Experiments demonstrate shorter paths in humanoid robots using geodesic distances, implying improved efficiency in movement.
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).
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Nicholas Muir (2026) studied this question.
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