TY  - CONF
AU  - Obradović, Aleksandar
AU  - Cherkasov, Oleg
AU  - Miličić, Luka
PY  - 2023
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/6897
AB  - The paper considers the procedure for determining the brachistochronic motion of the Chaplygin sleigh in a vertical plane, where the blade is such that it prevents the motion of the contact point in one direction only. The position of the sleigh mass center and orientation at the final positions is specified, as well as the initial value of mechanical energy. The simplest formulation of a corresponding optimal control problem is given and it is solved by applying Pontryagin’s maximum principle. For some cases, analytical solutions of differential equations of the two-point boundary value problem (TPBVP) of the maximum principle, were found. Numerical integration was carried out for other cases using the shooting method, where the assessment of missing terminal conditions was given and it was shown that the solution obtained represents the global minimum time for the brachistochronic motion.
PB  - Belgrade : Serbian Society of Mechanics
C3  - 9 th International Congress of Serbian Society of Mechanics Vrnjačka Banja, Serbia, July 5-7, 2023
T1  - THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT
SP  - T.4.3
UR  - https://hdl.handle.net/21.15107/rcub_machinery_6897
ER  - 

@conference{
author = "Obradović, Aleksandar and Cherkasov, Oleg and Miličić, Luka",
year = "2023",
abstract = "The paper considers the procedure for determining the brachistochronic motion of the Chaplygin sleigh in a vertical plane, where the blade is such that it prevents the motion of the contact point in one direction only. The position of the sleigh mass center and orientation at the final positions is specified, as well as the initial value of mechanical energy. The simplest formulation of a corresponding optimal control problem is given and it is solved by applying Pontryagin’s maximum principle. For some cases, analytical solutions of differential equations of the two-point boundary value problem (TPBVP) of the maximum principle, were found. Numerical integration was carried out for other cases using the shooting method, where the assessment of missing terminal conditions was given and it was shown that the solution obtained represents the global minimum time for the brachistochronic motion.",
publisher = "Belgrade : Serbian Society of Mechanics",
journal = "9 th International Congress of Serbian Society of Mechanics Vrnjačka Banja, Serbia, July 5-7, 2023",
title = "THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT",
pages = "T.4.3",
url = "https://hdl.handle.net/21.15107/rcub_machinery_6897"
}

Obradović, A., Cherkasov, O.,& Miličić, L.. (2023). THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT. in 9 th International Congress of Serbian Society of Mechanics Vrnjačka Banja, Serbia, July 5-7, 2023
Belgrade : Serbian Society of Mechanics., T.4.3.
https://hdl.handle.net/21.15107/rcub_machinery_6897

Obradović A, Cherkasov O, Miličić L. THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT. in 9 th International Congress of Serbian Society of Mechanics Vrnjačka Banja, Serbia, July 5-7, 2023. 2023;:T.4.3.
https://hdl.handle.net/21.15107/rcub_machinery_6897 .

Obradović, Aleksandar, Cherkasov, Oleg, Miličić, Luka, "THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT" in 9 th International Congress of Serbian Society of Mechanics Vrnjačka Banja, Serbia, July 5-7, 2023 (2023):T.4.3,
https://hdl.handle.net/21.15107/rcub_machinery_6897 .

TY  - JOUR
AU  - Obradović, Aleksandar
AU  - Cherkasov, Oleg
AU  - Miličić, Luka
AU  - Šalinić, Slaviša
PY  - 2023
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/7711
AB  - The paper considers the procedure for determining the brachistochronic motion of the Chaplygin sleigh in a vertical plane, where the blade
is such that it prevents the motion of the contact point in one direction only.
The position of the sleigh mass center and orientation at the final positions is
specified, as well as the initial value of mechanical energy. The simplest formulation of a corresponding optimal control problem is given and it is solved by
applying Pontryagin’s maximum principle. For some cases, analytical solutions
of differential equations of the two-point boundary value problem (TPBVP)
of the maximum principle were found. Numerical integration was carried out
for other cases using the shooting method, where the assessment of missing
terminal conditions was given and it was shown that the solution obtained
represents the global minimum time for the brachistochronic motion. The
method of the brachistochronic motion by means of a single holonomic and a
single unilateral nonholonomic mechanical constraint is presented.
PB  - Serbian Society of Mechanics and Mathematical Institute of the Serbian Academy of Sciences and Arts, Beograd
T1  - REALIZATION OF THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT
EP  - 183
IS  - 2
SP  - 171
VL  - 50
DO  - 10.2298/TAM231017011O
ER  - 

@article{
author = "Obradović, Aleksandar and Cherkasov, Oleg and Miličić, Luka and Šalinić, Slaviša",
year = "2023",
abstract = "The paper considers the procedure for determining the brachistochronic motion of the Chaplygin sleigh in a vertical plane, where the blade
is such that it prevents the motion of the contact point in one direction only.
The position of the sleigh mass center and orientation at the final positions is
specified, as well as the initial value of mechanical energy. The simplest formulation of a corresponding optimal control problem is given and it is solved by
applying Pontryagin’s maximum principle. For some cases, analytical solutions
of differential equations of the two-point boundary value problem (TPBVP)
of the maximum principle were found. Numerical integration was carried out
for other cases using the shooting method, where the assessment of missing
terminal conditions was given and it was shown that the solution obtained
represents the global minimum time for the brachistochronic motion. The
method of the brachistochronic motion by means of a single holonomic and a
single unilateral nonholonomic mechanical constraint is presented.",
publisher = "Serbian Society of Mechanics and Mathematical Institute of the Serbian Academy of Sciences and Arts, Beograd",
title = "REALIZATION OF THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT",
pages = "183-171",
number = "2",
volume = "50",
doi = "10.2298/TAM231017011O"
}

Obradović, A., Cherkasov, O., Miličić, L.,& Šalinić, S.. (2023). REALIZATION OF THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT. 
Serbian Society of Mechanics and Mathematical Institute of the Serbian Academy of Sciences and Arts, Beograd., 50(2), 171-183.
https://doi.org/10.2298/TAM231017011O

Obradović A, Cherkasov O, Miličić L, Šalinić S. REALIZATION OF THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT. 2023;50(2):171-183.
doi:10.2298/TAM231017011O .

Obradović, Aleksandar, Cherkasov, Oleg, Miličić, Luka, Šalinić, Slaviša, "REALIZATION OF THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT", 50, no. 2 (2023):171-183,
https://doi.org/10.2298/TAM231017011O . .

TY  - CONF
AU  - Miličić, Luka
AU  - Obradović, Aleksandar
AU  - Todić, Ivana
PY  - 2022
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/4077
AB  - Numerical techniques for solving optimal control problems fall into two general classes: indirect methods and direct methods. In an indirect method, we rely on the Pontryagin's maximum principle and other necessary conditions to obtain a two-point boundary-value problem, which is then numerically solved for optimal trajectories. However, indirect methods are frequently subject to severe convergence problems. We examine the possibility of implementing these methods in guidance algorithms using a single processor. Calculations were performed in real time and conclusions are drawn about the robustness of these methods.
PB  - Univerzitet u Beogradu, Mašinski fakultet
C3  - Abstract book : Mathematics, Numerics and Applications MNA 2022, Budva 1-3 June, 2022
T1  - Overview of numerical methods for solving optimal control problem in guidance  algorithms
EP  - 17
SP  - 17
UR  - https://hdl.handle.net/21.15107/rcub_machinery_4077
ER  - 

@conference{
author = "Miličić, Luka and Obradović, Aleksandar and Todić, Ivana",
year = "2022",
abstract = "Numerical techniques for solving optimal control problems fall into two general classes: indirect methods and direct methods. In an indirect method, we rely on the Pontryagin's maximum principle and other necessary conditions to obtain a two-point boundary-value problem, which is then numerically solved for optimal trajectories. However, indirect methods are frequently subject to severe convergence problems. We examine the possibility of implementing these methods in guidance algorithms using a single processor. Calculations were performed in real time and conclusions are drawn about the robustness of these methods.",
publisher = "Univerzitet u Beogradu, Mašinski fakultet",
journal = "Abstract book : Mathematics, Numerics and Applications MNA 2022, Budva 1-3 June, 2022",
title = "Overview of numerical methods for solving optimal control problem in guidance  algorithms",
pages = "17-17",
url = "https://hdl.handle.net/21.15107/rcub_machinery_4077"
}

Miličić, L., Obradović, A.,& Todić, I.. (2022). Overview of numerical methods for solving optimal control problem in guidance  algorithms. in Abstract book : Mathematics, Numerics and Applications MNA 2022, Budva 1-3 June, 2022
Univerzitet u Beogradu, Mašinski fakultet., 17-17.
https://hdl.handle.net/21.15107/rcub_machinery_4077

Miličić L, Obradović A, Todić I. Overview of numerical methods for solving optimal control problem in guidance  algorithms. in Abstract book : Mathematics, Numerics and Applications MNA 2022, Budva 1-3 June, 2022. 2022;:17-17.
https://hdl.handle.net/21.15107/rcub_machinery_4077 .

Miličić, Luka, Obradović, Aleksandar, Todić, Ivana, "Overview of numerical methods for solving optimal control problem in guidance  algorithms" in Abstract book : Mathematics, Numerics and Applications MNA 2022, Budva 1-3 June, 2022 (2022):17-17,
https://hdl.handle.net/21.15107/rcub_machinery_4077 .

TY  - CONF
AU  - Kuzmanović, Vladimir
AU  - Todić, Ivana
AU  - Miličić, Luka
PY  - 2021
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/4489
AB  - The precision of the Inertial Navigational System (INS) is mostly related to the drift of the gyroscopes. Stability of biases and minimisation of drift can be achieved by highly and accurately stabilised temperature of sensors themselves as well as all related electronic circuits. In this paper, we present a very compact and economical solution for temperature stabilisation of INS with the use of Peltier elements controlled by a single microcontroller. The basis of the INS container is an aluminium block which provides the most homogeneous temperature field with its high-temperature conductivity. Temperature stability of the INS container is achieved by assigning a group of four Peltier elements to the sides of the block, each coupled with a temperature sensor. The aluminium block is isolated on all six sides, and the Peltier modules are the only "openings" for heat flux. The mathematical model of the Peltier element is derived and verified through measured performance. This model is expanded to take into account the influence of the environment as well as the internal heat source. Theoretical limitations are obtained using this mathematical model, which is later compared to experimentally obtained limits. This type of temperature stabilisation can be used for different purposes where precise temperature stability is needed in its end application. Temperature stabilisation achieved in this manner is highly adaptable to the changes in the object's surroundings and keeps the object's inner temperature stable. Groups of Peltier modules and temperature sensors enable the object to have fully independent temperature stabilisation on each of its sides, which in turn allows the temperature stabilisation algorithm to adapt its performance to the object's surroundings. All Peltier elements are controlled and monitored by a single microcontroller, which also exposes a simple and intuitive communication interface for the end-user. This concept was tested in a highly non-stationary environment with rapid changes in surrounding conditions, and the object's inner temperature was kept stable up to the second decimal. Hardware limitations were introduced, and the coefficient of performance was compared to its theoretical value.
C3  - Proceedings of VII International Congress Engineering, Environment And Materials In Process Industry EEM2021,Jahorina, March 17-19, 2021
T1  - Temperature stabilization using Peltier modules in highly dynamic environment
EP  - 303
SP  - 295
UR  - https://hdl.handle.net/21.15107/rcub_machinery_4489
ER  - 

@conference{
author = "Kuzmanović, Vladimir and Todić, Ivana and Miličić, Luka",
year = "2021",
abstract = "The precision of the Inertial Navigational System (INS) is mostly related to the drift of the gyroscopes. Stability of biases and minimisation of drift can be achieved by highly and accurately stabilised temperature of sensors themselves as well as all related electronic circuits. In this paper, we present a very compact and economical solution for temperature stabilisation of INS with the use of Peltier elements controlled by a single microcontroller. The basis of the INS container is an aluminium block which provides the most homogeneous temperature field with its high-temperature conductivity. Temperature stability of the INS container is achieved by assigning a group of four Peltier elements to the sides of the block, each coupled with a temperature sensor. The aluminium block is isolated on all six sides, and the Peltier modules are the only "openings" for heat flux. The mathematical model of the Peltier element is derived and verified through measured performance. This model is expanded to take into account the influence of the environment as well as the internal heat source. Theoretical limitations are obtained using this mathematical model, which is later compared to experimentally obtained limits. This type of temperature stabilisation can be used for different purposes where precise temperature stability is needed in its end application. Temperature stabilisation achieved in this manner is highly adaptable to the changes in the object's surroundings and keeps the object's inner temperature stable. Groups of Peltier modules and temperature sensors enable the object to have fully independent temperature stabilisation on each of its sides, which in turn allows the temperature stabilisation algorithm to adapt its performance to the object's surroundings. All Peltier elements are controlled and monitored by a single microcontroller, which also exposes a simple and intuitive communication interface for the end-user. This concept was tested in a highly non-stationary environment with rapid changes in surrounding conditions, and the object's inner temperature was kept stable up to the second decimal. Hardware limitations were introduced, and the coefficient of performance was compared to its theoretical value.",
journal = "Proceedings of VII International Congress Engineering, Environment And Materials In Process Industry EEM2021,Jahorina, March 17-19, 2021",
title = "Temperature stabilization using Peltier modules in highly dynamic environment",
pages = "303-295",
url = "https://hdl.handle.net/21.15107/rcub_machinery_4489"
}

Kuzmanović, V., Todić, I.,& Miličić, L.. (2021). Temperature stabilization using Peltier modules in highly dynamic environment. in Proceedings of VII International Congress Engineering, Environment And Materials In Process Industry EEM2021,Jahorina, March 17-19, 2021, 295-303.
https://hdl.handle.net/21.15107/rcub_machinery_4489

Kuzmanović V, Todić I, Miličić L. Temperature stabilization using Peltier modules in highly dynamic environment. in Proceedings of VII International Congress Engineering, Environment And Materials In Process Industry EEM2021,Jahorina, March 17-19, 2021. 2021;:295-303.
https://hdl.handle.net/21.15107/rcub_machinery_4489 .

Kuzmanović, Vladimir, Todić, Ivana, Miličić, Luka, "Temperature stabilization using Peltier modules in highly dynamic environment" in Proceedings of VII International Congress Engineering, Environment And Materials In Process Industry EEM2021,Jahorina, March 17-19, 2021 (2021):295-303,
https://hdl.handle.net/21.15107/rcub_machinery_4489 .