Time-Varying Stiffness Identification via Basis Function Expansion
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current time-varying stiffness identification methods are inaccurate and limited in applicability to dynamic interactions, requiring large datasets for consistency and being unsuitable for situations where limbs interact with the environment.
Innovation Solution
A dynamic interaction-oriented method using a collaborative robotic arm to collect displacement and force data, applying linear parameter varying and basis function expansion techniques to iteratively decouple dynamic interaction and restoring forces, allowing for accurate identification of time-varying stiffness in a single perturbation scenario.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If short data segments method or ensemble-based method is used to identify time-varying stiffness, then measurement precision is improved, but device complexity and loss of time increase due to requiring large datasets and lengthy experiment processes
Solution Approach 1:
The patent applies preliminary action by pre-defining basis functions (Fourier series, wavelets, or polynomials) to represent the time-varying stiffness characteristics before actual measurement. This allows the system to directly fit measured force and displacement data to these predefined functions, eliminating the need for lengthy experimental data collection and processing required by traditional methods.
Solution Approach 2:
The patent substitutes the mechanical data collection process with a mathematical modeling approach. Instead of collecting large datasets through physical experimentation, the method uses basis function expansion to directly represent and identify time-varying stiffness from limited measurement data, replacing the mechanical experimentation system with a computational mathematical system.
2Measurement precision
If short data segments method or ensemble-based method is used to identify time-varying stiffness, then measurement precision is improved, but device complexity increases due to requiring large datasets and multiple time-varying behavior consistency checks
Solution Approach 1:
The patent replaces complex mechanical data collection and processing systems with a mathematical basis function expansion approach. The time-varying stiffness is directly represented by expanding force and displacement data into predefined basis functions, eliminating the need for complex dataset management, segmentation, and consistency verification procedures.
Solution Approach 2:
The patent changes the parameter representation from raw time-series data requiring extensive processing to coefficients of basis functions. By expressing time-varying stiffness as a combination of predefined basis functions with time-dependent coefficients, the method simplifies the parameter space and reduces computational complexity while maintaining measurement precision.
3Loss of time
If linear parameter varying method or basis function expansion method is used, then loss of time is reduced by using single experiment data, but measurement precision deteriorates because these methods cannot be applied when limbs interact with the environment
Solution Approach 1:
The patent applies dynamics by using time-varying basis function coefficients to represent the dynamic characteristics of limb stiffness during environmental interaction. The method models stiffness as a dynamic parameter that changes over time through basis function expansion, allowing accurate representation of time-varying behavior during actual interaction tasks rather than static or isolated measurements.
Solution Approach 2:
The patent achieves universality by creating a method that works for both isolated limb measurements and environmental interaction scenarios. The basis function expansion approach can represent time-varying stiffness in various conditions, making the identification method universally applicable whether the limb is interacting with the environment or not, unlike previous methods limited to specific conditions.
4Adaptability or versatility
If traditional methods are used for time-varying stiffness identification, then adaptability is reduced because they cannot handle dynamic interaction scenarios, but device complexity is lowered
Solution Approach 1:
The patent achieves universality by developing an identification method based on basis function expansion that can handle both isolated limb measurements and environmental interaction scenarios. The time-varying stiffness model using basis functions is universally applicable across different interaction conditions, making the system adaptable to various dynamic scenarios while maintaining a relatively simple algorithmic structure.
Solution Approach 2:
The patent uses parameter changes by representing stiffness characteristics through time-varying coefficients of basis functions rather than fixed parameters. This allows the model to adapt to different interaction scenarios by changing the temporal behavior of the coefficients while keeping the underlying mathematical structure simple and consistent, achieving high adaptability without proportionally increasing algorithmic complexity.
Data Source
AI summary
The disclosure provides a dynamic interaction-oriented subject's limb time-varying stiffness identification method and device. The method includes: the combination of subject's limb displacement and measured force data or the combination of angle and measured torque data is collected; based on the time-varying dynamic system constructed based on a second-order impedance model, the linear parameter varying method is utilized to substitute the time-varying impedance parameters and reconstruct the restoring force/torque expression; iterative identification is performed on variable weights, dynamic interaction force/torque, and restoring force/torque by using time-varying dynamic parameters based on the dynamic interaction force/torque expression expanded from basis function; the time-varying stiffness is solved by using variable weights and dynamic interaction force/torque according to expression with substituted the time-varying impedance parameters. The disclosure not only improves the accuracy of the time-varying stiffness identification technology but also expands the application scenarios of the time-varying stiffness identification technology.