Robot Path Planning in Three Dimensions Using the Direct Subspace

Abstract

An efficient subspace approach is used to find collision-free paths in congested workspaces for a general class of robots having revolute and/or prismatic joints. A three-dimensional joint space is formed by mapping the workspace obstacles represented by polyhedral elements into the robot’s primary degrees-of-freedom comprising the first three robot links, also modeled by polyhedral elements. In this approach the secondary degrees-of-freedom (>3), including objects grasped by the robot end-effector, are bounded by a box attached to the distal primary link. The joint space obstacles represent forbidden space that limits the allowable robot configurations. Paths are then planned on a two-dimensional direct subspace of the joint space using graphics cursor input. Methods of iteration elimination are used to reduce the computational time required to transform obstacles into the joint space.