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.

Algorithmic path planning of static robots in three dimensions using configuration space metrics

“…In addition, the total number of imaginary lines in the v-graph can be computed as: (24) where, 'd k ' is the number of edges of the kth . obstacle.…”

“…A majority of these models are nothing but extrapolation of proven 2D techniques in 3D space 16,28,34 However, new methods for the generation of c-space in such cases (i.e. 24 The usefulness of several new algorithms using v-graph technique has been demonstrated in spatial robotic workspace. 2,5,31 Customised solution for rapid computation of c-space obstacles has been addressed, 3 using geometric properties of collision detection between known static obstacles and the manipulator body, while sub-space method is being utilised in this regard.…”

A New Algorithm for CAD-Directed CMM Dimensional Inspection

“…In a configuration space method [4][5][6] the objects considered are polyhedrons. Configuration space characterises the position and orientation of an object.…”

Collision Free Path Planning for Multi-DoF Manipulators

“…As in the case of 2-DoF case, we have no idea about the direction to choose in order to avoid the obstacle. In this case, an earlier method, proposed by Red et al (Red et al, 1987), consists of using the 3D space made of the robots primary DoF. Then, by using a graphical user interface (GUI), the user moves the screen cursor to intermediate interference free points on the screen.…”