# Optimal Motion Planning using Finite Fourier Series in a Learning-based Collision Field

arXiv: https://arxiv.org/abs/2312.09073 · HTML: https://mlsanity.com/paper/2312.09073/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 36 references that are in the map.
- First posted on arXiv 14 Dec 2023.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Learning Sampling Distributions for Robot Motion Planning](https://mlsanity.com/paper/1709.05448/) (2017)
- [Continuous-Time Gaussian Process Motion Planning via Probabilistic Inference](https://mlsanity.com/paper/1707.07383/) (2017)
- [Differentiable Gaussian Process Motion Planning](https://mlsanity.com/paper/1907.09591/) (2019)
- [Learning-Based Proxy Collision Detection for Robot Motion Planning Applications](https://mlsanity.com/paper/1902.08164/) (2019)
- [Generalized Lazy Search for Robot Motion Planning: Interleaving Search and Edge Evaluation via Event-based Toggles](https://mlsanity.com/paper/1904.02795/) (2019)
- [Motion Planning by Learning the Solution Manifold in Trajectory Optimization](https://mlsanity.com/paper/2107.05842/) (2021)
- [Multimodal Trajectory Optimization for Motion Planning](https://mlsanity.com/paper/2003.07054/) (2020)
- [Memory of Motion for Warm-starting Trajectory Optimization](https://mlsanity.com/paper/1907.01474/) (2019)
- [Stochastic Optimization for Trajectory Planning with Heteroscedastic Gaussian Processes](https://mlsanity.com/paper/1907.07521/) (2019)
- [Adaptive Gaussian Process based Stochastic Trajectory Optimization for Motion Planning](https://mlsanity.com/paper/2112.14953/) (2021)
- [New perspective on sampling-based motion planning via random geometric graphs](https://mlsanity.com/paper/1602.05460/) (2016)
- [Incrementally Stochastic and Accelerated Gradient Information mixed Optimization for Manipulator Motion Planning](https://mlsanity.com/paper/2108.09490/) (2021)

## Abstract (arXiv)

This paper utilizes finite Fourier series to represent a time-continuous motion and proposes a novel planning method that adjusts the motion harmonics of each manipulator joint. Primarily, we sum the potential energy for collision detection and the kinetic energy up to calculate the Hamiltonian of the manipulator motion harmonics. Though the adaptive interior-point method is designed to modify the harmonics in its finite frequency domain, we still encounter the local minima due to the non-convexity of the collision field. In this way, we learn the collision field through a support vector machine with a Gaussian kernel, which is highly convex. The learning-based collision field is applied for Hamiltonian, and the experiment results show our method's high reliability and efficiency.