Proxima: An Approach for Time or Accuracy Budgeted Collision Proximity Queries

—Many applications in robotics require computing a robot manipulator’s “proximity” to a collision state in a given configuration. This collision proximity is commonly framed as a summation over closest Euclidean distances between many pairs of rigid shapes in a scene. Computing many such pairwise distances is inefficient, while more efficient approximations of this procedure, such as through supervised learning, lack accuracy and robustness. In this work, we present an approach for computing a collision proximity function for robot manipulators that formalizes the trade-off between efficiency and accuracy and provides an algorithm that gives control over it. Our algorithm, called P ROXIMA , works in one of two ways: (1) given a time budget as input, the algorithm returns an as-accurate-as-possible proximity approximation value in this time; or (2) given an accuracy budget , the algorithm returns an as-fast-as-possible proximity approximation value that is within the given accuracy bounds. We show the robustness of our approach through analytical investigation and simulation experiments on a wide set of robot models ranging from 6 to 132 degrees of freedom. We demonstrate that controlling the trade-off between efficiency and accuracy in proximity computations via our approach can enable safe and accurate real-time robot motion-optimization even on high-dimensional robot models. a self-collision; end-effector translation error (summed in the case of robots with multiple end-effectors); end-effector rotation error in radians (summed in the case of robots with multiple end-effectors); and the average joint velocity.