Robot Stiffness Ellipse Calculation Using Algebraic Solutions
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Solution Overview
Problem
Existing methods for controlling the stiffness of a robot's hand tip are inefficient when the lengths of two links are different, leading to poor controllability and slow calculation of the optimal stiffness ellipse, which is essential for flexible interaction with external forces.
Innovation Solution
A robot apparatus with three pairs of antagonistic actuators and a controlling device that uses operational expressions to algebraically calculate stiffness instruction values, reducing the calculation load and enabling rapid formation of the stiffness ellipse even when link lengths differ.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a convergent calculation method is used to form the optimal stiffness ellipse when link lengths are different, then the stiffness ellipse can be formed, but the calculation time becomes excessively long and controllability deteriorates
Solution Approach 1:
The invention changes the calculation parameters by deriving closed-form algebraic solutions for the stiffness ellipse parameters (tilt angle, major axis, minor axis) based on the Jacobian matrix and actuator stiffness values. This eliminates the need for time-consuming iterative convergent calculations while maintaining accuracy, directly resolving the contradiction between formation accuracy and calculation time.
Solution Approach 2:
The invention substitutes the mechanical iterative calculation process with an algebraic analytical solution system. By using direct mathematical formulas that compute the stiffness ellipse parameters from the actuator configuration and stiffness values, the system replaces the slow convergent calculation mechanism with a fast algebraic computation mechanism.
2Productivity
If algebraic solution methods are used to solve the relational expression for stiffness ellipse, then calculation speed improves, but the method is not applicable when link lengths are different
Solution Approach 1:
The invention generalizes the algebraic solution by deriving parameter expressions that explicitly account for different link lengths. The stiffness ellipse parameters are expressed as functions of the Jacobian matrix elements and actuator stiffness values, which naturally adapt to any link length configuration. This maintains calculation speed while achieving universality across different robotic arm geometries.
Solution Approach 2:
The invention creates a universal algebraic solution framework that can handle both equal and unequal link length cases. The derived formulas for the stiffness ellipse parameters work regardless of the specific link length relationship, making the method universally applicable to various robotic manipulator configurations while maintaining high calculation speed.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
The solution allows for rapid and efficient formation of the stiffness ellipse, improving the controllability of the robot's hand tip by reducing calculation time and enabling flexible interaction with external forces.
Implementation Method 1
A pneumatic rubber artificial muscle represented by McKibben artificial muscle in artificial muscles has viscoelastic characteristic similar to that of a muscle.
Data Source
AI summary
There is provided a robot apparatus that can rapidly obtain an ellipse indicating a stiffness characteristic, even if lengths of two links are different from each other.