Towards Planning and Control of Hybrid Systems with Limit Cycle using LQR Trees
This work addresses the challenge of controlling hybrid dynamical systems, such as robotic walkers, by providing a multi-query recovery policy that avoids discretization, though it is incremental as it builds on the existing LQR Tree method.
The authors tackled the problem of planning and control for hybrid systems with limit cycles by extending the LQR Tree algorithm to handle continuous control sets and discrete transitions, demonstrating successful stabilization of a compass gait model's walking limit cycle from random initial conditions with perturbations and noise.
We present a multi-query recovery policy for a hybrid system with goal limit cycle. The sample trajectories and the hybrid limit cycle of the dynamical system are stabilized using locally valid Time Varying LQR controller policies which probabilistically cover a bounded region of state space. The original LQR Tree algorithm builds such trees for non-linear static and non-hybrid systems like a pendulum or a cart-pole. We leverage the idea of LQR trees to plan with a continuous control set, unlike methods that rely on discretization like dynamic programming to plan for hybrid dynamical systems where it is hard to capture the exact event of discrete transition. We test the algorithm on a compass gait model by stabilizing a dynamic walking hybrid limit cycle with point foot contact from random initial conditions. We show results from the simulation where the system comes back to a stable behavior with initial position or velocity perturbation and noise.