Whole-Body Control Framework for Humanoid Robots with Heavy Limbs: A Model-Based Approach

TL;DR

Problem: heavy limbs create base-limb coupling that destabilizes humanoid balance during dynamic motion and on irregular terrain. Approach: a model-based whole-body control framework that couples a kino-dynamics planner (MPC with centroidal dynamics) and a HQP-based hierarchical optimization to generate reference motions and contact forces while accounting for mass and inertia shifts from limb motion. Contributions: (i) a simplified planner enabling real-time MPC, (ii) physical-consistency enforcement via full-dynamics in the tracker, (iii) explicit collision and friction constraints with an RBF-based penalty, and (iv) validation showing dynamic walking up to $1.2$ m/s, disturbance rejection up to $60$ N, and robust terrain traversal, with real-time performance around 7 ms planner and 0.5 ms tracking. Significance: demonstrates practical viability for humanoids with heavy limbs in real-world settings.

Abstract

Humanoid robots often face significant balance issues due to the motion of their heavy limbs. These challenges are particularly pronounced when attempting dynamic motion or operating in environments with irregular terrain. To address this challenge, this manuscript proposes a whole-body control framework for humanoid robots with heavy limbs, using a model-based approach that combines a kino-dynamics planner and a hierarchical optimization problem. The kino-dynamics planner is designed as a model predictive control (MPC) scheme to account for the impact of heavy limbs on mass and inertia distribution. By simplifying the robot's system dynamics and constraints, the planner enables real-time planning of motion and contact forces. The hierarchical optimization problem is formulated using Hierarchical Quadratic Programming (HQP) to minimize limb control errors and ensure compliance with the policy generated by the kino-dynamics planner. Experimental validation of the proposed framework demonstrates its effectiveness. The humanoid robot with heavy limbs controlled by the proposed framework can achieve dynamic walking speeds of up to 1.2~m/s, respond to external disturbances of up to 60~N, and maintain balance on challenging terrains such as uneven surfaces, and outdoor environments.

Figures (6)

• Figure 1: Illustration of a humanoid robot with two 6-DoF manipulators and two 6-DoF legs, walking over uneven terrain.
• Figure 2: Illustration of the humanoid robots frames (inertial $\mathcal{I}$ and centroidal $\mathcal{G}$), contact forces $\boldsymbol{f}_{c_i}$, and the collision constraint ${d_i}({\boldsymbol{x}},{\boldsymbol{u}},t)$.
• Figure 3: The block diagram illustrates the proposed framework for a humanoid robot with heavy limbs. First, the kino-dynamics planner generates reference motion and forces ($\boldsymbol{x}^*$ and $\boldsymbol{u}^*$) based on the user input ($\boldsymbol{x}^{ref}$ and $\boldsymbol{u}^{ref}$) and state estimator. Then, a hierarchical optimization problem is formulated to track $\boldsymbol{x}^*$ and $\boldsymbol{u}^*$, generating torque commands ${\boldsymbol{\tau }}_j^d$ for the humanoid robot's actuators.
• Figure 4: Simulation results of dynamic walking with a desired velocity of 1.0 m/s. (a) is the velocity tracking response. The red solid line is the result caused by the cH, the blue solid line is the result caused by the cNH, and the green dotted line is the desired command. (b) is the limb tracking error. (c) is the height tracking response. (d), (e) and (f) are the orientation tracking response of roll, pitch, and yaw, respectively.
• Figure 5: Simulation results of disturbance rejection with an external force of 40 N applied to the base at the fifth second for 1 second. (a) and (b) are the motion responses in the x-axis and y-axis directions, respectively. (c) is the motion responses in the height. (d), (e) and (f) are the orientation responses of roll, pitch, and yaw, respectively. The red solid line is the result caused by the cH and the blue solid line is the result caused by the cNH.