Vol.6, Special Issue, 2007 pp. 53-70
UDC 007.52+004.8(045)=111
QUANTITATIVE AND QUALITATIVE ESTIMATIONS OF THE MANIPULATOR END-EFFECTOR TRAJECTORY PLANNING BY SINERGETIC CRITERION
Marina Kolesova, Aleksandr Polyakov, Mihail Kalinin
Department of the technical mechanics and machinery, Sevastopol National Technical University, SevNTU – FESTO, 99053, Sevastopol, Ukraine
e-mail: apolyakov.mail@gmail.com 
Abstract. In this work from several viewpoints the task of end-effector trajectory planning in two dimensional workspace for the model of two link planar anthropomorphous manipulator with revolute joints is considered. The set of solutions by criteria of the minimum torques-change, the minimum total work, and also by a new criterion of the minimum error of a linear synergy are received. Their relative quantitative and qualitative estimations are made. The criterion of the minimum error of a linear synergy is proved from the biomechanical point of view. It is shown that the task of a trajectory planning at its using has solutions, which correspond to a set of experimental data and in general are characterized by kinematic and dynamic invariance, which are peculiar to free movements of the human arm. The numerical solutions of the task are received by using of the Jacobi orthogonal polynomials for various directions of end-effector movements to the target and for two variants of manipulator links parameters.
Key words: end-effector, trajectory planning, synergetic criterion, minimum torques-change criterion, Poisson – Euler equations, orthogonal polynomials
KVANTITATIVNE I KVALITATIVNE PROCENE PUTANJE KRAJNJEG EFEKTORA MANIPULATORA PLANIRANE SINERGETSKIM KRITERIJUMOM
U ovom radu razmatra se putanja krajnjeg efektora planirana u dvodimenzionalnom radnom prostoru za primer dvosegmentong antropomorfnog manipulatora sa okretnim spojevima. Set rešenja dobija se kriterijumima minimalne obrtne promene, minimalnog celokupnog rada, i takodje novim kriterijumom minimalne greške linearne sinergije. Dobijene su njihove relativne kvantitativne i kvalitativne procene. Kriterijum minimalne greške linearne sinergije dokazan je biomehaničkim stanovištem. Pokazano je da zadatak putanje planirane za upotrebu ima rešenja koja odgovaraju setu eksperimentalnih podataka i generativno su obeležena kinematičkom i dinamičnom invarijantom koja je karakteristična za slobodne pokrete ljudske ruke. Brojna rešenja zadataka dobijena su Jacobi ortogonalnim polinomom za različite pravce pokreta krajnjeg efektora i za dve varijante manipulatora link parametara.
Ključne reči: krajnji efektor, planirana putanja, sinergetski kriterijum, kriterijum minimalne obrtne promene, Poisson-Euler jednačine, ortogonalni polinomi