The main purpose of this paper is to introduce a new method to analyze the effects of the white and colored noise perturbations on the robotic arms. To show the efficiency of the presented idea the simplest manipulator, two link robotic arm, is considered. Most previous noise analyses of manipulators are done using mechanical or electrical modeling. Applying exact kinematic equations of the robots is the novelty of the proposed research. For this purpose, by adding white and colored noise terms in each angle function of the robotic arm, the end effector linear velocity is studied. Also, mechanical variation's effect on the final velocity in noisy space is considered. The longer the length of the links, the more the noise effect. Analysis of simulation results shows that the root mean square error in 2nd order is more than when angle functions are of the first order. Also, the mean square error is less when colored noise is added in comparison to the white noise. The Matlab programming is used to perform numerical examples to show the efficiency and accuracy of the presented idea.
[1] A. Aleksandr and K. Sutyrkina, On the Position and Stationary Motion Stabilization Problems of a Two-Link Robot Manipulator, 1st International Conference on Control Systems, Mathematical Modelling, Automation and Energy Efficiency (SUMMA) IEEE, (2019).
[2] Ch. K. Alexander and M. N. D. Sadiku, Vibration and Kinematic Analysis of Scara Robot Structure, Diyala Journal of Engineering Sciences, 6 (2013), 127–143.
[3] R. Ashkiani, A. Mahmoudi, M. Karimi, and K. Ansari-Asl, Closed-Form Estimator for Frequency Estimation of Complex Sinusoidal Signals in Multiplicative and Additive Noise, Circuits, Systems, and Signal Processing, (2020).
[4] T. Caraballo and X. Han, Applied Nonautonomous and Random Dynamical Systems, Applied Dynamical Systems, Springer International Publishing, (2016).
[5] L.C. Evans, An Introduction to Stochastic Differential Equations, AMS, (2013).
[6] R. Farnoosh, P. Nabati, R. Rezaeyan, and M. Ebrahimi, A stochastic perspective of RL electrical circuit using different noise terms, The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 30 (2011), 812–822.
[7] R. Farnoosh, P. Nabati, and A. Hajrajabi, Parameter estimation for RL electrical circuits based on least square and Bayesian approach, The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 31 (2012), 1711–1725.
[8] A. Fazli and M. H. Kazemi, Manipulator Dynamic Nonlinearity Approximation Based on Polytopic LPV Mod- eling for Robot Tracking Control Problem, Iranian Journal of Science and Technology, Transactions of Electrical Engineering, 46 (2022), 537–547.
[9] T. R. Field and R. J. A. Tough, Stochastic dynamics of the scattering amplitude generating K-distributed noise, J. Math. Phy., 44 (2000), 5212–5223.
[10] D. Guo, F. Xu, L. Yan, Z. Nie, and H. Shao, A New Noise-Tolerant Obstacle Avoidance Scheme for Motion Planning of Redundant Robot Manipulators, Front. Neurorobot, (2018).
[11] D. Ham and A. Hajimiri, Complete noise analysis for CMOS switching mixtures via SDEs, IEEE Custom Inte- grated circuits conference, (2000), 439–442.
[12] K. Jahnavi and P. Sivraj, Teaching and learning robotic arm model, International Conference on Intelligent Computing, Instrumentation and Control Technologies, IEEE, (2017), 1570–1575.
[13] M. Kaur, S. Sondhi, and V. K. Yanumula, Kinematics Analysis and Jacobian calculation for six Degrees of Freedom Robotic Arm, IEEE 17th India Council International Conference (INDICON), (2020).
[14] E. Kolarova and L. Brancik, Confidence intervals for RLCG cell influenced by coloured noise, The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 36 (2017), 838–849.
[15] P. Nabati, A simulation study of the COVID-19 pandemic based on the Ornstein-Uhlenbeck processes, Computa- tional Methods for Differential Equations, 10 (2022), 738–745.
[16] P. Nabati, and R. Farnoosh, Stochastic approach for noise analysis and parameter estimation for RC and RLC electrical circuits, Int. J. Nonlinear Anal. Appl, 12 (2018), 433–444.
[17] P. Nabati, H. Babazadeh, and H. Azadfar, Noise analysis of Band Pass Filters using stochastic differential equations , The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 38 (2019), 693–702.
[18] C. Shi, F. Wang, M. Sellathurai, and J. Zhou, Low probability of intercept-based distributed MIMO radar waveform design against barrage jamming in signal-dependent clutter and coloured noise, IET Signal Proc., 13 (2019), 415– 423.
[19] B. Siciliano and O. Khatib, Springer Handbook of Robotics, Springer, (2008).
[20] B. Siciliano, L. Sciavicco, L. Villani, and G. Oriolo, Robotics: modelling, planning and control, Springer Science and Business Media, (2010).
[21] M. W. Spong, S. Hutchinson, and M. Vidyasagar, Robot Modeling and Control, Wiley, (2005).
[22] M. Sung Ahn, H. Chae, D. Noh, H. Nam, and D. Hong, Analysis and Noise Modeling of the Intel RealSense D435 for Mobile Robots, 16th International Conference on Ubiquitous Robots (UR), (2019).
[23] M. E. Uk, F. B. Sajjad Ali Shah, M. Soyaslan, and O. Eldogan, Modeling, control, and simulation of a SCARA PRR-type robot manipulator, Scientia Iranica B, 27 (2020), 330–340.
[24] G. Uhlenbeck and L. Ornstein, On the theory of Brownian motion, Physics Review, 36 (1930), 823-841.
[25] M. Wang and G. Uhlenbeck, On the theory of Brownian motion. II, Reviews of Modern Physics,17 (1945), 323– 342.
[26] X. Zhang and R. Yuan, Pullback attractor for random chemostat model driven by colored noise, Applied Mathe- matics Letters, (2020).
Babazadeh, H., & Nabati, P. (2024). Numerical simulation of two link robotic manipulator with white and colored noise. Computational Methods for Differential Equations, 12(1), 149-158. doi: 10.22034/cmde.2023.54929.2283
MLA
Hadiseh Babazadeh; Parisa Nabati. "Numerical simulation of two link robotic manipulator with white and colored noise". Computational Methods for Differential Equations, 12, 1, 2024, 149-158. doi: 10.22034/cmde.2023.54929.2283
HARVARD
Babazadeh, H., Nabati, P. (2024). 'Numerical simulation of two link robotic manipulator with white and colored noise', Computational Methods for Differential Equations, 12(1), pp. 149-158. doi: 10.22034/cmde.2023.54929.2283
VANCOUVER
Babazadeh, H., Nabati, P. Numerical simulation of two link robotic manipulator with white and colored noise. Computational Methods for Differential Equations, 2024; 12(1): 149-158. doi: 10.22034/cmde.2023.54929.2283
)
