# 通过神经网络近似加速 Graphs of Convex Sets 上的优化

> 原文链接：https://robotics.hellobike.com/papers/2026-08-15-2608-15440
> 频道：papers | 更新日期：2026-08-15 | 标签：arxiv, cs.RO
> 核心摘要：针对GCS在线重规划中子问题计算昂贵，方法以GAT和排序网络替代凸松弛，并在多类机器人规划任务上验证。

# 通过神经网络近似加速 Graphs of Convex Sets 上的优化

::: v-pre
> 原文链接：[Accelerating Optimization over Graphs of Convex Sets via Neural Network Approximations](https://arxiv.org/abs/2608.15440)（arXiv 2608.15440 · 发布日期：2026-08-15）

**Accelerating Optimization over Graphs of Convex Sets via Neural Network Approximations**

针对GCS在线重规划中子问题计算昂贵，方法以GAT和排序网络替代凸松弛，并在多类机器人规划任务上验证。

## 核心要点

- 碰撞规避导航和接触丰富操作可表述为离散决策与连续轨迹耦合优化。
- 用Graph Attention Network预测高概率候选路径，再由轻量排序网络按估计轨迹代价排序。
- 按排序评估候选并提前终止，在凸与非凸代价和约束设置中恢复近最优运动计划。
- 在多样任务中较nominal GCS最高加速两个数量级且成功率100%，代码和视频已公开。

**验证范围与局限**：验证范围为3D四旋翼、7-DoF机械臂无碰撞规划和平面推挤接触规划，解存在一定次优性。

## 英文摘要 (Abstract)

Motion planning problems such as collision-free navigation and contact-rich manipulation can be naturally formulated as optimization problems that couple discrete decisions with continuous trajectories. The Graphs of Convex Sets (GCS) framework offers a practical solution to these problems. It represents discrete decisions as nodes of a graph and encodes continuous trajectories in the edges connecting them. However, the resulting optimization subproblems can become computationally prohibitive for online replanning. In this work, we propose a learning-based strategy to mitigate this limitation. Specifically, we replace the costly convex relaxation step required by nominal GCS with a single forward pass through a Graph Attention Network that predicts a set of highly probable candidate paths through the graph. A lightweight ranking network then orders these candidates by their estimated trajectory cost. Evaluating them in this order, we terminate our search early while still recovering a near-optimal motion plan. We validate the resulting pipeline across diverse robotic tasks, including collision-free motion planning for a 3D quadrotor and a 7-DoF manipulator, and planning through contact for planar pushing. Across both convex and non-convex cost and constraint settings, our approach yields up to two orders of magnitude speedup over nominal GCS while maintaining a 100% success rate, at the cost of some suboptimality in the recovered solutions. Code implementations and video demonstrations can be found at https://neural-gcs.github.io/.

作者：Ananya Trivedi, Sarvesh Prajapati, Zhexin Xu, Mohamed Khalid M Jaffar, David M. Rosen, Taşkın Padır
:::

## 原始参考来源 (Sources)

- [arXiv 2608.15440：Accelerating Optimization over Graphs of Convex Sets via Neural Network Approximations](https://arxiv.org/abs/2608.15440)