TY  - JOUR
AU  - Obradović, Aleksandar
AU  - Vuković, J.
AU  - Mladenović, Nikola
AU  - Mitrović, Zoran
PY  - 2011
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/1227
AB  - The problem of time minimization of a holonomic scleronomic mechanical system on a prescribed trajectory between two specified positions in configuration space is solved. The generalized force with restricted coordinates is taken as the controlling force. The application of the Green theorem (the well-known Miele method in flight mechanics) has shown that at every instant at least one control is at its boundary and possesses controlling functions with interruptions. It is assumed that at least one generalized coordinate exists that is monotonous during the interval of movement. An algorithm for numerical computation is presented for assessing the boundary of the admissible domain in the state space, thus, solving the problem of finding the optimal control as a function of time. Numerical integration is, therefore, carried out forward from the start point and backward from the end point by the use of the Runge-Kutta method. The mentioned procedure is illustrated in the example of time minimization for a manipulator which has its tip moving in a straight line. The application of the presented method simplifies solving of this type of problem compared to other methods, for instance, dynamic programming.
PB  - Springer, Dordrecht
T2  - Meccanica
T1  - Time optimal motions of mechanical system with a prescribed trajectory
EP  - 816
IS  - 4
SP  - 803
VL  - 46
DO  - 10.1007/s11012-010-9339-3
ER  - 

@article{
author = "Obradović, Aleksandar and Vuković, J. and Mladenović, Nikola and Mitrović, Zoran",
year = "2011",
abstract = "The problem of time minimization of a holonomic scleronomic mechanical system on a prescribed trajectory between two specified positions in configuration space is solved. The generalized force with restricted coordinates is taken as the controlling force. The application of the Green theorem (the well-known Miele method in flight mechanics) has shown that at every instant at least one control is at its boundary and possesses controlling functions with interruptions. It is assumed that at least one generalized coordinate exists that is monotonous during the interval of movement. An algorithm for numerical computation is presented for assessing the boundary of the admissible domain in the state space, thus, solving the problem of finding the optimal control as a function of time. Numerical integration is, therefore, carried out forward from the start point and backward from the end point by the use of the Runge-Kutta method. The mentioned procedure is illustrated in the example of time minimization for a manipulator which has its tip moving in a straight line. The application of the presented method simplifies solving of this type of problem compared to other methods, for instance, dynamic programming.",
publisher = "Springer, Dordrecht",
journal = "Meccanica",
title = "Time optimal motions of mechanical system with a prescribed trajectory",
pages = "816-803",
number = "4",
volume = "46",
doi = "10.1007/s11012-010-9339-3"
}

Obradović, A., Vuković, J., Mladenović, N.,& Mitrović, Z.. (2011). Time optimal motions of mechanical system with a prescribed trajectory. in Meccanica
Springer, Dordrecht., 46(4), 803-816.
https://doi.org/10.1007/s11012-010-9339-3

Obradović A, Vuković J, Mladenović N, Mitrović Z. Time optimal motions of mechanical system with a prescribed trajectory. in Meccanica. 2011;46(4):803-816.
doi:10.1007/s11012-010-9339-3 .

Obradović, Aleksandar, Vuković, J., Mladenović, Nikola, Mitrović, Zoran, "Time optimal motions of mechanical system with a prescribed trajectory" in Meccanica, 46, no. 4 (2011):803-816,
https://doi.org/10.1007/s11012-010-9339-3 . .