Title: Towards Planning and Control of Hybrid Systems with Limit Cycle using LQR Trees,
Abstract: 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.