Balance Control Using Both ZMP and COM Height Variations: A Convex Boundedness Approach

Abstract

Developments for 3D control of the center of mass (CoM) of biped robots are currently located in two local minima: on the one hand, methods that allow CoM height variations but only work in the 2D sagittal plane; on the other hand, nonconvex direct transcriptions of centroidal dynamics that are delicate to handle. This paper presents an alternative that controls the CoM in 3D via an indirect transcription that is both low-dimensional and solvable fast enough for realtime control. The key to this development is the notion of boundedness condition, which quantifies the capturability of 3D CoM trajectories.

Stair Climbing Stabilization of the HRP-4 Humanoid Robot using Whole-body Admittance Control

“…We mitigated this by delaying CoM lift to the end of the step, unfortunately thus increasing knee torques as well. A better way to improve this in future work will be to switch to a pattern generation method taking height variations into account [19], [21], [33].…”

“…Its contact wrench is characterized by the position z of the ZMP on the contact surface. These simplifications come at the expense of balance recovery strategies: the IPM sacrifices the hip strategy [17] while the LIPM sacrifices the height-variation strategy [18], [19]. Accordingly, the dimension of the contact wrench decreases from six to three in the IPM and two in the LIPM.…”

Capturability-Based Pattern Generation for Walking With Variable Height

“…To break down how much of the speed-up is due to the problem reformulation and how much is due to our custom least squares implementation, we also test our SQP method 8 We only report averages for IPOPT computation times as they lie on a different scale. These averages are higher than those reported in [11] because we evaluate both feasible and unfeasible problems (for reasons made clear in the next section), while all random initial conditions in [11] were zerostep capturable. For n = 10 and projecting performance statistics on feasible problems only, IPOPT's computation times decrease to 1600 ± 790 µs.…”

“…Previous studies [8], [9], [10] focused on its balance control for planar motions (sagittal and vertical only). In a preliminary version of this work [11], we extended the analysis from 2D to 3D balance control. In the present work, we bridge the gap from balancing to walking.…”

DCM-Based Gait Generation for Walking on Moving Support Surfaces

“…Unlike other methods (e.g. [13], [22], [23]) that use a time-varying virtual pendulum length and thus parameter b, in our work the constant average CoM height ∆z vrp (corresponding to a time constant b) leads to an equivalent usage of eCMP e and VRP v for both planning and control 7 . Any corresponding eCMP/VRP points and trajectories are simply offset vertically by ∆z vrp .…”