Stabilization of Energy-Conserving Gaits for Point-Foot Planar Bipeds

Abstract

The problem of designing and stabilizing impact-free, energy-conserving gaits is considered for underactuated, point-foot planar bipeds. Virtual holonomic constraints are used to design energy-conserving gaits. A desired gait corresponds to a periodic hybrid orbit and is stabilized using the Impulse Controlled Poincaré Map approach. Numerical simulations for the case of a five-link biped demonstrate convergence to a desired gait from arbitrary initial conditions.

Figures (6)

• Figure 1: An $n$-link point-foot planar biped.
• Figure 2: Hybrid dynamics of biped over a step with a single impulsive actuation during the swing phase. The different components are: $1 $: continuous-time dynamics, $2 $: jump in states due to impulsive actuation, $3 $: jump in states due to foot-ground in interaction, and $4 $: change of states due to coordinate relabelling.
• Figure 3: Hybrid dynamics of biped over a step for an energy-conserving gait; it is a simpler version of the dynamics shown in Fig.\ref{['Fig2']}. The different components are: $1 $: continuous-time dynamics, $4 $: change of states due to coordinate relabelling.
• Figure 4: Evolution of system trajectory during an energy-conserving gait.
• Figure 5: Schematic of the ICPM approach to orbital stabilization of an energy-conserving gait. The desired orbit is shown in red. The different components of the hybrid dynamics, namely, $1 $, $2 $, $3 $ and $4 $ are described by \ref{['eq13']}.

Theorems & Definitions (4)

• Remark 1
• Remark 2
• Remark 3
• Remark 4