Inverse Kinematics Numerical Method for Offset Wrist Robots
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Solution Overview
Problem
Existing methods for inverse kinematics calculation of six-degree-of-freedom serial robots with an offset wrist require extensive calculations, leading to high burdens on robot controllers and poor real-time performance due to the lack of analytical solutions.
Innovation Solution
A numerical method that uses the analytical solution of a non-offset wrist as an approximate solution for an offset wrist, iteratively refining the joint variables using a Jacobian matrix to minimize computation and improve convergence.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If geometric method or algebraic elimination method is used to solve inverse kinematics of six-degree-of-freedom serial robot with offset wrist, then analytical solution can be obtained, but calculation amount increases greatly causing heavy burden on robot controller
Solution Approach 1:
The patent applies preliminary action by using the analytical solution of a non-offset wrist robot as an initial approximate solution for the offset wrist robot. This preliminary result serves as a starting point for iterative refinement, reducing the computational burden compared to solving from scratch using geometric or algebraic elimination methods.
Solution Approach 2:
The patent introduces an intermediary approach by using the analytical solution of a simplified non-offset wrist model as a mediator to obtain an initial approximation. This intermediary solution then guides the iterative numerical method, bridging the gap between simple analytical solutions and complex exact solutions for offset wrist robots.
2Measurement precision
If optimization methods such as tabu searching method or hill-climbing method are used, then numerical solution can be obtained, but real-time performance deteriorates due to large calculation amount
Solution Approach 1:
The patent uses preliminary action by pre-calculating or using available analytical solutions of non-offset wrist robots as initial guesses. This preliminary information significantly reduces the number of iterations needed for convergence, thereby improving real-time performance compared to optimization methods that start from random or heuristic initial points.
Solution Approach 2:
The patent implements feedback through the iterative numerical method where the error between the calculated end-effector pose and the desired pose is continuously evaluated. This feedback drives the correction of joint variables using the Jacobian matrix, ensuring convergence to the accurate solution while maintaining computational efficiency for real-time applications.
3Strength
If six-degree-of-freedom serial robot with offset wrist is used instead of non-offset wrist, then structure rigidity and 360-degree rotation capability are improved, but inverse kinematics calculation burden increases
Solution Approach 1:
The patent applies preliminary action by utilizing the analytical solution of a non-offset wrist robot (a simplified model) as an initial approximation for the offset wrist robot. This preliminary solution provides a good starting point that is computationally inexpensive to obtain, and then iterative refinement achieves the accurate solution needed for the more complex offset wrist configuration.
Solution Approach 2:
The patent uses parameter changes by transitioning from the exact analytical solution approach (which is computationally heavy) to an iterative numerical approach starting from a preliminary solution. This changes the computational parameters from exact but expensive calculations to approximate but efficient iterative refinements, reducing the overall calculation burden while maintaining accuracy.
Data Source
AI summary
Disclosed is a method for obtaining the inverse kinematics of a six-degree-of-freedom serial robot with an offset wrist. The method uses the analytical solution of the inverse kinematics of the six-degree-of-freedom serial robot with a non-offset wrist as an approximate solution of the inverse kinematics of the six-degree-of-freedom serial robot with an offset wrist and an initial point for iteration, and obtains a numerical solution of the inverse kinematics of the six-degree-of-freedom serial robot with an offset wrist meeting the accuracy through continuously iterative approaching. The present disclosure has faster convergence and less calculation amount relative to the traditional calculation method, reduces the computation burden for a robot controller, and improves the real-time performance.