Centroidal Trajectory Generation and Stabilization based on Preview Control for Humanoid Multi-contact Motion

TL;DR

This work tackles the challenge of enabling stable, dynamic multi-contact motion for humanoid robots with efficient real-time planning. It introduces centroidal online trajectory generation based on preview control, paired with a stabilization scheme that uses the online-derived resultant wrench as a feedforward element and post-hoc wrench projection to satisfy contact constraints. The method achieves high update rates (around $1\ \mathrm{ms}$) for a horizon of $2\ \mathrm{s}$ (400 samples) and demonstrates stable bipedal walking, hand-supported locomotion, and ladder-like multi-contact tasks in simulation, notably with varied contact transitions and friction. By connecting centroidal preview control to DCM-based approaches and validating fast computation alongside accurate wrench distribution, the paper offers a practically impactful route toward real-time, versatile humanoid multi-contact control in complex environments.

Abstract

Multi-contact motion is important for humanoid robots to work in various environments. We propose a centroidal online trajectory generation and stabilization control for humanoid dynamic multi-contact motion. The proposed method features the drastic reduction of the computational cost by using preview control instead of the conventional model predictive control that considers the constraints of all sample times. By combining preview control with centroidal state feedback for robustness to disturbances and wrench distribution for satisfying contact constraints, we show that the robot can stably perform a variety of multi-contact motions through simulation experiments.

Figures (8)

• Figure 1: Overall components of the control system for humanoid multi-contact motion.
• Figure 2: Contact constraints in wrench distribution.
• Figure 3: Results of bipedal walking. (A) The reference, planned, and actual CoMs correspond to $\bm{r}^{\mathrm{ref}}$, $\bm{r}^{\mathrm{p}}$, and $\bm{r}^{\mathrm{a}}$ in Fig. \ref{['fig:system']}, respectively. (B) The planned, desired, and actual ZMPs are calculated from $\bm{\bar{w}}^{\mathrm{p}^\prime}$, $\bm{w}^{\mathrm{d}}_{\mathrm{i}}$, and $\bm{w}_{\mathrm{i}}^{\mathrm{a}}$ in Fig. \ref{['fig:system']}, respectively. The gray shaded region indicates the support region. The wrench distribution uses contact polygon vertices with inner margins, and the black dashed lines indicate their boundaries.
• Figure 4: Simulation of multi-contact motion. The friction coefficient is set to 0.6 for all environments. (A) Stepping on scaffold boards with 25 degree incline while keeping the hand on a vertical wall. (B) Climbing four steps of 150 mm height with handrails. (C) Climbing a vertical ladder with 200 mm steps. The depth of the ladder rungs is 75 mm, which is less than half the depth of the robot's sole. (D) With both hands on the support surfaces at the height of 500 mm, moving forward by swinging both feet simultaneously. (E) Balancing on the floors and walls, which move periodically in translation and rotation with an amplitude of 20 mm and 2 degrees. Damping control allows feet and hands to adapt to floor and wall movements.
• Figure 5: Results of walking with hands on the wall in Fig. \ref{['fig:exp-multi-contact']} (A). The CoM and resultant wrench are represented in the world coordinates, and the contact forces are represented in the coordinates at each limb end (see Fig. \ref{['fig:wrench-distrib']}). (B) The reference, planned, desired, and actual resultant forces are calculated from $\bar{f}^{\mathrm{ref}}_*$, $\bm{\bar{w}}^{\mathrm{p}^\prime}$, $\bm{w}^{\mathrm{d}}_{\mathrm{i}}$, and $\bm{w}^{\mathrm{a}}_{\mathrm{i}}$, respectively. (C) The desired and actual forces correspond to $\bm{w}^{\mathrm{d}}_{\mathrm{i}}$ and $\bm{w}^{\mathrm{a}}_{\mathrm{i}}$, respectively. (D) Contact forces of the left hand (1-6 s) and right hand (6-10 s).