Reduced-Order Model Guided Contact-Implicit Model Predictive Control for Humanoid Locomotion

TL;DR

This work tackles the problem of controlling high-dimensional, nonlinear hybrid humanoid locomotion by marrying a robust reduced-order gait model with a flexible, contact-aware optimization framework. Specifically, it couples the Hybrid Linear Inverted Pendulum (HLIP) with Contact-Implicit Model Predictive Control (CI-MPC) to generate nominal gait references while allowing whole-body CI-MPC to adapt contact sequences and exploit environmental contacts in real time. The approach is validated in simulation on the 24-DoF Achilles humanoid, demonstrating rough-terrain walking, disturbance rejection, multi-contact stabilization, and interaction with environment features, all at a 50 Hz planning cadence. The framework relies on HLIP for stable gait guidance and CI-MPC (via inverse dynamics trajectory optimization with a differentiable contact model) for expressive, online optimization over contacts, yielding robust and adaptable locomotion with clear potential for hardware realization, subject to addressing current limitations such as collision modeling and self-collision constraints.

Abstract

Humanoid robots have great potential for real-world applications due to their ability to operate in environments built for humans, but their deployment is hindered by the challenge of controlling their underlying high-dimensional nonlinear hybrid dynamics. While reduced-order models like the Hybrid Linear Inverted Pendulum (HLIP) are simple and computationally efficient, they lose whole-body expressiveness. Meanwhile, recent advances in Contact-Implicit Model Predictive Control (CI-MPC) enable robots to plan through multiple hybrid contact modes, but remain vulnerable to local minima and require significant tuning. We propose a control framework that combines the strengths of HLIP and CI-MPC. The reduced-order model generates a nominal gait, while CI-MPC manages the whole-body dynamics and modifies the contact schedule as needed. We demonstrate the effectiveness of this approach in simulation with a novel 24 degree-of-freedom humanoid robot: Achilles. Our proposed framework achieves rough terrain walking, disturbance recovery, robustness under model and state uncertainty, and allows the robot to interact with obstacles in the environment, all while running online in real-time at 50 Hz.

Figures (7)

• Figure 1: A simulated Achilles humanoid walks over unmodeled terrain near a wall. The HLIP reduced-order model provides a nominal gait, while CI-MPC adjusts the contact sequence, bracing the arm against the wall.
• Figure 2: Control architecture that combines the HLIP with CI-MPC. User commands are given to the HLIP. Then, via inverse kinematics and finite difference, we obtain a state trajectory where after combination produces a trajectory for the legs. CI-MPC tracks this trajectory that is interpolated and passed to low-level control of the robot.
• Figure 3: The proposed framework enables the robot to automatically discover heel-to-toe foot strikes during forward walking and toe-to-heel strikes when moving backward. Shown is an example contact schedule for the right foot when we reach a stable walking gait.
• Figure 4: The Achilles humanoid in various simulation test scenarios. HLIP guides the robot toward a reasonable gait, while CI-MPC provides the flexibility to make and break contact on the fly.
• Figure 5: Velocity tracking with HLIP only, CI-MPC only, and our proposed approach that combines the two. CI-MPC only and our proposed approach both take some time before moving forward, as the lowest-cost behavior at small velocity commands is to remain standing in place. Additionally, at low velocities, the the standing configuration reference dominates in \ref{['ref_combo']}.

Theorems & Definitions (1)

• Remark 1