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：本文提出将机器人几何形状学习为距离场（RDF），该距离场扩展了包含关节构型的机器人带符号距离场（SDF）。与现有方法将关节空间与欧氏空间共同编码为隐式表示不同，所提出的RDF方法利用机器人的运动学链，降低了问题的维度和复杂度，从而获得更精确可靠的SDF。本文提出一种简单灵活的方法，利用基函数表示单个机器人连杆的SDF，相较于神经网络，该方法提供了更平滑的表示并提升了效率。RDF天然具备连续性和可微性，使其可直接作为代价函数集成到机器人任务中。该方法还能以任意期望的空间分辨率获取高精度机器人表面点，并具备全身操控能力。我们通过仿真实验和七轴Franka Emika机器人实验验证了所提RDF表示的有效性。将所提方法与基线方法进行对比，并在双臂场景中展示了其在避碰和全身操控任务上的效率。项目页面：https://sites.google.com/view/lrdf/home