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1
Content available Caster Car - underactuated ground vehicle with caster wheels
Korczak Sebastian
Archives of Control Sciences
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2024
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Vol. 34, No. 1
91--116
EN
This paper presents a new type of underactuated ground mobile robot called Caster Car. The platform consists of a front-driven and steered wheel and two uncontrolled rear caster wheels. The Caster Car model presented can be an interesting alternative for mobile robots that connects dynamic properties of hovercrafts and classical 4-wheeled cars. Underactuated properties of the Caster Car cause that classical proportional-derivative feedback control give the ability to affect only selected configuration variables. Three mathematical models of the Caster Car are proposed: a dynamic model with free-moving casters, a dynamic model with blocked casters, and a simplified hovercraft description. Models were tested during tracking tasks with demanding trajectory using selective and full-state control. This full state control was based on the computed torque technique with the pseudoinverse operation and proportional-derivative feedback. It gives the ability to suppress unstable behaviors of uncontrolled orientation but in cost of overall effect (higher position errors).
2
Content available remote Sliding mode control to stabilization of nonlinear underactuated mechanical systems
Saidi Imen, Touati Nahla
Przegląd Elektrotechniczny
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2021
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R. 97, nr 7
106--109
EN
In this paper, a sliding mode control was applied to a particular underactuated mechanical system, the inertia wheel inverted pendulum. This mechanical system presents strong non-linearities and instabilities in its dynamic modeling. The technique found for control by sliding mode is very easy to implement, it presents a simple control algorithm which can be easily implemented in a real time system. The simulation results obtained are very interesting, they show the efficiency of the proposed approach and that it has good performance in terms of robustness and stability of convergence both for stabilization and for the rejection of external point disturbances to the system.
PL
W tym artykule, sterowanie trybem ślizgowym zostało zastosowane do konkretnego niedostatecznie uruchamianego układu mechanicznego, odwróconego wahadła koła bezwładności. Ten układ mechaniczny wykazuje silne nieliniowości i niestabilności w modelowaniu dynamicznym. Technika sterowania w trybie przesuwnym jest bardzo łatwa do wdrożenia, przedstawia prosty algorytm sterowania, który można łatwo zaimplementować w systemie czasu rzeczywistego. Uzyskane wyniki symulacji są interesujące, pokazują skuteczność proponowanego podejścia oraz dobre wyniki w zakresie odporności i stabilności zbieżności zarówno dla stabilizacji, jak i dla zewnętrznych zakłóceń punktowych do systemu.
3
Content available remote Nonlinear predictive control for trajectory tracking of underactuated mechanical systems
Saidi Imen, Touati Nahla
Przegląd Elektrotechniczny
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2021
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R. 97, nr 6
30--33
EN
The objective of this article is to present an automatic demonstrator of underactuated mechanical systems. It is the inertia wheel inverted pendulum, which has two degrees of freedom and a single actuator. Nonlinear predictive control is applied to the underactuated system allowing dynamic control for optimal tracking of periodic reference trajectories. The simulation results show the performance and efficiency of the proposed control.
PL
Celem tego artykułu jest przedstawienie automatycznego demonstratora niedostatecznie uruchomionych układów mechanicznych. Jest to odwrócone wahadło stabilizowane kołem zamachowym, które ma dwa stopnie swobody i jeden siłownik. Nieliniowe sterowanie predykcyjne jest stosowane do niedostatecznie uruchomionego systemu, umożliwiając dynamiczne sterowanie w celu optymalnego śledzenia okresowych trajektorii odniesienia. Wyniki symulacji pokazują wydajność i skuteczność proponowanego sterowania.
4
Content available Method of cooperative formation control for underactuated USVs based on nonlinear backstepping and cascade system theory
Dong Zaopeng, Liu Yang, Wang Hao, Qin Tao
Polish Maritime Research
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2021
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nr 1
149--162
EN
This paper presents a method for the cooperative formation control of a group of underactuated USVs. The problem of formation control is first converted to one of stabilisation control of the tracking errors of the follower USVs using system state transformation design. The followers must keep a fixed distance from the leader USV and a specific heading angle in order to maintain a certain type of formation. A global differential homeomorphism transformation is then designed to create a tracking error system for the follower USVs, in order to simplify the description of the control system. This makes the complex formation control system easy to analyse, and allows it to be decomposed into a cascaded system. In addition, several intermediate state variables and virtual control laws are designed based on nonlinear backstepping, and actual control algorithms for the follower USVs to control the surge force and yaw moment are presented. A global system that can ensure uniform asymptotic stability of the USVs’ cooperative formation control is achieved by combining Lyapunov stability theory and cascade system theory. Finally, several simulation experiments are carried out to verify the validity, stability and reliability of our cooperative formation control method.
5
Content available Fault detection based on Lyapunov exponents estimation for stabilized mechanical systems
Puzyrov Volodymyr, Acho Leonardo, Pujol Gisela, Rodellar José
Journal of Theoretical and Applied Mechanics
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2019
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Vol. 57 nr 2
519--531
EN
We study a stabilizable mechanical system in the vicinity of an equilibrium position. This position, as a rule, is unstable, and the system is underactuated. It is assumed that faults affect the technical process and its control. We suggest a fault diagnosis technique based on estimation of Lyapunov characteristic exponents of measured variables. A model of a linear switching system is involved for the system with faults description, and a common quadratic Lyapunov function is used to evaluate the deviation of the maximum exponent with respect to the default system. A scheme of fault magnitude estimation is suggested related to the degree of this deviation. An example of a 2-degree of freedom system is presented to illustrate the procedure.
6
Content available Design of an optimal fuzzy controller of an under-actuated manipulator based on teaching-learning-based optimization
Mahmoodabadi Mohammad Javad, Yazdizadeh-Baghini Amineh
Acta Mechanica et Automatica
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2019
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Vol. 13, no. 3
166--172
EN
In this paper, an optimal fuzzy controller based on the Teaching-Learning-Based Optimization (TLBO) algorithm has been presented for the stabilization of a two-link planar horizontal under-actuated manipulator with two revolute (2R) joints. For the considered fuzzy control method, a singleton fuzzifier, a centre average defuzzifier and a product inference engine have been used. The TLBO algorithm has been implemented for searching the optimum parameters of the fuzzy controller with consideration of time integral of the absolute error of the state variables as the objective function. The proposed control method has been utilized for the 2R under-actuated manipulator with the second passive joint wherein the model moves in the horizontal plane and friction forces have been considered. Simulation results of the offered control method have been illustrated for the stabilization of the considered robot system. Moreover, for different initial conditions, the effectiveness and the robustness of the mentioned strategy have been challenged.
7
Content available Path following control of the underactuated USV based on the improved line-of-sight guidance algorithm
Liu T., Dong Z., Du H., Song L., Mao Y.
Polish Maritime Research
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2017
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nr 1
3--11
EN
The path following control problem of the underactuated unmanned surface vessel (USV) is studied in this paper. An improved line-of-sight (LOS) guidance algorithm is proposed which can adjust adaptively based on the path following error. The global asymptotically stable path following controller is designed based on the nonlinear backstepping method and the Lyapunov stability theory. Firstly, the USV path following error model is established in the Serret-Frenet (SF) coordinate frame. The path following error in the inertial coordinate frame is transformed into the SF coordinate frame, which is used to define the path following control problem. Secondly, inspired by the traditional LOS guidance algorithm, the longitudinal path following error in the SF coordinate frame is introduced into the improved LOS guidance algorithm. This allows the algorithm to adjust adaptively to the desired path. Thirdly, in order to solve the underactuated problem of the USV path following control system, the tangential velocity of the desired path is designed as a virtual input. The underactuated problem is converted to a virtual fully actuated problem by designing the virtual control law for the tangential velocity. Finally, by combining backstepping design principles and the Lyapunov stability theory, the longitudinal thrust control law and the yaw torque control law are designed for the underactuated USV. Meanwhile, the global asymptotic stability of the path following error is proved. Simulation experiments demonstrate the effectiveness and reliability of the improved LOS guidance algorithm and the path following controller.
8
Content available Implementation of factitious force method for control of 5R manipulator with skid-steering platform REX
Mazur A., Cholewiński M.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2016
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Vol. 64, nr 1
71--80
EN
In the paper implementation of the factitious force concept for a controlling complex mobile manipulator has been presented. As the nonholonomic constraint only lack of longitudinal slippage of wheels has been chosen - in skid-steering platforms lateral slippage is necessary to change orientation of such a platform. From a control theory point of view such a system is dynamically underactuated. As a solution to a underactuation problem a method of factitious force has been proposed. This method assumes extension on the dynamics level, in the form of an additional control inputs uv, which values are equal to zero equivalently. For a mobile manipulator, consisting of platform REX and 5R robotic onboard arm, a cascaded control law has been proposed. A simulation study was conducted for a mathematical model of a considered object with real values of physical parameters, i.e. lengths, masses, inertia moments etc. obtained from the 3D model. Results obtained in simulations have shown a proper action of the control system and convergence of tracking errors, occurring in a platform and in joints of a manipulator, to zero.
9
Content available Tracking control of an underactuated rigid body with a coupling input force
Korczak S.
Archives of Control Sciences
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2014
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Vol. 24, no. 3
321--332
EN
This paper presents a set of basic problems concerning the control of an underactuated dynamic system. Exemplary system of a planar rigid body with a coupling input force is described. Lie brackets method is used to show accessibility of the system. A tracking problem is solved with computed torque algorithm. The coupling force makes the convergence to zero of all state variables errors impossible. After numerical simulation, stability of the system is mentioned.
10
Content available Stabilizacja wahadła odwróconego z napędem inercyjnym przy pomocy regulatora LQR
Owczarkowski A., Gośliński J.
Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska
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2012
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nr 4a
7-10
PL
Niniejszy artykuł opisuje metodę stabilizacji obiektu zwanego wahadłem odwróconym z napędem inercyjnym IWP (ang. Interia Wheel Pendulum). Jest to nieliniowy układ mechaniczny w postaci wahadła odwróconego składającego się z masztu i kola zamachowego umieszczonego na szczycie napędzanego silnikiem prądu stałego. Autorzy zaproponowali stabilizację przy pomocy regulacji LQR, która do funkcjonowania wymaga linearyzacji i dyskretyzacji równań matematycznych obiektu. Wykonano działania symulacyjno-eksperymentalne potwierdzające poprawność działania proponowanej metody.
EN
Work is about stabilizing the inverted pendulum object called IWP (Inertia Wheel Pendulum). It is a non-linear mechanical system in the form of an inverted pendulum containing a flywheel mounted on top accelerated by DC motor. The authors suggested stabilization by LQR control, which requires the linearization and discretization of the mathematical equations of the object. Simulation and experiment have confirmed proper operation of the proposed method.
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