Omnidirectional Mobile Robot Dynamic Model Identification by NARX Neural Network and Stability Analysis Using the APLF Method
Abstract
:1. Introduction
2. Omnidirectional Mobile Robot Model
2.1. Robot Kinematic Model
2.2. Robot Dynamic Model
3. Using NARX Neural Network to Identify Dynamic Model
3.1. Introduction to NARX Neural Network
3.2. NARX Neural Network Training Data Selection And Experiment
4. NARX Neural Network Stability Conditions
4.1. Use LDI Method to Represent NARX Neural Network
4.2. Minimum Representation
4.3. NARX Neural Network Stability Analysis
5. Optimized APLF Method
Algorithm 1 optimized APLF 

6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Parameter  Parameter Description  Value 

m  Robot mass  10 kg 
${R}_{a}$  Motor armature resistance  1.2 $\Omega $ 
L  Wheel to robot centroid distance  0.17 m 
r  Wheel radius  0.05 m 
${I}_{0}$  Wheel inertia  1.5 × 10${}^{5}$ kg·m${}^{2}$ 
${I}_{v}$  Robot inertia  0.125 kg·m${}^{2}$ 
${K}_{b}$  Motor back EMF  460 r·min/V 
${K}_{t}$  Motor torque  0.025 N·m/A 
n  Gear reduction ratio  27 
Method  APLF  Optimized APLF  

K  1  2  3  1  2  3  4 
Computation time(s)  3.2  57.5  663  4.7  29.7  72.7  153.8 
Number of LMI  30  650  15751  30  380  812  1406 
Number of P ∖ Lenth of $\mathsf{\Theta}$  5  25  125  5  19  28  37 
${\gamma}_{\mathsf{\Theta}}^{*}$        0.8516  0.8459  0.8418  0.8418 
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Xin, L.; Wang, Y.; Fu, H. Omnidirectional Mobile Robot Dynamic Model Identification by NARX Neural Network and Stability Analysis Using the APLF Method. Symmetry 2020, 12, 1430. https://doi.org/10.3390/sym12091430
Xin L, Wang Y, Fu H. Omnidirectional Mobile Robot Dynamic Model Identification by NARX Neural Network and Stability Analysis Using the APLF Method. Symmetry. 2020; 12(9):1430. https://doi.org/10.3390/sym12091430
Chicago/Turabian StyleXin, Liang, Yuchao Wang, and Huixuan Fu. 2020. "Omnidirectional Mobile Robot Dynamic Model Identification by NARX Neural Network and Stability Analysis Using the APLF Method" Symmetry 12, no. 9: 1430. https://doi.org/10.3390/sym12091430