Invariant Extended Kalman Filtering for Hybrid Models of Bipedal Robot Walking

This paper introduces a hybrid invariant extended Kalman filtering (HInEKF) method for a class of nonlinear hybrid dynamical systems with state-triggered jumps and group affine continuous-time subsystems. The method is derived based on the provable extension of the existing InEKF design for group affine systems without state-triggered jumps. Sufficient stability conditions are provided to guarantee the asymptotic error convergence for the hybrid system. Furthermore, the complete characterization of nonlinear jump maps whose associated error jump maps are identity on the matrix Lie group is provided along with the simplified observer design for such systems. Simulation results of bipedal walking on a dynamic rigid surface (i.e., rigid surfaces that move in the inertial frame) validate the theoretical results.