Hybrid Systems Neural Control with Region-of-Attraction Planner
This work addresses the stability problem in hybrid systems for robotics applications, offering a novel method that improves efficiency and performance over existing baselines.
The authors tackled the challenge of stabilizing hybrid systems with complex continuous and discrete dynamics by proposing a hierarchical neural network-based method that learns Lyapunov functions and controllers for each mode, along with a differentiable planner for mode switching. Their approach achieved a 0.25X reduction in training time compared to other learning-based methods, with 10-50X faster running time than MPC, and higher stability/success rates across benchmarks like car tracking and bipedal walker locomotion.
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.