# One-DoF Robotic Design of Overconstrained Limbs with Energy-Efficient, Self-Collision-Free Motion

arXiv: https://arxiv.org/abs/2509.22002 · HTML: https://mlsanity.com/paper/2509.22002/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Sep 2025.

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

- [asRoBallet: Closing the Sim2Real Gap via Friction-Aware Reinforcement Learning for Underactuated Spherical Dynamics](https://mlsanity.com/paper/2604.24916/) (2026)

## Abstract (arXiv)

While it is expected to build robotic limbs with multiple degrees of freedom (DoF) inspired by nature, a single DoF design remains fundamental, providing benefits that include, but are not limited to, simplicity, robustness, cost-effectiveness, and efficiency. Mechanisms, especially those with multiple links and revolute joints connected in closed loops, play an enabling factor in introducing motion diversity for 1-DoF systems, which are usually constrained by self-collision during a full-cycle range of motion. This study presents a novel computational approach to designing one-degree-of-freedom (1-DoF) overconstrained robotic limbs for a desired spatial trajectory, while achieving energy-efficient, self-collision-free motion in full-cycle rotations. Firstly, we present the geometric optimization problem of linkage-based robotic limbs in a generalized formulation for self-collision-free design. Next, we formulate the spatial trajectory generation problem with the overconstrained linkages by optimizing the similarity and dynamic-related metrics. We further optimize the geometric shape of the overconstrained linkage to ensure smooth and collision-free motion driven by a single actuator. We validated our proposed method through various experiments, including personalized automata and bio-inspired hexapod robots. The resulting hexapod robot, featuring overconstrained robotic limbs, demonstrated outstanding energy efficiency during forward walking.