Abstract
Parameter and state estimation problems are encountered when modeling processes that involve uncertain quantities to be estimated from measurements. The aim of this paper was to show the interval arithmetic approach as the suitable tool to solve problems of estimating the parameters of nonlinear systems in a bounded-error context. Perturbations are assumed bounded but otherwise unknown. This approach computes outer (or inner) approximations of the set of all parameters. An example of planar robot manipulator is presented to illustrate the effectiveness and potential of an interval approach in parameter’s estimation. A simulation is conducted to compare these estimates in terms of mean squared.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Farkhodeh, S.: A Kinematics Based Tolerance Analysis of Mechanisms, Thesis, Tabriz University, Iran (2008)
Flores, P.; et al.: Modeling and analysis of planar rigid multibody systems with translational clearance joints based on the non-smooth dynamics approach. Multibody Syst. Dyn. (2010)
Flores, P.: A methodology for quantifying the position errors due to manufacturing and assemble tolerances. J. Mech. Eng. 57(6), 457–467 (2011)
Milanese, M.; Belforte, G.: Estimation theory and uncertainty intervals evaluation in presence of unknown but bounded errors: linear families of models. IEEE Trans. Autom. Control AC-27(2), 408–413 (1982)
Jaulin, et al.: Applied Interval Analysis, with Examples in Parameter and State Estimation, Robust Control and Robotics. Springer, Londres (2001)
Adrot, O.; et al.: Estimation of bounded model uncertainties. J. Robotics Mechatron. 18(5), 661–671 (2006)
Granvilliers, L.; et al.: Parameter estimation using interval computations. SIAM J. Sci. Comput. 26(2), 591–612 (2004)
Zalewski, B.F.: Uncertainties in the Solutions to Boundary Element, Method an Interval Approach, thesis, Case Western Reserve University (2008)
Ning, S.; Kearfott, R.B.: A comparison of some methods for solving linear interval equations. SIAM. J. Numer. Anal. 34, 1289–1305 (1997)
Revol, N.: Arithmétique par intervalles, résolution de systèmes linéaires et précision”,Arénaire/LIP (2004)
Moore, R.E.; et al.: Introduction to interval analysis. SIAM (2009)
Marghitu, D.B.: Mechanisms and Robots Analysis with MATLAB. Springer, Berlin (2009)
Schweppe, F.C.: Recursive state estimation: unknown but bounded errors and system inputs. IEEE Trans. Autom. Control, AC-13(1) (1968)
Hu, C.: Using interval function approximation to estimate uncertainty. Interval/Probab. Uncertain. Non-Class. Logics Adv. Soft Comput. 46, 341–352 (2008)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Karkar, N., Benmhammed, K. & Bartil, A. Parameter Estimation of Planar Robot Manipulator Using Interval Arithmetic Approach. Arab J Sci Eng 39, 5289–5295 (2014). https://doi.org/10.1007/s13369-014-1199-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13369-014-1199-z