7-DOF Robotic Arm Angle Intervals Without IK Singularities

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Solution Overview

Problem

Existing inverse kinematics solving methods for 7-DOF robotic arms are prone to errors and singularities, and analytical methods are inadequate for robotic arms with redundancy, leading to inaccuracies in calculating arm angle intervals.

Innovation Solution

A method for calculating the arm angle interval of a 7-DOF robotic arm using a joint angle calculation model and differential relationship model, which involves obtaining extreme arm angles and joint angles at maximum and minimum values to determine the arm angle interval, allowing for accurate control of the robotic arm's joints.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Adaptability or versatility

If numerical solving using Jacobian iterative calculations is used, then the robotic arm can handle complex 7-DOF configurations, but calculation errors and singularities occur leading to inaccurate arm angle intervals

Engineering Contradiction:

Improvecapability to handle 7-DOF configurationsVSAvoidaccuracy of arm angle intervals

Core Design Contradiction:

Adaptability or versatilityVSMeasurement precision

Solution Approach 1:

The patent replaces the numerical iterative calculation system (Jacobian method) with an analytical solution system based on trigonometric equations and differential relationships. This substitution eliminates the computational errors and singularities inherent in numerical methods while maintaining the ability to solve 7-DOF inverse kinematics, thereby improving measurement precision without sacrificing adaptability.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Solution Approach 2:

The patent introduces differential relationships as an intermediary between joint angles and arm angles. By establishing differential equations that relate changes in joint angles to changes in arm angles, the method provides a precise analytical pathway to determine arm angle intervals, avoiding the direct iterative calculation errors of the Jacobian method.

Inventive Principle:

Principle #24Intermediary (Mediator)

2Measurement precision

If analytical solving methods are used, then calculation accuracy is improved, but the method is only applicable to 6-DOF or fewer robotic arms and becomes difficult to extend to 7-DOF redundant robotic arms

Engineering Contradiction:

Improveaccuracy of arm angle intervalsVSAvoidapplicability to 7-DOF redundant robotic arms

Core Design Contradiction:

Measurement precisionVSAdaptability or versatility

Solution Approach 1:

The patent segments the 7-DOF robotic arm system into a 6-DOF core system (for which analytical solutions exist) plus one redundant degree of freedom. By applying analytical methods to the 6-DOF subsystem and separately determining the interval of the redundant joint, the method extends analytical precision to 7-DOF configurations without requiring complete rederivation of the analytical solution.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The patent adds the dimension of interval analysis to the traditional point-wise analytical solution. Instead of solving for single joint angle values, the method solves for intervals of joint angles that satisfy the inverse kinematics constraints, thereby extending analytical methods to handle the redundancy of 7-DOF systems while maintaining calculation accuracy.

Inventive Principle:

Principle #17Another dimension (Dimensionality change)

3Ease of operation

If traditional inverse solving methods are used, then the robotic arm can operate with flexibility, but the arm angle interval calculations are inaccurate due to errors and singularities

Engineering Contradiction:

Improveoperational flexibilityVSAvoidaccuracy of arm angle intervals

Core Design Contradiction:

Ease of operationVSMeasurement precision

Solution Approach 1:

The patent replaces the error-prone numerical iterative system with an analytical trigonometric system that provides exact solutions. This substitution maintains operational flexibility by still solving the full 7-DOF inverse kinematics problem, but eliminates calculation errors and singularities that plague the Jacobian method, thereby improving the accuracy of arm angle interval calculations.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Data Source

PatentUS12528183B2Arm angle interval solving method and robotic arm using the same

Publication Date: 2026.01.20 UBTECH ROBOTICS CORP LTD

AI summary

A robotic arm angle interval inverse solving method and a robotic arm using the same are provided. The method includes: obtaining a joint angle calculation model and a differential relationship model of a target joint of the robotic arm; obtaining extreme arm angles corresponding to a joint angle of the differential relationship model at extreme values based on the differential relationship model; obtaining a joint arm angle interval corresponding to the target joint based on the extreme arm angle and the joint angle calculation model; and obtaining a target arm angle interval corresponding to the robotic arm based on the joint arm angle interval corresponding to the target joint of the robotic arm. In comparison with the existing method to solve the arm angle interval of the robotic arm, a more accurate arm angle interval can be obtained.