6-Axis Robot Joint Angle Calculation for Offset Wrist Kinematics
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Solution Overview
Problem
The analysis of inverse kinematics for PUMA-type robots with offsets in the wrist portion is computationally intensive, requiring high-speed processors for real-time calculations to ensure smooth operation.
Innovation Solution
A robot control apparatus that determines the angle of each joint in a 6-axis vertical articulated robot by calculating a point of interest on a circle around the intersection point of the fifth and sixth axes, estimating the intersection point of the fifth and fourth axes based on an inner product value, and calculating the rotation angles of the first three joints using geometric relationships.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If analytical inverse kinematics calculation is used for PUMA-type robot with wrist offset, then accurate joint angles can be obtained, but calculation load becomes heavy and processing time increases
Solution Approach 1:
The inverse kinematics calculation is divided into two independent parts: (1) calculating the wrist center position using the end effector position and orientation, and (2) calculating the joint angles from the wrist center position. This segmentation allows each part to be computed separately and efficiently, reducing the overall calculation load while maintaining accuracy.
Solution Approach 2:
The wrist center position is calculated in advance as an intermediate step before computing the final joint angles. By performing this preliminary calculation, the complex six-axis inverse kinematics problem is broken down into simpler sub-problems that can be solved more quickly, enabling real-time control.
2Productivity
If high-speed processor is used to perform real-time inverse kinematics calculation, then smooth robot operation is achieved, but system cost and complexity increase
Solution Approach 1:
The patent replaces the need for high-speed hardware processors with an optimized mathematical algorithm. By substituting the computational approach rather than relying on brute-force processing power, the system achieves real-time performance with standard processors, reducing hardware complexity and cost.
3Reliability
If conventional inverse kinematics algorithm is used for robot with wrist offset, then complete mathematical solution is obtained, but calculation time exceeds real-time control requirements
Solution Approach 1:
The patent extracts and isolates the wrist offset parameters from the general inverse kinematics equations. By separating the offset-related terms, the algorithm can directly compensate for the offset effect without performing complete symbolic manipulation of all parameters, significantly reducing calculation time while maintaining mathematical accuracy.
Data Source
AI summary
In a method of obtaining an angle of each joint of a 6-axis vertical articulated robot when a position and a posture of an end effector attached on a sixth axis are given, a predetermined amount of offset exists between a sixth axis and a fourth axis, and the method includes sequentially determining a point of interest, which is a point on a circumference of a circle having the predetermined amount as a radius, around a first intersection point, on a plane which includes the first intersection point which is an intersection point of the sixth axis and the fifth axis and the plane which is orthogonal to the sixth axis, calculating a second intersection point, which is an intersection point of the fourth axis and the third axis, when it is assumed that the point of interest is an intersection point of the fifth axis and the fourth axis, calculating an inner product value of a first vector directed from the calculated second intersection point to the point of interest and a second vector directed from the point of interest to the first intersection point, and estimating that the point of interest, when an absolute value of the inner product value is less than or equal to a predetermined threshold, is an intersection point of the fifth axis and the fourth axis.