Meeting Abstract

86.6  Tuesday, Jan. 6  How Center-of-Mass Dynamics of Hexapedal Locomotion Collapses to a Single Leg Template Model SEIPEL, Justin E*; FULL, Robert J; Univ. of California, Berkeley jseipel@berkeley.edu

Many running animals and some robots produce similar center-of-mass motions and force patterns, like a pogo-stick. We found that the simplest pogo-stick template models explain steady-state motion, but identified a need to explain the robust response to perturbations common in animal locomotion and compliant-legged robots. Spring-Loaded Inverted Pendulum models driven by a Clock with the capability of Torque generation at the hip (CT-SLIP) appear sufficient to explain perturbed center-of-mass behavior in cockroaches and the hexapedal robot, RHex. Using formal mathematical reduction and supporting experimental data, we show how the dynamics of a cockroach’s tripod support are effectively reduced to a single virtual leg CT-SLIP model. A sagittal plane model of the tripod support of the cockroach is formalized as a set of Euler-Lagrange equations of motion. Similarly, equations are found for the single leg CT-SLIP. We analyzed the tripod and single-leg systems local responses to perturbations along identical steady-gaits by calculating respective Jacobians. We found that despite apparent structural differences in the equations of motion, the two systems have similar dynamic responses to perturbations. This result shows how tripod-stance dynamics can be represented by a single virtual leg and offers theoretical proof of effective simplification or collapse of dimensions in complex systems. This approach demonstrates how such templates could lead to effective strategies that simplify control. This effort contributes to the methodology of "templates and anchors," for modeling complex systems including animals, robots, and other devices, as well as enabling design of both controllers and whole systems.