Perceptive Variable-Timing Footstep Planning for Humanoid Locomotion on Disconnected Footholds

2026-03-08

AI Summary

This work addresses stable locomotion of humanoid robots over complex terrains with obstacles and unsafe regions, where footholds are discontinuous. The authors propose an onboard perception-aware hybrid integer model predictive control framework that integrates gait-level discrete capture point (DCM) dynamics with a probabilistic local elevation map constructed from depth images to jointly optimize foot placement and step timing. A key innovation lies in embedding capturability constraints directly into the DCM space by introducing lateral one-step and longitudinal infinite-step boundaries, enabling real-time intra-step replanning to enhance robustness against disturbances and model inaccuracies. Formulated as a mixed-integer quadratic program (MIQP), the approach achieves millisecond-level solve times in simulation on the Digit robot, generating terrain-aware, dynamically consistent adaptive stepping sequences that maintain balance under random stepping stones and external perturbations.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

Many real-world walking scenarios contain obstacles and unsafe ground patches (e.g., slippery or cluttered areas), leaving a disconnected set of admissible footholds that can be modeled as stepping-stone-like regions. We propose an onboard, perceptive mixed-integer model predictive control framework that jointly plans foot placement and step duration using step-to-step Divergent Component of Motion (DCM) dynamics. Ego-centric depth images are fused into a probabilistic local heightmap, from which we extract a union of convex steppable regions. Region membership is enforced with binary variables in a mixed-integer quadratic program (MIQP). To keep the optimization tractable while certifying safety, we embed capturability bounds in the DCM space: a lateral one-step condition (preventing leg crossing) and a sagittal infinite-step bound that limits unstable growth. We further re-plan within the step by back-propagating the measured instantaneous DCM to update the initial DCM, improving robustness to model mismatch and external disturbances. We evaluate the approach in simulation on Digit on randomized stepping-stone fields, including external pushes. The planner generates terrain-aware, dynamically consistent footstep sequences with adaptive timing and millisecond-level solve times.

Problem

• humanoid locomotion
• disconnected footholds
• footstep planning
• stepping-stone terrain
• safe walking

Innovation

• mixed-integer MPC
• Divergent Component of Motion
• stepping-stone locomotion
• capturability constraints
• online replanning