Piecewise-affine (PWA) systems are widely used for modeling and control of robotics problems including modeling contact dynamics. A common approach is to encode the control problem of the PWA system as a Mixed-Integer Convex Program (MICP), which can be solved by general-purpose off-the-shelf MICP solvers. To mitigate the scalability challenge of solving these MICP problems, existing work focuses on devising efficient and strong formulations of the problems, while less effort has been spent on exploiting their specific structure to develop specialized solvers. The latter is the theme of our work. We focus on efficiently handling one-hot constraints, which are particularly relevant when encoding PWA dynamics. We have implemented our techniques in a tool, Soy, which organically integrates logical reasoning, arithmetic reasoning, and stochastic local search. For a set of PWA control benchmarks, Soy solves more problems, faster, than two state-of-the-art MICP solvers.

翻译：分段仿射（PWA）系统广泛应用于机器人问题的建模与控制，包括接触动力学建模。常见方法是将PWA系统的控制问题编码为混合整数凸规划（MICP），并通过通用现成MICP求解器进行求解。为缓解求解此类MICP问题的可扩展性挑战，现有研究侧重于设计高效且强健的问题形式化表达，而较少关注利用其特定结构开发专用求解器。后者正是本文的研究主题。我们重点研究了高效处理one-hot约束的方法——该约束在编码PWA动力学中尤为关键。我们已将所提出的技术集成至工具Soy中，该工具有机融合了逻辑推理、算术推理与随机局部搜索。在多个PWA控制基准测试中，相较于两款最先进的MICP求解器，Soy在更短时间内解决了更多问题。