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:混合系统在机器人技术中应用广泛。然而,由于其复杂的连续和离散动态,在确保混合系统的稳定性方面具有挑战性。即使一个系统的所有系统模式都是稳定的,它仍然可能不稳定,在模式转换时需要特殊处理来稳定系统。在本研究中,我们提出了一种基于神经网络(NN)的分层方法来控制一般混合系统。针对每个系统模式,我们首先学习一个NN李雅普诺夫函数和一个控制器,以确保可以稳定处于吸引子区域(RoA)内的状态。然后学习一个RoA NN估计器来跨越不同模式进行估计。在模式切换时,提出了一个可微分的规划器,以确保切换后的状态可以落在下一个模式的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,并在汽车跟踪控制,pogobot导航和双足行走器运动等领域进行了实验。我们的方法只需要其他基于学习的方法所需的0.25倍的训练时间。在运行时间较短(比模型预测控制(MPC)快10-50倍)的情况下,我们的控制器在其他基线(如MPC、强化学习(RL)、常见李雅普诺夫方法(CLF)、线性二次调节器(LQR)、二次规划(QP)和基于哈密尔顿-雅各比方法(HJB)的控制器)上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。