George Council

James Zhu, Nathan J. Kong, George Council et al.

Many controllers for legged robotic systems leverage open- or closed-loop control at discrete hybrid events to enhance stability. These controllers appear in several well studied phenomena such as the Raibert stepping controller, paddle juggling and swing leg retraction. This work introduces hybrid event shaping (HES): a generalized method for analyzing and producing stable hybrid event controllers. HES utilizes the saltation matrix, which gives a closed-form equation for the effect that hybrid events have on stability. We also introduce shape parameters, which are higher order terms that can be tuned completely independently from the system dynamics to promote stability. Optimization methods are used to produce values of these parameters that optimize a stability measure. Hybrid event shaping captures previously developed control methods while also producing new optimally stable trajectories without the need for continuous-domain feedback.

George Council, Shai Revzen

If robots are ever to achieve autonomous motion comparable to that exhibited by animals, they must acquire the ability to quickly recover motor behaviors when damage, malfunction, or environmental conditions compromise their ability to move effectively. We present an approach which allowed our robots and simulated robots to recover high-degree of freedom motor behaviors within a few dozen attempts. Our approach employs a behavior specification expressing the desired behaviors in terms as rank ordered differential constraints. We show how factoring these constraints through an encoding template produces a recipe for generalizing a previously optimized behavior to new circumstances in a form amenable to rapid learning. We further illustrate that adequate constraints are generically easy to determine in data-driven contexts. As illustration, we demonstrate our recovery approach on a physical 7 DOF hexapod robot, as well as a simulation of a 6 DOF 2D kinematic mechanism. In both cases we recovered a behavior functionally indistinguishable from the previously optimized motion.