Optimal Dexterity Path Planning for Robotic Manipulators Using Rapid Workspace Density Approximation

Abstract

This paper introduces a path planning algorithm for executing robotic manipulation tasks with maximum dexterity in the workspace. This is achieved by using the workspace density of the end-effector as the objective function in a sampling-based planner. In doing so, the path planning algorithm prioritizes joint configurations that correspond to the highest density of local end-effector positions. This results in a singularity avoidant path planning algorithm that favors redundancy, making it a favorable approach for manipulation scenarios in which dexterity is paramount. However, due to the exponential relationship between the number of possible end-effector positions and the number of joints, computing the workspace density via traditional methods is computationally intractable for most modern industrial robots. In this paper, a newly developed approach is taken wherein the workspace density is approximated by a Gaussian mixture model that solves for the optimal workspace density function subject to higher-order statistical moment constraints. The statistical moments of the workspace density function are computed recursively with a minimum number of sample points by using a non-product quadrature rule known as the Conjugate Unscented Transform (CUT). This results in a computationally efficient framework that allows the user to trade accuracy and computation time by varying the number of mixture components and the number of statistical moments used in the workspace density approximation. To demonstrate, the algorithm is implemented on the Precision Assembled Space Structure (PASS) platform at NASA illustrating its effectiveness in dexterous robotic assembly tasks.