Geometrically Modulable Gait Design for Quadrupeds

TL;DR

This paper introduces a geometric mechanics-based framework for designing and modulating simple two-beat gaits in quadruped robots, enabling control of speed and direction with minimal computational resources.

Contribution

It develops a modular, geometric approach to gait design that allows continuous modulation of locomotion parameters for quadrupedal robots with limited onboard computation.

Findings

Designed decoupled subgaits for quadrupeds using geometric tools.

Demonstrated control of speed and steering through modulation of gait parameters.

Provided a framework for open-loop gait planning with resource-constrained robots.

Abstract

Miniature-legged robots are constrained by their onboard computation and control, thus motivating the need for simple, first-principles-based geometric models that connect \emph{periodic actuation or gaits} (a universal robot control paradigm) to the induced average locomotion. In this paper, we develop a \emph{modulable two-beat gait design framework} for sprawled planar quadrupedal systems under the no-slip using tools from geometric mechanics. We reduce standard two-beat gaits into unique subgaits in mutually exclusive shape subspaces. Subgaits are characterized by a locomotive stance phase when limbs are in ground contact and a non-locomotive, instantaneous swing phase where the limbs are reset without contact. During the stance phase, the contacting limbs form a four-bar mechanism. To analyze the ensuing locomotion, we develop the following tools: (a) a vector field to generate nonslip actuation, (b) the kinematics of a four-bar mechanism as a local connection, and (c) stratified panels that combine the kinematics and constrained actuation to encode the net change in the system's position generated by a stance-swing subgait cycle. Decoupled subgaits are then designed independently using flows on the shape-change basis and are combined with appropriate phasing to produce a two-beat gait. Further, we introduce ``scaling" and ``sliding" control inputs to continuously modulate the global trajectories of the quadrupedal system in gait time through which we demonstrate cycle-average speed, direction, and steering control using the control inputs. Thus, this framework has the potential to create uncomplicated open-loop gait plans or gain schedules for robots with limited resources, bringing them closer to achieving autonomous control.