# Learning Differentiable Reachability Maps for Optimization-based Humanoid Motion Generation

arXiv: https://arxiv.org/abs/2508.11275 · HTML: https://mlsanity.com/paper/2508.11275/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Aug 2025.

## Built on by (most cited first, 1 of 1)

- [RAM: Reachability Across Morphologies](https://mlsanity.com/paper/2606.09108/) (2026)

## Abstract (arXiv)

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.