Geodesic
Solving kinematic problem of optimal nonlinear stabilization of arbitrary program movement of free rigid body
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 2, pp. 198-207

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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. 
@article{ISU_2016_16_2_a10,
     author = {Yu. N. Chelnokov and E. I. Nelaeva},
     title = {Solving kinematic problem of optimal nonlinear stabilization of arbitrary program movement of free rigid body},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {198--207},
     publisher = {mathdoc},
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     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2016_16_2_a10/}
}
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Yu. N. Chelnokov; E. I. Nelaeva. Solving kinematic problem of optimal nonlinear stabilization of arbitrary program movement of free rigid body. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 2, pp. 198-207. http://geodesic.mathdoc.fr/item/ISU_2016_16_2_a10/