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Robust task space trajectory tracking control of robotic manipulators

Galicki M.

International Journal of Applied Mechanics and Engineering

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2016

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Vol. 21, no. 3

547--568

EN

This work deals with the problem of the accurate task space trajectory tracking subject to finite-time convergence. Kinematic and dynamic equations of a redundant manipulator are assumed to be uncertain. Moreover, globally unbounded disturbances are allowed to act on the manipulator when tracking the trajectory by the end-effector. Furthermore, the movement is to be accomplished in such a way as to reduce both the manipulator torques and their oscillations thus eliminating the potential robot vibrations. Based on suitably defined task space non-singular terminal sliding vector variable and the Lyapunov stability theory, we propose a class of chattering-free robust controllers, based on the estimation of transpose Jacobian, which seem to be effective in counteracting both uncertain kinematics and dynamics, unbounded disturbances and (possible) kinematic and/or algorithmic singularities met on the robot trajectory. The numerical simulations carried out for a redundant manipulator of a SCARA type consisting of the three revolute kinematic pairs and operating in a two-dimensional task space, illustrate performance of the proposed controllers as well as comparisons with other well known control schemes.

2

Local dynamics in a Leslie-Gower system model

Dragomirescu F. I., Caruntu B., Georgescu R. M.

Journal of Mathematics and Applications

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2011

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Vol. 34

15-26

EN

Mathematical ecology or/and biology requires the study of populations that interact. This is the reason for the intensive study of the predator-pray models. A Leslie-Gower model of such type is considered here and the stability properties of its equilibrium points are analyticallyand numerically investigated. Dynamics and bifurcations are deduced. Level curves for corresponding Lyapunov functions for various values of the physical parameters in the parameter space are graphically presented emphasizing the stability regions.

3

Analiza stabilności nieliniowej pętli synchronizacji fazy z filtrem o aproksymacji Cauera

Walczak J., Kiełtyka G.

Prace Naukowe Politechniki Śląskiej. Elektryka

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2008

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z. 4

39-48

PL

W artykule przedstawiono analizę stabilności nieliniowej pętli synchronizacji fazy z filtrem o aproksymacji Cauera drugiego rzędu dla dwóch różnych wartości współczynnika falowania. Analizę tą oparto na metodzie Lapunowa, za pomocą której wyznaczono punkty osobliwe pętli i zbadano, czy są one stabilne dla różnych wartości parametrów opisujących układ pętli. Uzyskane wyniki zilustrowano przykładem.

EN

In the paper stability analysis of nonlinear phase-locked loop with second order Cauer lowpass filter for two different values ripple coefficient has been presented. The analysis based on the Lyapunov method, which assistance at definite reinforcement singular points and research its stability for different values describing of the loop system. Presented results were illustrated by an example.