Hybrid systems are prevalent in robotics. However, ensuring the stability of hybrid systems is challenging due to sophisticated continuous and discrete dynamics. A system with all its system modes stable can still be unstable. Hence special treatments are required at mode switchings to stabilize the system. In this work, we propose a hierarchical, neural network (NN)-based method to control general hybrid systems. For each system mode, we first learn an NN Lyapunov function and an NN controller to ensure the states within the region of attraction (RoA) can be stabilized. Then an RoA NN estimator is learned across different modes. Upon mode switching, we propose a differentiable planner to ensure the states after switching can land in next mode's RoA, hence stabilizing the hybrid system. We provide novel theoretical stability guarantees and conduct experiments in car tracking control, pogobot navigation, and bipedal walker locomotion. Our method only requires 0.25X of the training time as needed by other learning-based methods. With low running time (10-50X faster than model predictive control (MPC)), our controller achieves a higher stability/success rate over other baselines such as MPC, reinforcement learning (RL), common Lyapunov methods (CLF), linear quadratic regulator (LQR), quadratic programming (QP) and Hamilton-Jacobian-based methods (HJB). The project page is on https://mit-realm.github.io/hybrid-clf.

翻译：混合系统在机器人领域普遍存在。然而，由于复杂的连续与离散动力学特性，确保混合系统的稳定性极具挑战性。即使所有系统模态均稳定，整体系统仍可能失稳。因此，在模态切换时需要特殊处理以稳定系统。本文提出一种基于分层神经网络（NN）的方法来控制通用混合系统。针对每个系统模态，我们首先学习一个NN李雅普诺夫函数和一个NN控制器，以确保位于吸引域（RoA）内的状态能够稳定。随后在不同模态间学习一个RoA-NN估计器。在模态切换时，我们提出一种可微规划器，确保切换后的状态能够落入下一模态的RoA中，从而稳定混合系统。我们提供了新颖的理论稳定性保证，并在车辆跟踪控制、pogobot导航和双足步行器运动控制中进行了实验验证。我们的方法仅需其他学习方法25%的训练时间。在低运行时间（比模型预测控制（MPC）快10-50倍）条件下，我们的控制器相比其他基线方法（包括MPC、强化学习（RL）、公共李雅普诺夫方法（CLF）、线性二次型调节器（LQR）、二次规划（QP）和基于哈密顿-雅可比的方法（HJB））实现了更高的稳定性/成功率。项目页面位于https://mit-realm.github.io/hybrid-clf。