# Learning Continuous Cost-to-Go Functions for Non-holonomic Systems

arXiv: https://arxiv.org/abs/2103.11168 · HTML: https://mlsanity.com/paper/2103.11168/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 38 references that are in the map.
- First posted on arXiv 20 Mar 2021.

## Builds on (most cited first, 17 of 17)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Not All Samples Are Created Equal: Deep Learning with Importance Sampling](https://mlsanity.com/paper/1803.00942/) (2018)
- [End-to-end Interpretable Neural Motion Planner](https://mlsanity.com/paper/2101.06679/) (2021)
- [Value Iteration Networks](https://mlsanity.com/paper/1602.02867/) (2016)
- [Learning Sampling Distributions for Robot Motion Planning](https://mlsanity.com/paper/1709.05448/) (2017)
- [Motion Planning Networks](https://mlsanity.com/paper/1806.05767/) (2018)
- [Dynamical Distance Learning for Semi-Supervised and Unsupervised Skill Discovery](https://mlsanity.com/paper/1907.08225/) (2019)
- [Learning What Data to Learn](https://mlsanity.com/paper/1702.08635/) (2017)
- [LEGO: Leveraging Experience in Roadmap Generation for Sampling-Based Planning](https://mlsanity.com/paper/1907.09574/) (2019)
- [Learned Critical Probabilistic Roadmaps for Robotic Motion Planning](https://mlsanity.com/paper/1910.03701/) (2019)
- [Asymptotically Optimal Sampling-based Kinodynamic Planning](https://mlsanity.com/paper/1407.2896/) (2014)
- [Probabilistic completeness of RRT for geometric and kinodynamic planning with forward propagation](https://mlsanity.com/paper/1809.07051/) (2018)
- [Dynamically Constrained Motion Planning Networks for Non-Holonomic Robots](https://mlsanity.com/paper/2008.05112/) (2020)
- [Asymptotically Optimal Planning by Feasible Kinodynamic Planning in State-Cost Space](https://mlsanity.com/paper/1505.04098/) (2015)
- [Learn and Link: Learning Critical Regions for Efficient Planning](https://mlsanity.com/paper/1903.03258/) (2019)
- [Higher-Order Function Networks for Learning Composable 3D Object Representations](https://mlsanity.com/paper/1907.10388/) (2019)
- [Cost-to-Go Function Generating Networks for High Dimensional Motion Planning](https://mlsanity.com/paper/2012.06023/) (2020)

## Abstract (arXiv)

This paper presents a supervised learning method to generate continuous cost-to-go functions of non-holonomic systems directly from the workspace description. Supervision from informative examples reduces training time and improves network performance. The manifold representing the optimal trajectories of a non-holonomic system has high-curvature regions which can not be efficiently captured with uniform sampling. To address this challenge, we present an adaptive sampling method which makes use of sampling-based planners along with local, closed-form solutions to generate training samples. The cost-to-go function over a specific workspace is represented as a neural network whose weights are generated by a second, higher order network. The networks are trained in an end-to-end fashion. In our previous work, this architecture was shown to successfully learn to generate the cost-to-go functions of holonomic systems using uniform sampling. In this work, we show that uniform sampling fails for non-holonomic systems. However, with the proposed adaptive sampling methodology, our network can generate near-optimal trajectories for non-holonomic systems while avoiding obstacles. Experiments show that our method is two orders of magnitude faster compared to traditional approaches in cluttered environments.