# Motion Planning With Gamma-Harmonic Potential Fields

arXiv: https://arxiv.org/abs/1606.09278 · HTML: https://mlsanity.com/paper/1606.09278/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jun 2016.

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

- [Neural Navigation Functions for Zero-Shot Generalizable Motion Planning](https://mlsanity.com/paper/2606.03756/) (2026)

## Abstract (arXiv)

This paper extends the capabilities of the harmonic potential field (HPF) approach to planning. The extension covers the situation where the workspace of a robot cannot be segmented into geometrical subregions where each region has an attribute of its own. The suggested approach uses a task-centered, probabilistic descriptor of the workspace as an input to the planner. This descriptor is processed, along with a goal point, to yield the navigation policy needed to steer the agent from any point in its workspace to the target. The approach is easily adaptable to planning in a cluttered environment containing a vector drift field. The extension of the HPF approach is based on the physical analogy with an electric current flowing in a nonhomogeneous conducting medium. The resulting potential field is known as the gamma-harmonic potential (GHPF). Proofs of the ability of the modified approach to avoid zero-probability (definite threat) regions and to converge to the goal are provided. The capabilities of the planer are demonstrated using simulation.