Variable Inertia Model Predictive Control for Fast Bipedal Maneuvers

TL;DR

This work introduces Variable Inertia MPC (VI-MPC) for bipedal locomotion, explicitly modeling state-dependent centroidal inertia via a Centroidal Composite Inertia Network (CCINN) and integrating Whole-Body Orientation (WBO) within a convex MPC framework. By coupling a CCINN-informed SRB-based MPC with a hierarchy of reference trajectory generation and a robust WBC, the approach reduces discrepancies with full-body dynamics and enables stable, high-speed walking and agile turns. Key contributions include offline CCINN training, online inertia prediction within a convex MPC, and demonstration on the DRACO 3 humanoid with improved velocity tracking and turning capabilities. The results suggest significant practical impact for real-time humanoid control, offering a scalable path toward high-speed, robust locomotion in dynamic environments.

Abstract

This paper proposes a novel control framework for agile and robust bipedal locomotion, addressing model discrepancies between full-body and reduced-order models. Specifically, assumptions such as constant centroidal inertia have introduced significant challenges and limitations in locomotion tasks. To enhance the agility and versatility of full-body humanoid robots, we formalize a Model Predictive Control (MPC) problem that accounts for the variable centroidal inertia of humanoid robots within a convex optimization framework, ensuring computational efficiency for real-time operations. In the proposed formulation, we incorporate a centroidal inertia network designed to predict the variable centroidal inertia over the MPC horizon, taking into account the swing foot trajectories -- an aspect often overlooked in ROM-based MPC frameworks. By integrating the MPC-based contact wrench planning with our low-level whole-body controller, we significantly improve the locomotion performance, achieving stable walking at higher velocities that are not attainable with the baseline method. The effectiveness of our proposed framework is validated through high-fidelity simulations using our full-body bipedal humanoid robot DRACO 3, demonstrating dynamic behaviors.

Figures (6)

• Figure 1: Illustration of the Variable Inertia MPC (VI-MPC framework): VI-MPC plans using the SRB in conjunction with variable centroidal inertia to minimize model discrepancies when compared to the full-body model.
• Figure 2: The Proposed Hierarchical Control Framework. The user input commands the gait type, speed, and direction. The model predictive controller then calculates the desired reaction forces, CoM position, whole-body orientation, and foot SE(3) commands. Finally, the whole-body controller computes joint position, velocity, and torque commands, which are sent to each joint-level controller.
• Figure 3: Centroidal Inertia Prediction. Using the CCINN, 6-dimensional centroidal rotational inertia tensors (in body frame) are predicted online across the MPC horizon (10 nodes) during forward walking at a speed of 1.2 m/s. The contact schedule is depicted with black for the contact phase and silver for the swing phase.
• Figure 4: MPC solve time. The proposed MPC solve time is illustrated. The solve time is mostly below 2 ms.
• Figure 5: Forward Walking Velocity Tracking Performance. Case 1 employs nominal inertia at a nominal configuration. Case 2 uses constant inertia over the MPC horizon and updates it at every iteration. Case 3 showcases the proposed method.

Theorems & Definitions (1)

• Remark 1