Energy and Phased Based Movement Recovery
2019 SIAM Conference on Dynamical Systems, 2019
Abstract
Retaining the ability to move despite body damage is a feature legged animals display - through injury, animals often compensate. Legged robots would be advantaged if they also had the ability to preserve a gait through damage, where we take a gait to be an exponentially stable limit cycle for a mechanical Lagrangian with periodic inputs. Given an prior gait, we wish to preserve that limit cycle by finding a control input that compensates for changes in the Lagrangian. We employ asymptotic phase, a cyclic coordinate, to compare the evolution of the original and new systems in a geometric way. To avoid models, we employ optimization. The complex dynamics of legged robots makes this optimization challenging. We enrich the optimization problem with necessary constraints that will improve convergence rate. For mechanical systems, the Lagrangian is determined via energy. We require that the phase evolution of mechanical power is preserved between the two systems, as well as that the new flow continues to be a semi-conjugacy with the original phase map. We see this practical, as energy is a physical quantity that can be found from data. We perform recovery on two systems. One, in simulation on a CT-SLIP, we recover a periodic motion by matching the phasing of kinetic energy. Two, we performed the optimization experimentally on a hexapod robot with springy legs. We see that the optimization produces a similar gait
BibTeX
@conference{Council-2019-SIAM,
author = {Council, G and Revzen, Shai},
title = {Energy and Phased Based Movement Recovery},
booktitle = {2019 SIAM Conference on Dynamical Systems},
year = {2019},
address = {Snowbird, UT},
organization = {SIAM},
url = {https://meetings.siam.org/sess/dsp_talk.cfm?p=99657}
}