Efficient Computation of Whole-Body Control Utilizing Simplified Whole-Body Dynamics via Centroidal Dynamics

TL;DR

This work tackles the computational burden of whole-body control (WBC) for humanoid robots with many DOF by introducing a reduced-dimension dynamics framework that partitions the kinematic chain into constrained and unconstrained parts, with the unconstrained chain represented via centroidal dynamics. The reduced dynamics are integrated into a two-stage Lexicographic Quadratic Program (LQP): LQP1 solves in the reduced space while LQP2 handles the unconstrained chain, using a centroidal-space equality constraint to decouple the stages. The approach leverages centroidal momentum concepts and projection-based dynamics to lower the effective DOF from n to n_cc + 6, achieving large computation-time savings (up to 67.7% in DOF-heavy scenarios) while maintaining comparable tracking performance. Evaluations on a 33-DOF TOCABI platform in MuJoCo with off-the-shelf solvers demonstrate robust speedups across single and double support walking tasks, suggesting practical benefits for real-time humanoid WBC and scalability with DOF. The method’s reliance on standard solvers and its modular two-part structure also point to easy integration with higher-level planners and broader WBC formulations.

Abstract

In this study, we present a novel method for enhancing the computational efficiency of whole-body control for humanoid robots, a challenge accentuated by their high degrees of freedom. The reduced-dimension rigid body dynamics of a floating base robot is constructed by segmenting its kinematic chain into constrained and unconstrained chains, simplifying the dynamics of the unconstrained chain through the centroidal dynamics. The proposed dynamics model is possible to be applied to whole-body control methods, allowing the problem to be divided into two parts for more efficient computation. The efficiency of the framework is demonstrated by comparative experiments in simulations. The calculation results demonstrate a significant reduction in processing time, highlighting an improvement over the times reported in current methodologies. Additionally, the results also shows the computational efficiency increases as the degrees of freedom of robot model increases.

Figures (5)

• Figure 1: Simplified representation of the robot's links, joints, illustrating the categorization into virtual chain, constraint chain, and unconstrained chain.
• Figure 2: Composition comparison between the full model and the reduced-dimension model. $n_{vc}$, $n_{cc}$, $n_{uc}$ represent the DOF of the virtual chain, constraint chain, and unconstrained chain, respectively.
• Figure 3: The algorithm flow chart of the proposed method.
• Figure 4: Tracking errors of COM and end-effector positions using conventional and proposed methods in the double support.
• Figure 5: Average computation time comparison by DOF of the robot, and the relative computation time percentage. The computation time of proposed method is the sum of LQP 1 and LQP 2.