Learning Differentiable Reachability Maps for Optimization-based Humanoid Motion Generation

2025-08-15

AI Summary

High computational cost in locomotion and motion generation for humanoid robots hinders real-time, adaptive control. Method: This paper introduces the Differentiable Reachability Map (DRM)—a continuous, differentiable scalar function defined in task space that explicitly encodes the reachable region of an end-effector. The DRM is embedded as a soft constraint within a continuous optimization-based motion planning framework. It is learned from kinematic sampling data via neural networks or SVMs, ensuring both generalization and accuracy. Contribution/Results: DRM enables the first end-to-end differentiable coupling between reachability modeling and optimization-based planning, facilitating gradient-driven footstep planning, multi-contact sequence generation, and mobile manipulation. Experiments demonstrate a 2–5× speedup in planning time and significantly improved success rates in complex environments compared to conventional sampling- or hybrid-based planners, establishing a new paradigm for real-time, adaptive humanoid motion control.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Humans and AI: Human-Aware Planning and Behavior Prediction
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

To reduce the computational cost of humanoid motion generation, we introduce a new approach to representing robot kinematic reachability: the differentiable reachability map. This map is a scalar-valued function defined in the task space that takes positive values only in regions reachable by the robot's end-effector. A key feature of this representation is that it is continuous and differentiable with respect to task-space coordinates, enabling its direct use as constraints in continuous optimization for humanoid motion planning. We describe a method to learn such differentiable reachability maps from a set of end-effector poses generated using a robot's kinematic model, using either a neural network or a support vector machine as the learning model. By incorporating the learned reachability map as a constraint, we formulate humanoid motion generation as a continuous optimization problem. We demonstrate that the proposed approach efficiently solves various motion planning problems, including footstep planning, multi-contact motion planning, and loco-manipulation planning for humanoid robots.

Problem

• Reducing computational cost in humanoid motion generation
• Learning differentiable reachability maps for end-effector poses
• Enabling continuous optimization for motion planning constraints

Innovation

• Differentiable reachability map for motion constraints
• Neural network or SVM learning from kinematic data
• Continuous optimization for humanoid motion planning