Gait-Net-augmented Implicit Kino-dynamic MPC for Dynamic Variable-frequency Humanoid Locomotion over Discrete Terrains

TL;DR

The paper addresses the challenge of dynamic humanoid locomotion with variable step timing by introducing a Gait-Net-augmented implicit kino-dynamic MPC that jointly optimizes step location, duration, and contact forces. By predicting the preferred step duration $dt$ and updating spatial momentum references within a sequential convex MPC framework, it achieves efficient real-time planning over discrete terrains with only a one-step terrain preview. The key contributions are the Gait-Net for step-duration prediction and its integration into a sequential CMPC that implicitly enforces kinematic feasibility, validated in high-fidelity simulations and small-scale hardware, including push recovery, unknown loads, and 20 cm terrain gaps at $0.75$ m/s. This approach offers robust, variable-frequency walking capabilities suitable for dynamic, real-world humanoid locomotion with reduced computational burden compared to full WB-MPC methods.

Abstract

Reduced-order-model-based optimal control techniques for humanoid locomotion struggle to adapt step duration and placement simultaneously in dynamic walking gaits due to their reliance on fixed-time discretization, which limits responsiveness to various disturbances and results in suboptimal performance in challenging conditions. In this work, we propose a Gait-Net-augmented implicit kino-dynamic model-predictive control (MPC) to simultaneously optimize step location, step duration, and contact forces for natural variable-frequency locomotion. The proposed method incorporates a Gait-Net-augmented Sequential Convex MPC algorithm to solve multi-linearly constrained variables by iterative quadratic programs. At its core, a lightweight Gait-frequency Network (Gait-Net) determines the preferred step duration in terms of variable MPC sampling times, simplifying step duration optimization to the parameter level. Additionally, it enhances and updates the spatial reference trajectory within each sequential iteration by incorporating local solutions, allowing the projection of kinematic constraints to the design of reference trajectories. We validate the proposed algorithm in high-fidelity simulations and on small-size humanoid hardware, demonstrating its capability for variable-frequency and 3-D discrete terrain locomotion with only a one-step preview of terrain data.

Figures (13)

• Figure 1: Gait-Net-augmented Kino-dynamic MPC. Hardware Experiment Snapshots. (a). Push-recovery in locomotion (b). Locomotion while carrying an unknown 0.75 kg object; (c). Locomotion over unknown uneven terrain; (d). Dynamic walking over terrain with a 20 cm terrain gap at 0.75 m/s; (e). Dynamic walking over terrain gap and obstacle. Full experiment video: https://youtu.be/UqLDYHGL5EA
• Figure 2: Control System Architecture
• Figure 3: Illustration of the Gait-frequency Network
• Figure 4: Feature Projection Bar Graphs along 6 Principle Axes. The feature with the highest projection in each axis (red bar) is selected to be part of the new feature space. Note that along principle axes 1 and 2, both left and right legs are equally weighted with opposite signs, making the single Gait-Net suitable for both legs' prediction.
• Figure 5: Bilinear Envelope Approximation by Neglecting Search Direction Product $\delta a\cdot\delta b$.