  This paper studies capturability and push recovery for quadrupedal
locomotion. Despite the rich literature on capturability analysis and push
recovery control for legged robots, existing tools are developed mainly for
bipeds or humanoids. Distinct quadrupedal features such as point contacts and
multiple swinging legs prevent direct application of these methods. To address
this gap, we propose a switched systems model for quadruped dynamics, and
instantiate the abstract viability concept for quadrupedal locomotion with a
time-based gait. Capturability is characterized through a novel specification
of dynamically balanced states that addresses the time-varying nature of
quadrupedal locomotion and balance. A linear inverted pendulum (LIP) model is
adopted to demonstrate the theory and show how the newly developed quadrupedal
capturability can be used in motion planning for quadrupedal push recovery. We
formulate and solve an explicit model predictive control (EMPC) problem whose
optimal solution fully characterizes quadrupedal capturability with the LIP.
Given this analysis, an optimization-based planning scheme is devised for
determining footsteps and center of mass references during push recovery. To
validate the effectiveness of the overall framework, we conduct numerous
simulation and hardware experiments. Simulation results illustrate the
necessity of considering dynamic balance for quadrupedal capturability, and the
significant improvement in disturbance rejection with the proposed strategy.
Experimental validations on a replica of the Mini Cheetah quadruped demonstrate
an up to 100% improvement as compared with state-of-the-art.
