Neural-network-based dynamics models learned from observational data have shown strong predictive capabilities for scene dynamics in robotic manipulation tasks. However, their inherent non-linearity presents significant challenges for effective planning. Current planning methods, often dependent on extensive sampling or local gradient descent, struggle with long-horizon motion planning tasks involving complex contact events. In this paper, we present a GPU-accelerated branch-and-bound (BaB) framework for motion planning in manipulation tasks that require trajectory optimization over neural dynamics models. Our approach employs a specialized branching heuristics to divide the search space into subdomains, and applies a modified bound propagation method, inspired by the state-of-the-art neural network verifier alpha-beta-CROWN, to efficiently estimate objective bounds within these subdomains. The branching process guides planning effectively, while the bounding process strategically reduces the search space. Our framework achieves superior planning performance, generating high-quality state-action trajectories and surpassing existing methods in challenging, contact-rich manipulation tasks such as non-prehensile planar pushing with obstacles, object sorting, and rope routing in both simulated and real-world settings. Furthermore, our framework supports various neural network architectures, ranging from simple multilayer perceptrons to advanced graph neural dynamics models, and scales efficiently with different model sizes.

翻译：基于神经网络、从观测数据中学习得到的动力学模型，在机器人操作任务中已展现出对场景动态的强大预测能力。然而，其固有的非线性特性给有效规划带来了显著挑战。当前依赖于大量采样或局部梯度下降的规划方法，在处理涉及复杂接触事件的长时域运动规划任务时往往力不从心。本文提出了一种GPU加速的分支定界（BaB）框架，用于需要在神经动力学模型上进行轨迹优化的操作任务运动规划。我们的方法采用一种专门的分支启发式策略将搜索空间划分为子域，并应用一种改进的边界传播方法——该方法受最先进的神经网络验证器alpha-beta-CROWN的启发——来高效估计这些子域内的目标边界。分支过程有效地引导规划，而定界过程则策略性地缩减搜索空间。我们的框架实现了卓越的规划性能，能生成高质量的状态-动作轨迹，并在模拟和真实场景中，于非抓取平面障碍推挤、物体分拣及绳索布线等具有挑战性、接触丰富的操作任务上超越了现有方法。此外，我们的框架支持从简单的多层感知机到先进的图神经动力学模型等多种神经网络架构，并能随不同模型规模高效扩展。