Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Chelnokov Y. N., Nelaeva E. I. Solving Kinematic Problem of Optimal Nonlinear Stabilization of Arbitrary Program Movement of Free Rigid Body. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2016, vol. 16, iss. 2, pp. 198-207. DOI: 10.18500/1816-9791-2016-16-2-198-207, EDN: WCNQLP

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
14.06.2016
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Language: 
Russian
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UDC: 
531.38
EDN: 
WCNQLP

Solving Kinematic Problem of Optimal Nonlinear Stabilization of Arbitrary Program Movement of Free Rigid Body

Autors: 
Chelnokov Yurii Nikolaevich, Saratov State University
Nelaeva Ekaterina Igorevna, Saratov State University
Abstract: 

The kinematic problem of nonlinear stabilization of arbitrary program motion of free rigid body is studied. Biquaternion kinematic equation of perturbed motion of a free rigid body is considered as a mathematical model of motion. Instant speed screw of body motion is considered as a control. There are two functionals that are to be minimized. Both of them characterize the integral quantity of energy costs of control and squared deviations of motion parameters of a free rigid body from their program values. Optimal control laws and differential equations of optimization problem are determined using the Pontryagin’s maximum principle. Analytical solution of this problem has been found. The control law obtained is used for numerical solution of the inverse kinematics of a Stanford robot arm. The analysis of the numerical solution is carried out.

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Received: 
19.01.2016
Accepted: 
26.05.2016
Published: 
30.06.2016