In this work, we propose to learn robot geometry as distance fields (RDF), which extend the signed distance field (SDF) of the robot with joint configurations. Unlike existing methods that learn an implicit representation encoding joint space and Euclidean space together, the proposed RDF approach leverages the kinematic chain of the robot, which reduces the dimensionality and complexity of the problem, resulting in more accurate and reliable SDFs. A simple and flexible approach that exploits basis functions to represent SDFs for individual robot links is presented, providing a smoother representation and improved efficiency compared to neural networks. RDF is naturally continuous and differentiable, enabling its direct integration as cost functions in robot tasks. It also allows us to obtain high-precision robot surface points with any desired spatial resolution, with the capability of whole-body manipulation. We verify the effectiveness of our RDF representation by conducting various experiments in both simulations and with the 7-axis Franka Emika robot. We compare our approach against baseline methods and demonstrate its efficiency in dual-arm settings for tasks involving collision avoidance and whole-body manipulation. Project page: https://sites.google.com/view/lrdf/home}{https://sites.google.com/view/lrdf/home

翻译：本文提出学习机器人几何形状作为距离场（RDF），该场将机器人的有符号距离场（SDF）与关节构型相结合。与现有方法将关节空间和欧氏空间编码在一起的隐式表示不同，所提出的RDF方法利用了机器人的运动学链，降低了问题的维度和复杂性，从而生成更准确可靠的SDF。我们提出了一种简单灵活的方法，利用基函数表示各个机器人连杆的SDF，与神经网络相比，该方法提供了更平滑的表示和更高的效率。RDF自然连续且可微，能够直接作为代价函数集成到机器人任务中。它还使我们能够以任意期望的空间分辨率获取高精度的机器人表面点，具备全身操控能力。通过在实际7轴Franka Emika机器人及仿真环境中进行多种实验，我们验证了RDF表示的有效性。我们将所提方法与基线方法进行比较，并展示了其在涉及避碰和全身操控的双臂任务中的效率。项目页面：https://sites.google.com/view/lrdf/home