Multi-objective optimization problems are ubiquitous in robotics, e.g., the optimization of a robot manipulation task requires a joint consideration of grasp pose configurations, collisions and joint limits. While some demands can be easily hand-designed, e.g., the smoothness of a trajectory, several task-specific objectives need to be learned from data. This work introduces a method for learning data-driven SE(3) cost functions as diffusion models. Diffusion models can represent highly-expressive multimodal distributions and exhibit proper gradients over the entire space due to their score-matching training objective. Learning costs as diffusion models allows their seamless integration with other costs into a single differentiable objective function, enabling joint gradient-based motion optimization. In this work, we focus on learning SE(3) diffusion models for 6DoF grasping, giving rise to a novel framework for joint grasp and motion optimization without needing to decouple grasp selection from trajectory generation. We evaluate the representation power of our SE(3) diffusion models w.r.t. classical generative models, and we showcase the superior performance of our proposed optimization framework in a series of simulated and real-world robotic manipulation tasks against representative baselines.

翻译：多目标优化问题在机器人领域普遍存在，例如机器人操作任务的优化需要综合考虑抓取姿态配置、碰撞约束与关节限位。虽然部分需求（如轨迹平滑性）可通过人工设计轻松实现，但诸多特定任务目标需从数据中学习。本文提出一种将数据驱动的SE(3)代价函数作为扩散模型进行学习的方法。扩散模型能够表征高表达能力多模态分布，并因其基于分数匹配的训练目标而在整个空间上呈现出良好的梯度特性。通过学习具有扩散模型形式的代价函数，可将其与其他代价函数无缝整合为单一可微目标函数，从而支持基于梯度的联合运动优化。本研究聚焦于面向6自由度抓取的SE(3)扩散模型学习，由此构建无需解耦抓取选择与轨迹生成的抓取-运动联合优化新框架。我们评估了所提SE(3)扩散模型相对于经典生成模型的表征能力，并在系列仿真与真实机器人操作任务中展示了该优化框架相较于代表性基准方法的卓越性能。