Learning Differentiable Reachability Maps for Optimization-Based Humanoid Motion Generation

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.