Multi-Axis Robot Inverse Kinematics With Axis-Invariant Modeling
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Solution Overview
Problem
Current methods for modeling and controlling multi-axis robots face challenges with complexity, accuracy, and computational efficiency, leading to stability issues and inefficiencies in developing autonomous control systems due to incomplete and inaccurate symbol frameworks and calculation methods.
Innovation Solution
A method using Axis-Invariant kinematics and dynamics modeling, which employs a chain topological symbol system and 3D operational algebra to describe multi-axis robots, enabling efficient calculation of kinematics and dynamics, and allowing for real-time control and parameterization of robot systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional modeling and control methods are used for multi-axis robots, then the system can be controlled, but the computational complexity increases substantially and the calculation accuracy is greatly affected
Solution Approach 1:
The patent segments the complex multi-axis robot system into modular components with standardized symbolic representations. By dividing the kinematic chain into discrete links and joints with defined transformation matrices, the computational problem becomes manageable through systematic decomposition rather than holistic complex calculation.
Solution Approach 2:
The patent transforms the modeling approach by changing parameters from traditional geometric descriptions to axis-invariant symbolic parameters. This parameter transformation enables consistent mathematical representations across different robot configurations, improving calculation accuracy while maintaining computational efficiency through standardized transformation rules.
2Adaptability or versatility
If the number of axes and degrees of freedom is increased to achieve more complex robot functions, then the robot capability is improved, but the system becomes complex and out-of-control
Solution Approach 1:
The patent establishes a universal symbolic framework that can represent any multi-axis robot configuration regardless of the number of degrees of freedom. The axis-invariant transformation matrices and standardized kinematic modeling approach provide a multi-functional solution that scales to complex systems without proportionally increasing computational burden.
Solution Approach 2:
The patent introduces dynamic adaptability through its symbolic framework that can accommodate varying numbers of axes and joint types. The system dynamically adjusts to different robot configurations by applying the same fundamental transformation principles, enabling complex capabilities while maintaining control through consistent mathematical relationships.
3Reliability
If traditional symbolic frameworks are used for robot modeling, then the model can be established, but the symbols and languages used are inaccurate and incomplete
Solution Approach 1:
The patent replaces traditional geometric and physical modeling approaches with a symbolic mathematical framework. By substituting conventional modeling methods with axis-invariant transformation matrices and standardized symbolic representations, the system achieves more accurate and complete models that can be systematically implemented.
4Reliability
If conventional control methods are applied to high complexity robots, then the robot can operate, but the computational time increases and real-time control is compromised
Solution Approach 1:
The patent performs preliminary establishment of axis-invariant transformation matrices and kinematic models before actual control operations. By pre-defining the symbolic framework and transformation relationships, the system reduces real-time computational requirements while maintaining control stability through consistently applied mathematical relationships.
Data Source
AI summary
The present invention proposes an inverse kinematics modeling and solving principle for multi-axis systems based on axis invariant, including: the D-H and D-H parameter determination principle based on fixed axis invarian, “Ju-Gibbs” quaternion and class direction cosine matrix principle, the inverse solution principle of general 6R and 7R robotic arms based on axial invariant. These principles are versatile, convenient, and precise. They can be set up as circuits, code, directly or indirectly, partially or completely within a multi-axis robot system. In addition, the present invention also includes analysis verification system constructed on these principles for designing and verifying multi-axis robot systems.