Energy-Based Optimization of Wire Paths in Free Space Using Discrete Elastic Rod Models

This paper explores a method for generating plausible cable routings in free space by combining curve-energy formulations from structural dynamics, knot theory, and robot path planning. The approach minimizes a composite energy functional—accounting for smoothness and collision avoidance—while encouraging a predefined cable length through an arc-length energy term. Preliminary results demonstrate the method’s ability to produce smooth, collision-free cable curves in simple example tasks, offering a physics-inspired foundation for early-stage design of electrical wiring in free space.