Redundant Robot Inverse Kinematics Using Jacobian Null Space
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Solution Overview
Problem
Existing methods for solving inverse kinematics in redundant robots face inefficiencies, such as high computational costs and uncontrollable results, particularly due to infinite solutions and potential joint angle discontinuities like jumps and flips.
Innovation Solution
The method utilizes the null space of the Jacobian matrix to select configurations based on energy criteria, optimizing joint angles for minimal energy consumption, ensuring continuous and smooth joint movements by projecting joint velocities into the null space and using an energy cost function to determine optimal solutions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If numerical iterative inverse kinematics based on Jacobian pseudoinverse matrix is used, then the end effector error converges to zero, but the computational amount is large and the iteration result is uncontrollable causing robot jitter and joint angle exceeding working range
Solution Approach 1:
The patent extracts and utilizes the null space component from the complete Jacobian inverse solution. By separating the null space motion from the primary inverse kinematics solution, the method eliminates unnecessary computational iterations while maintaining accuracy. The null space projection directly provides the optimal joint angle configuration without requiring iterative convergence processes.
Solution Approach 2:
The patent performs preliminary calculation of the null space basis matrix before the inverse kinematics solving process. This pre-computed null space information is then directly applied to obtain the optimal solution, eliminating the need for iterative refinement and reducing computational complexity while ensuring the solution remains within working ranges.
2Productivity
If analytical inverse kinematics with additional geometric constraints is used, then the computational amount is small and accurate solutions are obtained, but the solution is not optimal among infinite inverse solutions and the robot cannot be solved directly at singular points
Solution Approach 1:
The patent merges the advantages of analytical methods (computational efficiency) with the benefits of numerical methods (handling infinite solutions). By combining the analytical Jacobian matrix computation with null space projection, the method achieves both computational efficiency and the ability to select optimal solutions from the infinite possibilities, including at singular points.
Solution Approach 2:
The patent introduces dynamic selection capability through null space projection. Instead of fixed geometric constraints, the method dynamically determines the optimal configuration by projecting onto the null space, allowing the robot to adaptively select the best solution from infinite possibilities based on current configuration and task requirements.
3Measurement precision
If numerical iterative method projects end effector error to each joint for proportional control, then the error converges to zero, but the joint angle easily exceeds working range and the robot will jitter
Solution Approach 1:
The patent introduces the null space projection as an intermediary between the end effector error and joint angle adjustments. This intermediary ensures that error correction occurs only in directions that do not violate joint working ranges, preventing jitter and maintaining stability while still achieving precise position and posture control.
Data Source
AI summary
An inverse kinematics solving method for redundant robot as well as a redundant robot using the same are provided. The method includes: obtaining an expression of a Jacobian matrix null space of a current configuration of each robotic arm of the redundant robot corresponding to a preset end pose of the robotic arm according to the preset end pose, and obtaining a relation between an angular velocity of the joints of the redundant robot in the Jacobian matrix null space of the current configuration based on the obtained expression; traversing the Jacobian matrix null space using the relation, and building an energy cost function of the redundant robot based on the relation; obtaining a target joint angle of each joint of the redundant robot based on the optimal inverse kinematics solution to transmit to the servo of the joint so as to control the joint.