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Parameter estimation Demo by Unscented Kalman Filter (UKF) 12. Example of dynamics is for the 1 DoF arm with spring, damping, and frictional forces at a joint. Joint angle is measured, then, unknown damping and frictional coefficients are identified by UKF 34. In spite of discontinuous model of frictional force, UKF can be applied dislike Extended Kalman Filter (EKF).
This code was employed to estimate unknown parameters for the following publication(s):
- Optimal swimming locomotion of snake-like robot in viscous fluids, Journal of Fluids and Structures, Vol. 123 (2023).
https://doi.org/10.1016/j.jfluidstructs.2023.104007
@article{YAMANO2023104007,
title = {Optimal swimming locomotion of snake-like robot in viscous fluids},
journal = {Journal of Fluids and Structures},
volume = {123},
pages = {104007},
year = {2023},
issn = {0889-9746},
doi = {https://doi.org/10.1016/j.jfluidstructs.2023.104007},
author = {A. Yamano and T. Kimoto and Y. Inoue and M. Chiba}
}
- Fluid force identification acting on snake-like robots swimming in viscous fluids, Journal of Fluids and Structures, Vol. 106 (2021). https://doi.org/10.1016/j.jfluidstructs.2021.103351
@article{YAMANO2021103351,
title = {Fluid force identification acting on snake-like robots swimming in viscous fluids},
journal = {Journal of Fluids and Structures},
volume = {106},
pages = {103351},
year = {2021},
issn = {0889-9746},
doi = {https://doi.org/10.1016/j.jfluidstructs.2021.103351},
author = {A. Yamano and K. Shimizu and M. Chiba and H. Ijima},
keywords = {Snake-like robot, Swimming motion, Highly viscous fluid, Unscented Kalman filter, Parameter estimation}
}
Dynamics for the 1 DoF arm with spring, damping, and frictional forces at a joint is denoted as follows,
where damping and friction coefficients;
Then, state space representation is denoted as,
where
Unknown damping and frictional coefficients are added to the expanded state vector as
Then, the expanded state representation is obtained as
where
After that, the dynamics is discretized for time to apply UKF ("./functions/c2d_func.m" [3]).
[Step 1] Edit parameters
Edit code in "param_setting.m".
Process model with the state-space representation
%% system parameter
%%[0] continuous time system
J = 1;
k = 1;
f =@( x)[ x(2);
-1/J*x(3)*x(2) - 1/J*x(4)*sign( x(2)) - 1/J*k*x(1);
0;
0];
B = [ 0;
1/J;
0;
0];
bd = [ 1;
1;
0;
0];
C = [ 1 0 0 0];
ut = @( t)( 1.0);
[Step 2] Start analysis
Execute "demo.m".
Time series of state
Time series of output
Identified damping and friction coefficients;
Footnotes
-
Julier, S.J., Uhlmann, J.K., 2004. Unscented filtering and nonlinear estimation. Proc. IEEE 92 (3), 401–422. ↩
-
Julier, S.J., Uhlmann, J.K., Durrant-Whyte, H.F., 1995. A new approach for filtering nonlinear systems. In: Proceedings of 1995 American Control Conference. ACC’95 3, pp. 1628–1632. http://dx.doi.org/10.1109/ACC.1995.529783. ↩
-
足立 修一,丸田 一郎,「カルマンフィルタの基礎」,東京電機大学出版局. ↩
-
Fluid force identification acting on snake-like robots swimming in viscous fluids, Journal of Fluids and Structures, Vol. 106 (2021).
https://doi.org/10.1016/j.jfluidstructs.2021.103351 ↩