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This research investigates the benefits of using geodesic distances for path planning in humanoid robots.

March 24, 2026Open Access

Geodesic Path Planning on Configuration Space Manifolds: Shorter, Smoother Trajectories for Humanoid Robots

Key Points

This research investigates the benefits of using geodesic distances for path planning in humanoid robots.
Compared geodesic distance to Euclidean distance in path planning algorithms.
Conducted tests on various robot morphologies including industrial arms and humanoid robots.
Utilized Boston Dynamics Atlas and Tesla Optimus for experimental validation.
Achieved path reductions of 26-29% compared to traditional methods across all tested robots.
Statistical significance indicated with p < 10^-20.
No modifications to existing hardware or algorithms were necessary.

Abstract

We demonstrate that replacing Euclidean distance with geodesic distance on the toroidal configuration space of revolute-joint robots produces 26-29% shorter paths across all tested morphologies, from 6-DOF industrial arms to 56-DOF humanoid robots (p < 10^-20). Tested on Boston Dynamics Atlas, Tesla Optimus, and industrial arms. No hardware or algorithm changes required. Patent pending (AU 2026902297).

Geodesic Path Planning on Configuration Space Manifolds: Shorter, Smoother Trajectories for Humanoid Robots

Key Points

Abstract

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