Offset-Arm Robot Inverse Kinematics for Stable Convergence
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional methods for inverse kinematics in robots with offset arms, such as those with a link length d5 connecting the fourth and sixth axes, face challenges in convergence calculation and accurate reach detection due to errors and divergence issues, especially when d5 is non-zero.
Innovation Solution
A controller is designed to perform inverse transformation by provisionally deciding angles and positions, setting d5 to zero for initial calculations, and iteratively refining these values until convergence is achieved, using a combination of angular and position calculations to ensure accurate axis angle determination.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional inverse transform methods are applied to robots with offset arms (d5≠0), then the structure avoids gaps and improves reliability, but the calculation diverges and convergence fails
Solution Approach 1:
The patent changes the parameter d5 (offset arm length) from its actual non-zero value to zero during the inverse transform calculation process. This parameter transformation allows the conventional inverse transform algorithm to converge properly while the system separately tracks and compensates for the actual offset through the relationship between P6 and P6' positions.
2Reliability
If the offset arm link length d5 is non-zero, then the robot structure is more reliable without gaps, but the calculation requires more repetition times and may diverge
Solution Approach 1:
The patent transforms the calculation parameter by setting d5=0, which dramatically improves calculation efficiency and convergence. The actual physical offset is preserved in the system model and compensated for through the positional relationship between the transformed coordinates (P6') and original coordinates (P6), maintaining accuracy while enabling fast convergence.
3Productivity
If d5 is set to zero for calculation, then convergence is achieved and calculation speed improves, but the offset component cannot be reflected correctly in the reach range
Solution Approach 1:
The patent introduces an intermediary coordinate system transformation where P6' represents the position in the transformed system (d5=0) and P6 represents the actual position (d5≠0). The relationship between these two coordinate systems serves as a mediator, allowing calculations to be performed in the simplified system while accurately reflecting the actual reach through the transformation relationship.
4Ease of operation
If conventional inverse transform is used with offset arm, then the robot can be controlled, but errors accumulate and precision is lost
Solution Approach 1:
The patent applies parameter transformation by setting d5=0 in the inverse transform algorithm, which eliminates the accumulation of errors that occurs with conventional methods. The transformation maintains controllability while preventing error accumulation through the mathematical relationship between the transformed coordinates and actual robot positions.
Data Source
Figure 1
Figure 2
Figure 3
AI summary
In an industrial robot provided with an offset arm, an inverse transform process can be used. One example is targeted to a robot (2) with a vertical 6-axis articulated arm having an offset arm (8), the offset am being provided with a fifth axis, mutually liking a fourth axis and a sixth axis, and having a link length (d5), shaft centers of the fourth and sixth axes being parallel with each other, the arm having a head portion designated as a control point, a position and an orientation targeted to the control point being processed by an inverse transform in order to calculate angles of the axes. The angle (θ6A) of the sixth axis provisionally decided, and from it angle, a direction of the offset arm (8) is obtained. A provisional target position (P6A) of the sixth axis is obtained by subtracting the link length d5 from a target position P6 of the sixth axis. The link length (d5) to the provisional target position (PA) is given zero in order to perform the inverse transform process. Processed results are then evaluated by an evaluation function. Until a difference between a calculated sixth-axis angles (θ6) and the provisionally decided sixth-axis angles (θ6A) becomes equal to or less than a predetermined value, processes started from the angel provisional decision of the sixth axis are repeatedly performed.