US 4,680,519 AGranted

Recursive methods for world-to-joint transformation for a robot manipulator

AssigneeGeneral Electric Company

InventorsSujeet Chand, Ahmad Sadre

Life of this patent

Estimating the term…

Loading patent…

Abstract

A method for controlling an articulated robot manipulator with an offset wrist made with only rotary joints. The method relates to transforming a given position and orientation of the robot tool or end effector in Cartesian space to the equivalent joint angles of the robot. Commands generated from the joint angles are sent to actuators connected to the rotary joints, where the desired motion of the robot tool is generated. This method of transforming a point in Cartesian space to joint angles is accomplished by providing a cross-product and dot-product recursive methods that employ the robot geometry to determine the location of the the end effector, such that the computational complexity of the techniques allows real-time computations for current state of the art microprocessors.

Claims12

Dependent claims

In an articulated manipulator of the type having at least a first, a second, and a third link respectively associated with a first, a second, and a third axis of rotation of motion about an offset wrist, each link and motion being associated with a first, a second, and a third joint, a method of determining a first, a second, and a third joint angle, respectively, for each of the axis of rotation to provide control data for activating actuators being associated with a corresponding joint, to permit positioning of an end of the manipulator at a desired point, said method comprising the steps of:

(A) obtaining data identifying a desired end point position and orientation, the data including an end point position vector and an end point approach orientation vector;
(B) multiplying the end point approach orientation vector by the length of the first link;
(C) producing a first set of coordinates, by subtracting the result of step (B) of multiplying from the end point position vector;
(D) determining a first vector from the first set of coordinates along the first axis of rotation with a length of the first link;
(E) setting initially a second set of coordinates equal to the first set of coordinates;
(F) determining from the second set of coordinates a second vector along the third axis of rotation, with a length of the third link;
(G) calculating the cross-product of the first vector and second vector, to produce a third vector;
(H) multiplying the third vector by the length of the second link;
(I) computing an estimate of the second set of coordinates by subtracting the result of step (H) of multiplying, from the first set of coordinates;
(J) repeating steps (F) of determining, through steps (I) of computing, until the difference between any two successive estimations is less than a predetermined minimum value;
(K) determining said joint angles from the second set of coordinates;
(L) generating position commands from said joint angles;
and
(M) sending the position commands to the actuator associated with a manipulator joint to control the manipulator joint.

11 more elements

In an articulated manipulator of the type having at least a first, a second, and a third link respectively associated with a first, a second, and a third axis of rotation of motion about an offset wrist, each link and motion being associated with a first, a second, and a third joint, a method of determining a first, a second, and a third joint angle for each of the axis of rotation, to provide control data for activating actuators being associated with a corresponding joint, to permit positioning of an end of the manipulator at a desired point, said method comprising the steps of:

(A) obtaining data identifying a desired end point position and orientation, the data including an end point position vector and an end point approach orientation vector;
(B) multiplying the end point approach orientation vector by the length of the first link;
(C) producing a first set of coordinates by subtracting the result of step (B) of multiplying, from the end point position vector;
(D) determining a first vector from the first set of coordinates along the second axis of rotation with a length of the second link;
(E) subtracting the first vector from the first set of coordinates to produce a second set of coordinates;
(F) constructing a second vector from the second set of coordinates along the first axis of rotation with a length of the third link;
(G) computing an estimate of said first joint angle from the dot product of the first vector and second vector;
(H) repeating steps (D) of determining through (G) of computing, until the absolute value of the estimate of said first joint angle is less than a predetermined minimum value;
(I) determining said joint angles from said first joint angle;
(J) generating position commands from said joint angles;
and
(K) sending the position commands to the actuator connected to a manipulator joint to control the manipulator joint.

9 more elements

In a computer controlled articulated manipulator of the type having at least a first, a second, and a third link respectively associated with a first, a second, and a third axis of rotation of motion about an offset wrist, each link and motion being associated with a first, a second, and a third joint, and having a first and second processing method associated with the computer, a method of determining a first, a second, and a third joint angles respectively for each of the axis of rotation to provide control data for activating actuators being associated with a corresponding joint, to permit positioning of an end of the manipulator at a desired point, said method comprising the steps of:

(A) providing data identifying a desired end point position, the data including a cartesian point on a trajectory of the end point, and predetermined limits for the second joint angle;
(B) testing the second joint angle against the predetermined limits for the second joint angle;
(C) computing the joint angles when the second joint angle is within the predetermined limits by the first processing method;
(D) computing the joint angles, when the second joint angle is outside the predetermined limits by the second processing method;
(E) generating position commands from said joint angles;
and
(F) sending position commands to the actuator connected to a manipulator to control the manipulator joint;

4 more elements

Dependencies are inferred from the claim text.