The signed distance field is a popular implicit shape representation in robotics, providing geometric information about objects and obstacles in a form that can easily be combined with control, optimization and learning techniques. Most often, SDFs are used to represent distances in task space, which corresponds to the familiar notion of distances that we perceive in our 3D world. However, SDFs can mathematically be used in other spaces, including robot configuration spaces. For a robot manipulator, this configuration space typically corresponds to the joint angles for each articulation of the robot. While it is customary in robot planning to express which portions of the configuration space are free from collision with obstacles, it is less common to think of this information as a distance field in the configuration space. In this paper, we demonstrate the potential of considering SDFs in the robot configuration space for optimization, which we call the configuration space distance field. Similarly to the use of SDF in task space, CDF provides an efficient joint angle distance query and direct access to the derivatives. Most approaches split the overall computation with one part in task space followed by one part in configuration space. Instead, CDF allows the implicit structure to be leveraged by control, optimization, and learning problems in a unified manner. In particular, we propose an efficient algorithm to compute and fuse CDFs that can be generalized to arbitrary scenes. A corresponding neural CDF representation using multilayer perceptrons is also presented to obtain a compact and continuous representation while improving computation efficiency. We demonstrate the effectiveness of CDF with planar obstacle avoidance examples and with a 7-axis Franka robot in inverse kinematics and manipulation planning tasks.

翻译：符号距离场是机器人学中一种常用的隐式形状表示方法，它以易于与控制、优化和学习技术相结合的形式，提供关于物体和障碍物的几何信息。通常，SDF用于表示任务空间中的距离，这对应于我们在三维世界中感知到的熟悉距离概念。然而，从数学上讲，SDF可以用于其他空间，包括机器人构型空间。对于机械臂而言，其构型空间通常对应于机器人每个关节的关节角度。虽然在机器人规划中习惯性地表达构型空间的哪些部分与障碍物无碰撞，但将这些信息视为构型空间中的距离场则较为少见。本文展示了在机器人构型空间中考虑SDF用于优化的潜力，我们称之为构型空间距离场。与任务空间中SDF的使用类似，CDF提供高效的关节角度距离查询和直接的导数访问。大多数方法将整体计算分为两部分：一部分在任务空间进行，随后一部分在构型空间进行。相反，CDF允许控制、优化和学习问题以统一的方式利用隐式结构。特别地，我们提出了一种高效的计算和融合CDF的算法，该算法可推广至任意场景。同时提出了一种使用多层感知器的神经CDF表示，以获得紧凑且连续的表示，同时提高计算效率。我们通过平面避障示例以及在7轴Franka机器人上进行的逆运动学和操作规划任务，验证了CDF的有效性。