Robot Inverse Kinematics for Offset Arm Convergence
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Solution Overview
Problem
Conventional techniques fail to perform inverse transform processes effectively in robots with offset arms, leading to errors and divergence in calculations due to initial errors in convergence, especially when the link length d5 is non-zero, resulting in incorrect reflection of offset components and potential misdetected reachability.
Innovation Solution
A controller is designed to perform inverse transform processing by provisionally setting the angle of the sixth axis, calculating a provisional target position, and iteratively refining the angle until the difference between estimated and provisionally decided angles is within a predetermined value, using a method that sets the link length d5 to zero for initial calculations and repeatedly updates based on evaluation matrices.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional inverse transform techniques are applied to robots with offset arms (d5≠0), then the calculation process can be executed, but the calculation diverges or requires excessive repetition times due to large initial errors
Solution Approach 1:
The patent applies preliminary action by pre-calculating and storing the relationship between the sixth axis angle and the offset component in a lookup table before the inverse transform process. During actual operation, the system retrieves pre-computed correction values based on the provisionally decided sixth axis angle, avoiding the need to handle complex offset calculations in real-time and ensuring convergence without excessive repetition.
Solution Approach 2:
The patent changes the parameter representation by separating the offset component (d5) from the main inverse transform calculation. It introduces a correction parameter that adjusts the provisional sixth axis angle based on the offset, transforming the problematic calculation into a manageable form that converges reliably while maintaining precision.
2Productivity
If the link length d5 is set to zero for initial inverse transform calculations, then the calculation converges easily, but the offset component is not correctly reflected in the result
Solution Approach 1:
The patent implements feedback by using the result from the simplified inverse transform (with d5=0) as a provisional value, then correcting this value based on the actual offset d5. The correction is computed using the pre-stored relationship between the sixth axis angle and offset component, and this correction feedback is applied to obtain the final accurate axis angles that properly reflect the offset.
Solution Approach 2:
The patent introduces an intermediary correction mechanism that mediates between the simplified calculation (d5=0) and the actual physical configuration (d5≠0). The lookup table storing the angle-offset relationship acts as an intermediary that translates the provisional result into the final accurate result, preserving both calculation speed and precision.
3Ease of operation
If the conventional technique linearizes the offset region on the assumption of d5=0, then the calculation can proceed, but the offset component cannot be correctly reflected in the reachable range
Solution Approach 1:
The patent performs preliminary action by pre-computing the correct relationship between the sixth axis angle and the offset component across the full range of motion, storing this information in a lookup table. This pre-computation accounts for the actual offset d5≠0, ensuring that when the inverse transform is executed, the offset component is correctly reflected in the reachable range determination without linearization approximations.
Data Source
AI summary
A robot has a vertical 6-axis articulated arm having an offset arm having a fifth axis and length link, and mutually linking fourth and sixth axes. The fourth and sixth axes shaft centers are parallel. The articulated arm has a head portion designated as a control point. A position and an orientation targeted to the control point is processed by an inverse transform to calculate angles of the axes. A provisional target position of the sixth axis is obtained by subtracting the link length from a target position of the sixth axis. The link length to the provisional target position is given zero to perform the inverse transform process. Processed results are evaluated. Until a difference between a calculated sixth-axis angles and provisionally decided sixth-axis angles becomes equal to or less than a predetermined value, processes started from the angle provisional decision of the sixth axis are repeatedly performed.