Inertial Parameter Identification in Robotics: A Survey
Abstract
:1. Introduction
1.1. Motivation and Related Works
1.2. Problem Formulation and Proposed Contributions
2. Robot Modeling and Control in the Context of Parameter Identification
2.1. Inverse and Direct Dynamic Models
2.2. Base Parameters and Identification Model
2.3. Control Strategy
3. Inverse Dynamic Identification Model (IDIM) and Least-Squares (LS) Estimation Methods
3.1. Ordinary, Weighted and Iteratively Reweighted Least-Squares (IDIM-OLS, -WLS, -IRLS)
3.2. Total Least-Squares (IDIM-TLS)
4. The Instrumental Variables (IV) and Maximum Likelihood (ML) Approaches
4.1. Inverse Dynamics Identification Model (IDIM) and Instrumental Variables (IV)
4.2. Maximum Likelihood (ML) Identification Method
5. The Output Error (OE) and Input Error (IE) Identification Approaches
5.1. Closed-Loop Output Error (CLOE)
5.2. Closed-Loop Input Error (CLIE)
5.3. The Direct and Inverse Dynamic Identification Model (DIDIM) Algorithm
6. Direct Dynamics Identification Model (DDIM) with Nonlinear Kalman Filtering (NKF) and Neural Networks (NN) Methods
6.1. Direct Dynamics Identification Model (DDIM) and Nonlinear Kalman Filtering (NKF)
6.2. Parameter Identification Using an Adaline Neural Network (AdaNN)
6.3. Parameter Identification with Hopfield-Tank Recurrent Neural Networks (HTRNN)
7. Enforcing Physical Consistency within Inertial Parameter Identification
7.1. Mathematical Formulation of the Physical Consistency Constraints within a Parameter Identification Process
7.2. Preventing Marginal Physicality
8. Introducing the BIRDy Matlab Toolbox: A Benchmark for Identification of Robot Dynamics
- 1.
- selecting an appropriate model for the studied system,
- 2.
- designing a state trajectory which excites the different components of this model,
- 3.
- collecting a bunch of experimental data by having the—real or simulated—system follow the generated excitation trajectory,
- 4.
- executing the selected identification process,
- 5.
- evaluating the quality of the results by comparing the predicted and actual torques along a validation trajectory.
8.1. Symbolic Model Generation
8.2. Trajectory Data Generation
8.3. Experiment Data Generation and Pre-Processing
9. Benchmarking Inertial Parameter Identification Algorithms: Monte Carlo Simulations and Validation Using BIRDy
9.1. Hardware Description and Experiment Setup
9.2. Selected Figures of Merit for Performance Evaluation
- 1.
- the average relative angle difference defined as
- 2.
- the average relative torque difference defined as
- 3.
- the mean total time that is required to compute one parameter estimate,
- 4.
- the mean number of iterations until convergence,
- 5.
- the mean number of model simulations (for methods which require it).
9.3. Implementation Details
9.3.1. IDIM-OLS, -WLS, -IRLS and -TLS Implementations
9.3.2. ML Implementation
- where denotes the error at iteration i, defined following (36) as ;
- , with j the index and i the iteration number.
- maximum number of iterations: .
9.3.3. IDIM-IV Implementation
- where denotes the error at iteration i, defined as ;
- , with j the index and i the iteration number.
- maximum number of iterations: .
9.3.4. DIDIM Implementation
- where denotes the torque error at iteration i, defined as . Please note that unlike IDIM-IV, we here make use of the simulated joint positions to compute the observation matrix;
- , with j the parameter index and i the iteration number.
- maximum number of iterations: .
9.3.5. Relevant Details of the CLIE and CLOE Implementations
- ,(resp. ), ,(resp. ) with j the parameter index and i the iteration number.
- maximum number of iterations: .
9.3.6. DDIM-NKF Implementation
9.3.7. AdaNN Implementation
9.3.8. HTRNN Implementation
9.3.9. Physically Consistent PC-OLS, -WLS, -IRLS, -IV and -DIDIM Implementations
9.4. Case Study on the Simulated TX40 and RV2SQ
9.5. Validation Experiments on the Real TX40 and RV2SQ
10. Results, Discussion and Perspectives
10.1. Analysis and Discussion of the Results
10.1.1. Noise Immunity
10.1.2. Estimation Accuracy
10.1.3. Convergence and Computational Complexity
10.2. General Discussion and Perspectives
11. Conclusions and Future Works
Funding
Informed Consent Statement
Data Availability Statement
- BIRDy source code: https://github.com/TUM-ICS/BIRDy
- Experimental data: http://doi.org/10.5281/zenodo.4728085
- Experimental results: http://doi.org/10.5281/zenodo.4679467
Acknowledgments
Conflicts of Interest
Abbreviations
AdaNN | Adaline Neural Network |
SMU | Set Membership Uncertainty |
IDIM | Inverse Dynamics Identification Model |
WLS | Weighted Least-Squares |
TLS | Total Least-Squares |
DIDIM | Direct and Inverse Dynamics Identification Model |
CLOE | Closed-Loop Output Error |
EKF | Extended Kalman Filter |
UKF | Unscented Kalman Filter |
CDKF | Central Difference Kalman Filter |
SPKF | Sigma-Point Kalman Filter |
NKF | Nonlinear Kalman Filter |
DoF | Degrees of Freedom |
DDM | Direct Dynamic Model |
FOM | Figure Of Merit |
PC | Physically Consistent |
HTRNN | Hopfield-Tank Recurrent Neural Network |
SDP | Semi-Definite Programming |
OLS | Ordinary Least-Squares |
IRLS | Iteratively Reweighted Least-Squares |
GTLS | Generalized Total Least-Square |
IV | Instrumental Variables |
CLIE | Closed-Loop Input Error |
SREKF | Square-Root Extended Kalman Filter |
SRUKF | Square-Root Unscented Kalman Filter |
SRCDKF | Square-Root Central Difference Kalman Filter |
ML | Maximum Likelihood |
PF | Particle Filter |
CoM | Center of Mass |
IDM | Inverse Dynamic Model |
MCS | Monte Carlo Simulation |
LMI | Linear Matrix Inequality |
Appendix A. List of Implemented Identification Methods
Least-Squares | OLS, WLS, TLS, IRLS |
Output Error | CLIE, CLOE, DIDIM |
Kalman Filters | EKF, SREKF, UKF, SRUKF, CDKF, SRCDKF |
Neural Networks | AdaNN, HTRNN |
Other | IDIM-IV, ML |
Physically Consistent | PC-OLS, PC-WLS, PC-IRLS, PC-IV, PC-DIDIM |
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MCS Experimental Conditions | TX40 Decimation 1 | TX40 Decimation 4 | RV2SQ Decimation 1 |
---|---|---|---|
MCS-TX40-1-1 | MCS-TX40-4-1 | MCS-RV2SQ-1-1 | |
MCS-TX40-1-2 | MCS-TX40-4-2 | MCS-RV2SQ-1-2 | |
MCS-TX40-1-3 | MCS-TX40-4-3 | MCS-RV2SQ-1-3 | |
MCS-TX40-1-4 | MCS-TX40-4-4 | MCS-RV2SQ-1-4 | |
MCS-TX40-1-5 | MCS-TX40-4-5 | MCS-RV2SQ-1-5 |
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Leboutet, Q.; Roux, J.; Janot, A.; Guadarrama-Olvera, J.R.; Cheng, G. Inertial Parameter Identification in Robotics: A Survey. Appl. Sci. 2021, 11, 4303. https://doi.org/10.3390/app11094303
Leboutet Q, Roux J, Janot A, Guadarrama-Olvera JR, Cheng G. Inertial Parameter Identification in Robotics: A Survey. Applied Sciences. 2021; 11(9):4303. https://doi.org/10.3390/app11094303
Chicago/Turabian StyleLeboutet, Quentin, Julien Roux, Alexandre Janot, Julio Rogelio Guadarrama-Olvera, and Gordon Cheng. 2021. "Inertial Parameter Identification in Robotics: A Survey" Applied Sciences 11, no. 9: 4303. https://doi.org/10.3390/app11094303
APA StyleLeboutet, Q., Roux, J., Janot, A., Guadarrama-Olvera, J. R., & Cheng, G. (2021). Inertial Parameter Identification in Robotics: A Survey. Applied Sciences, 11(9), 4303. https://doi.org/10.3390/app11094303