Control of a Planar Underactuated Biped on a Complete Walking Cycle

Abstract

We address the problem of stabilizing a planar biped robot on a complete walking cycle. Our approach is based on singling out the three fundamental phases of motion of a biped : single and double-support, separated (sequentially) by an impact "instantaneous" phase. We propose control laws to drive the robot for a finite time during each phase, while ensuring certain robustness vis-a-vis the impacts which are treated as external perturbations. We also provide some simulation results.

Dynamic Surface Control of Uncertain Nonlinear Systems

“…To prove stable walking of the nonlinear controller based on biped robot models, the Poincaré method was introduced to analyze the closed-loop system of the biped model formulated as a nonlinear system with impulse effects [35]. Another approach was to use a Lyapunov function candidate and to show the existence of the controller gains to guarantee the stability under appropriate assumptions [17]. However, due to the mathematical complexity of the dynamic model, none of these control approaches has produced a closed-loop system with provable stability properties.…”

“…A double-leg support phase (DSP) model has been usually neglected due to its complexity (see [101] and references therein). In [17,63], a three-phase model including SSP, DSP, and double impact phase (DIP) models was proposed and it was claimed that DSP is necessary to realize the stable motion over a wide range of walking speeds (see Fig. 9.1).…”

“…The equation of motion for DSP with two holonomic constraints is written as follows [17,63]: D(θ)θ + H (θ,θ)θ + G(θ ) = J T (θ )λ + T θ , (9.2a)…”

Stability analysis and time-varying walking control for an under-actuated planar biped robot

“…There exist various studies about the walking control of the under-actuated mechanical systems [1][2][3][4][5]. Most controllers of these systems are based on tracking reference motions.…”

Differentially Flat Design of Bipeds Ensuring Limit-Cycles

“…In between these two extremes is the class of underactuated bipeds. Previous works on under-actuated bipeds include [5], [6], [7], [8]. The most critical requirement for any system to be used as a biped is existence of limit cycles.…”