Mechanics-based control of underactuated 3D robotic walking: Dynamic gait generation under torque constraints

This paper presents a novel method of stabilizing hybrid models of torque-constrained, underactuated walking robots - without using nonlinear gait optimization - by leveraging properties of the mechanics of the robot. At its core, the controller stabilizes the transfer of angular momentum from one leg to the next through continuous-time control coupled with hybrid system models that capture impacts that occur at foot strike. In particular, conservation of angular momentum at impact allows for computation of the exact transfer of momentum as a function of the robot's step length and vertical center of mass velocity just prior to foot impact. This motivates the construction of continuous-time reference trajectories for the robot's step length and vertical center of mass with endpoints corresponding to a desired transfer of angular momentum. Stabilization to these trajectories results in stable walking, as indicated by numeric Poincaré analysis. The controller is implemented in simulation of a five-link, underactuated 3D robot via Model Predictive Control which provides a means of achieving walking under non-trivial actuation limits.