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，例如机械臂操作任务的优化需要联合考虑抓取姿态配置、碰撞检测与关节极限约束。虽然某些需求（如轨迹平滑度）易于手工设计，但多种任务特定目标需从数据中学习。本文提出一种将数据驱动的SE(3)代价函数建模为扩散模型的学习方法。扩散模型能够表征高度表达性的多模态分布，并通过其分数匹配训练目标在整个空间上提供合适的梯度。将代价函数建模为扩散模型，使其能够与其他代价函数无缝集成至单一可微目标函数中，从而实现基于梯度的联合运动优化。本文聚焦于学习六自由度抓取的SE(3)扩散模型，由此构建无需将抓取选择与轨迹生成解耦的抓取与运动联合优化新框架。我们评估了SE(3)扩散模型相较于经典生成模型的表达能力，并通过一系列仿真与真实机器人操作任务，展示了所提优化框架相较于代表性基线方法的优越性能。