Embedded optimization-based planning for hybrid systems is challenging due to the use of mixed-integer programming, which is computationally intensive and often sensitive to the specific numerical formulation. To address that challenge, this article proposes a framework for motion planning of hybrid systems that pairs hybrid zonotopes - an advanced set representation - with a new alternating direction method of multipliers (ADMM) mixed-integer programming heuristic. A general treatment of piecewise affine (PWA) system reachability analysis using hybrid zonotopes is presented and extended to formulate optimal planning problems. Sets produced using the proposed identities have lower memory complexity and tighter convex relaxations than equivalent sets produced from preexisting techniques. The proposed ADMM heuristic makes efficient use of the hybrid zonotope structure. For planning problems formulated as hybrid zonotopes, the proposed heuristic achieves improved convergence rates as compared to state-of-the-art mixed-integer programming heuristics. The proposed methods for hybrid system planning on embedded hardware are experimentally applied in a combined behavior and motion planning scenario for autonomous driving.

翻译：基于优化的嵌入式混合系统规划面临挑战，主要源于混合整数规划的计算复杂性及其对特定数值公式的敏感性。为应对这一挑战，本文提出一种混合系统运动规划框架，该框架将混合Zonotope（一种先进的集合表示方法）与新型交替方向乘子法（ADMM）混合整数规划启发式算法相结合。本文系统阐述了使用混合Zonotope进行分段仿射系统可达性分析的一般方法，并将其扩展至最优规划问题的建模。相较于现有技术生成的等价集合，基于所提恒等式生成的集合具有更低的内存复杂度与更紧的凸松弛特性。所提出的ADMM启发式算法能高效利用混合Zonotope的结构特性。对于以混合Zonotope形式建模的规划问题，该启发式算法相比当前最先进的混合整数规划启发式算法实现了更优的收敛速率。所提出的嵌入式硬件混合系统规划方法，已在自动驾驶的行为与运动联合规划场景中进行了实验验证。