标题： 路径积分控制用于混合动态系统 显示英文标题

标题： Path Integral Control for Hybrid Dynamical Systems

摘要： 本文介绍了一种求解混合动态系统在不确定条件下最优控制问题的新方法。 与环境接触的机器人系统可以建模为混合系统。 在扰动下的混合系统控制器设计由于不连续的跳跃动力学、模式变化导致的状态维数不一致以及由噪声引起的跳跃时间和状态的变化而变得复杂。 我们将该问题表述为具有混合跃迁约束的随机控制问题，并提出混合路径积分（H-PI）框架以获得最优控制器。 尽管在随机路径样本中存在随机模式变化，我们证明了具有不同漂移项的混合路径分布之间的比率仍类似于平滑路径分布。 然后我们表明可以通过评估具有混合约束的路径积分来获得最优控制器。 引入了用于路径分布的重要性采样，以减少路径积分评估的方差，在此过程中我们利用最近开发的混合迭代线性二次调节器（H-iLQR）控制器来诱导具有低方差的混合路径分布提议。 所提出的方法通过各种混合系统的数值实验和广泛的消融研究进行了验证。 所有采样过程均在图形处理单元（GPU）上并行执行。 显示英文摘要

摘要： This work introduces a novel paradigm for solving optimal control problems for hybrid dynamical systems under uncertainties. Robotic systems having contact with the environment can be modeled as hybrid systems. Controller design for hybrid systems under disturbances is complicated by the discontinuous jump dynamics, mode changes with inconsistent state dimensions, and variations in jumping timing and states caused by noise. We formulate this problem into a stochastic control problem with hybrid transition constraints and propose the Hybrid Path Integral (H-PI) framework to obtain the optimal controller. Despite random mode changes across stochastic path samples, we show that the ratio between hybrid path distributions with varying drift terms remains analogous to the smooth path distributions. We then show that the optimal controller can be obtained by evaluating a path integral with hybrid constraints. Importance sampling for path distributions with hybrid dynamics constraints is introduced to reduce the variance of the path integral evaluation, where we leverage the recently developed Hybrid iterative-Linear-Quadratic-Regulator (H-iLQR) controller to induce a hybrid path distribution proposal with low variance. The proposed method is validated through numerical experiments on various hybrid systems and extensive ablation studies. All the sampling processes are conducted in parallel on a Graphics Processing Unit (GPU).