# Constrained Gaussian Process Motion Planning via Stein Variational Newton Inference

arXiv: https://arxiv.org/abs/2504.04936 · HTML: https://mlsanity.com/paper/2504.04936/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 63 references that are in the map.
- First posted on arXiv 7 Apr 2025.

## Builds on (most cited first, 30 of 33)

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- [SegFormer: Simple and Efficient Design for Semantic Segmentation with Transformers](https://mlsanity.com/paper/2105.15203/) (2021)
- [Pyramid Vision Transformer: A Versatile Backbone for Dense Prediction without Convolutions](https://mlsanity.com/paper/2102.12122/) (2021)
- [PVT v2: Improved Baselines with Pyramid Vision Transformer](https://mlsanity.com/paper/2106.13797/) (2021)
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- [InternImage: Exploring Large-Scale Vision Foundation Models with Deformable Convolutions](https://mlsanity.com/paper/2211.05778/) (2022)
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- [CSRNet: Dilated Convolutional Neural Networks for Understanding the Highly Congested Scenes](https://mlsanity.com/paper/1802.10062/) (2018)
- [Composition Loss for Counting, Density Map Estimation and Localization in Dense Crowds](https://mlsanity.com/paper/1808.01050/) (2018)
- [Rethinking Counting and Localization in Crowds:A Purely Point-Based Framework](https://mlsanity.com/paper/2107.12746/) (2021)
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- [Context-Aware Crowd Counting](https://mlsanity.com/paper/1811.10452/) (2018)
- [Dynamic Snake Convolution based on Topological Geometric Constraints for Tubular Structure Segmentation](https://mlsanity.com/paper/2307.08388/) (2023)
- [An End-to-End Transformer Model for Crowd Localization](https://mlsanity.com/paper/2202.13065/) (2022)
- [Boosting Crowd Counting via Multifaceted Attention](https://mlsanity.com/paper/2203.02636/) (2022)
- [Point in, Box out: Beyond Counting Persons in Crowds](https://mlsanity.com/paper/1904.01333/) (2019)
- [On the Connection between Local Attention and Dynamic Depth-wise Convolution](https://mlsanity.com/paper/2106.04263/) (2021)
- [TransCrowd: weakly-supervised crowd counting with transformers](https://mlsanity.com/paper/2104.09116/) (2021)
- [ADCrowdNet: An Attention-injective Deformable Convolutional Network for Crowd Understanding](https://mlsanity.com/paper/1811.11968/) (2018)
- [Point-Query Quadtree for Crowd Counting, Localization, and More](https://mlsanity.com/paper/2308.13814/) (2023)
- [A Self-Training Approach for Point-Supervised Object Detection and Counting in Crowds](https://mlsanity.com/paper/2007.12831/) (2020)
- [AutoScale: Learning to Scale for Crowd Counting and Localization](https://mlsanity.com/paper/1912.09632/) (2019)
- [HA-CCN: Hierarchical Attention-based Crowd Counting Network](https://mlsanity.com/paper/1907.10255/) (2019)
- [CCTrans: Simplifying and Improving Crowd Counting with Transformer](https://mlsanity.com/paper/2109.14483/) (2021)
- [Large Separable Kernel Attention: Rethinking the Large Kernel Attention Design in CNN](https://mlsanity.com/paper/2309.01439/) (2023)
- [Exploring Fine-Grained Image-Text Alignment for Referring Remote Sensing Image Segmentation](https://mlsanity.com/paper/2409.13637/) (2024)
- [Crowd Counting via Perspective-Guided Fractional-Dilation Convolution](https://mlsanity.com/paper/2107.03665/) (2021)
- [Scene-Adaptive Attention Network for Crowd Counting](https://mlsanity.com/paper/2112.15509/) (2021)

## Abstract (arXiv)

Gaussian Process Motion Planning (GPMP) is a widely used framework for generating smooth trajectories within a limited compute time--an essential requirement in many robotic applications. However, traditional GPMP approaches often struggle with enforcing hard nonlinear constraints and rely on Maximum a Posteriori (MAP) solutions that disregard the full Bayesian posterior. This limits planning diversity and ultimately hampers decision-making. Recent efforts to integrate Stein Variational Gradient Descent (SVGD) into motion planning have shown promise in handling complex constraints. Nonetheless, these methods still face persistent challenges, such as difficulties in strictly enforcing constraints and inefficiencies when the probabilistic inference problem is poorly conditioned. To address these issues, we propose a novel constrained Stein Variational Gaussian Process Motion Planning (cSGPMP) framework, incorporating a GPMP prior specifically designed for trajectory optimization under hard constraints. Our approach improves the efficiency of particle-based inference while explicitly handling nonlinear constraints. This advancement significantly broadens the applicability of GPMP to motion planning scenarios demanding robust Bayesian inference, strict constraint adherence, and computational efficiency within a limited time. We validate our method on standard benchmarks, achieving an average success rate of 98.57% across 350 planning tasks, significantly outperforming competitive baselines. This demonstrates the ability of our method to discover and use diverse trajectory modes, enhancing flexibility and adaptability in complex environments, and delivering significant improvements over standard baselines without incurring major computational costs.