Stability and Control of a Pacing Quadruped Using Stabilizing Switching Design.

In this paper we present a method for control and stabilizing a pacing quadruped robot using state feedback switching. In the pacing gait, a quadruped cycles between the left and right pairs of legs to achieve locomotion. This results in two discrete stance configurations, each being unstable. The quadruped can achieve dynamic stability by switching between these stances in an appropriate manner. We model our system using two sets of non-linear dynamical equations which we have the control of switching between actively. In order to stabilize our system, we propose a state feedback switching law based on the linearized models of our system for each set of equations. Using this switching law, we are able to stabilize the robot in the roll direction. This, combined with the passive stability achieved with the design of the robot's legs, results in a stable pacing gait. The performance of the proposed controller is evaluated on a complete dynamical model in simulation and stability is verified using a Poincaré map.