-and-bound mixed-integer solver. The hybrid zonotope structure is further leveraged to reduce the number of matrix factorizations that need to be computed within the QP sub-problems. Simulation studies are presented for obstacle-avoidance and risk-aware motion planning problems using polytopic maps and occupancy grids. In most cases, the proposed solver finds the optimal solution an order of magnitude faster than a state-of-the-art commercial solver. Processor-in-the-loop studies demonstrate the utility of the solver for real-time implementations on embedded hardware.

翻译：自动驾驶车辆运动规划问题常涉及非凸约束，这成为在嵌入式硬件上实时应用模型预测控制的主要障碍。本文提出一种利用无障碍空间的混合zonotope表示来高效求解混合整数MPC运动规划问题的方法。通过采用非凸约束的混合zonotope表示，将MPC优化问题构建为多阶段混合整数二次规划问题。通过在MPC代价函数中为无障碍空间的不同区域分配代价，实现了风险感知规划功能。本文提出了一种多阶段MIQP求解器，该求解器充分利用混合zonotope约束的结构特性。研究证明，对于特定混合zonotope表示形式，其凸松弛具有紧致性，即等于凸包。结合自动驾驶运动规划场景衍生的逻辑约束，该性质被用于在分支定界混合整数求解器中生成紧致的二次规划子问题。通过进一步利用混合zonotope结构，有效减少了QP子问题中需要计算的矩阵分解次数。研究通过多面体地图和占据栅格地图进行了避障与风险感知运动规划的仿真实验。在多数案例中，所提求解器获得最优解的速度比当前最先进的商业求解器快一个数量级。处理器在环实验验证了该求解器在嵌入式硬件上实时实施的可行性。