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1
Content available Comparison of curvilinear parametrization methods and avoidance of orthogonal singularities in the path following task
Dyba Filip, Mazur Alicja
Journal of Automation Mobile Robotics and Intelligent Systems
|
2023
|
Vol. 17, No. 3
46--64
EN
In this paper applications of curvilinear parametrizations (Serret–Frenet, Bishop) in the path following task have been considered. The parametrizations allow one to derive manipulator’s equations with respect to a path. The full mathematical model of the path following task involves two groups of equations, i.e., the dynamics of the manipulator and the equations obtained from the parametrization method, connected in the cascaded system. Based on those relations two path following algorithms have been designed according to the backstepping integrator method (dedicated to the cascaded systems). Depending on the chosen parametrization method the algorithms differ in requirements and performance. In the paper an in-depth analysis comparing features of both considered methods has been presented. The parametric description of a path requires projection of a robot on the path. In this article the orthogonal projection has been taken into account. It introduces a singularity in the robot description. We have proposed a new form of the orthogonal projection constraint which allows a robot to not only approach the path, but also move along it. This novelty design is an important enhancement of the algorithms used so far. The problem of partially known dynamic parameters of a robot has also been addressed. In this paper, we have shown how to apply an adaptive controller to the path following task. Theoretical considerations have been verified with a simulation study conducted for a holonomic stationary manipulator. Achieved results emphasized why it is strongly recommended to use the algorithm version with the orthogonal singularity outside the path. Moreover, the comparative analysis results may be used to select the best curvilinear parametrization method according to the considered task requirements.
2
Content available Adaptive and robust following of 3D paths by holonomic manipulator
Mazur Alicja, Kaczmarek Mirela
Journal of Automation Mobile Robotics and Intelligent Systems
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2023
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Vol. 17, No. 3
65--77
EN
This paper addresses the problem of the following three-dimensional path by holonomic manipulator with parametric or structural uncertainty in the dynamics. Description of the manipulator relative to a desired three-dimensional path was presented. The path is parameterized orthogonally to the Serret-Frenet frame, which is moving along the curve. The adaptive and robust control laws for a stationary manipulator which ensures realization of the task were specified. Theoretical considerations are supported by the results of computer simulations conducted for an RTR manipulator.
3
Content available The non-orthogonal Serret-Frenet parametrization applied to the path following problem of a manipulator with partially known dynamics
Mazur Alicja, Dyba Filip
Archives of Control Sciences
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2023
|
Vol. 33, No. 2
339--370
EN
In this paper an application of the Serret-Frenet parametrization of a curve to the path following task is presented. This curvilinear parametrization method is used to obtain a control object description relative to the desired curve defined in the three-dimensional space. In order to derive proper equations, the innovative approach of the non-orthogonal projection of a control object on the given path is investigated. The non-orthogonal projection allows to design a global control algorithm. The proposed solution results in a cascade structure of the control system. Thus, the backstepping integrator algorithm was applied to create a control law. Due to the partial knowledge of control object dynamic parameters, an adaptive algorithm is taken into account. Theoretical considerations are confirmed with simulation study. Conducted simulations illustrated following paths at different levels of complexity by a holonomic non-redundant manipulator with a fixed base.
4
Content available Pre-filtered backstepping control for underactuated ship path following
Liu Zhiquan
Polish Maritime Research
|
2019
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nr 2
68--75
EN
Robust path following control for underactuated surface ships is an important issue in marine control practice. This paper aims to improve the robustness of the close-loop system with model uncertainties and time-varying disturbances. A practical adaptive backstepping control scheme with a pre-filter is proposed to force a surface vessel to track the predefined path generated by the virtual ship. Based on the Lyapunov stability theorem, this algorithm can guarantee all error signals in the overall system to be uniformly ultimately bounded, and it can be implemented without exact knowledge of the nonlinear damping structure and environmental disturbances. The proposed pre-filter can smooth the commanded heading order and obtain a better performance of the waypoint-based navigation control system. Two simulation cases are drawn to illustrate the validity of the proposed control strategy.
5
Śledzenie trajektorii przez BSP z wykorzystaniem algorytmu PSO
Pawłowski Piotr, Konatowski Stanisław
Elektronika : konstrukcje, technologie, zastosowania
|
2019
|
Vol. 60, nr 3
34--37
PL
W artykule opisano wykorzystanie algorytmu optymalizacyjnego PSO do wykonania zadanej trajektorii przez bezzałogowy statek powietrzny w postaci samolotu. Algorytm optymalizuje orientację przestrzenną samolotu, według której wykonywany jest lot z zadaną prędkością.
EN
This article presents an application of PSO optimization algorithm for fixed-wing UAV path-following task. The algorithm optimizes spatial orientation of UAV, which determines UAV’s displacement direction.
6
Content available Trajectory tracking and collision avoidance for the formation of two-wheeled mobile robots
Kowalczyk W., Kozłowski K.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2019
|
Vol. 67, nr 5
915--924
EN
This paper presents control method for multiple two-wheeled mobile robots moving in formation. Trajectory tracking algorithm from [7] is extended by collision avoidance, and is applied to the different type of formation task: each robot in the formation mimics motion of the virtual leader with a certain displacement. Each robot avoids collisions with other robots and circular shaped, static obstacles existing in the environment. Artificial potential functions are used to generate repulsive component of the control. Stability analysis of the closed-loop system is based on Lyapunov-like function. Effectiveness of the proposed algorithm is illustrated by simulation results.
7
Content available Path following control of fully actuated autonomous underwater vehicle based on LADRC
Lamraoui H. C., Qidan Z.
Polish Maritime Research
|
2018
|
nr 4
39--48
EN
This paper presents an active disturbances rejecter controller (ADRC) for position and path following control of a fully actuated autonomous underwater vehicle (AUV). The unmodeled, undesirable dynamics and disturbances reduce the performances of classical controllers and complicate the design of appropriate and efficient controllers. In the proposed approach, the different modeling complexities; such as uncertain parameters, non-linearities, and external disturbances are considered all as a part of disturbance which is estimated in real-time by the extended state observer ESO, and effectively compensated from the control law. The ESO is also able to estimate the position and velocity of the system in real-time, in case where the full state measurement of the AUV is not possible during experiments. Computer simulations demonstrate the high ability of the AUV tracking control based on ADRC, to follow the desired trajectory in the horizontal plane and space with high precision, and showed high robustness and efficiency in rejecting the external and internal disturbances caused by significant changes in parameters of the system, and the added position disturbances.
8
Content available Modification and reliability estimation of vector based Dubins path approach for autonomous ground vehicles path re-planning
Skačkauskas P., Sokolovskij E.
Eksploatacja i Niezawodność
|
2018
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Vol. 20, no. 4
549--557
EN
Due to global purposes to ensure growth of a competitive and sustainable transport system, also to solve traffic safety and environmental problems, various engineering solutions are being sought out. It can be assumed that autonomous vehicles are the technology, which will ensure the positive change in the transport system. Even though many studies successfully advanced toward realisation of autonomous vehicles, a significant amount of technical and policy framework problems still has to be solved. This paper addresses the problem of predefined path feasibility and proposes an effective methodology for a path to follow re-planning. The proposed methodology is composed of three parts and is based on the Dubins path approach. In order to modify the vector based Dubins path approach and to ensure the path feasibility, the optimisation problem was solved. A cost function with different inequality constraints was formulated. The performance and reliability of the proposed methodology were analysed and evaluated by carrying out an experimental research while using the autonomous test vehicle.
PL
Dla zapewnienia rozwoju konkurencyjnego i zrównoważonego systemu transportowego, oraz w celu rozwiązania problemów związanych z bezpieczeństwem ruchu i środowiskiem, poszukiwane są różne rozwiązania techniczne. Można założyć, że autonomiczne pojazdy są technologią, która zapewni pozytywną zmianę w systemie transportowym. Mimo że wiele badań z powodzeniem dotyczyło realizacji autonomicznych pojazdów, należy jeszcze rozwiązać wiele problemów technicznych i prawnych. W niniejszym dokumencie poruszono problem predefiniowanej wykonalności ścieżki i zaproponowano skuteczną metodologię dla ścieżki do śledzenia ponownego planowania. Proponowana metodologia składa się z trzech części i opiera się na metodzie Dubinsa. Aby zmodyfikować metodę trajektorii Dubinsa i zapewnić optymalną trajektorię, w publikacji rozwiązano zadanie optymalizacji. Sformułowana funkcja celu z różnymi nieliniowymi ograniczeniami. Skuteczność i niezawodność proponowanej metodologii została przeanalizowana i oceniona po przeprowadzeniu eksperymentalnych badań z wykorzystaniem autonomicznego pojazdu badawczego.
9
Content available Path following for two HOG wheels mobile robot
Joniak P., Muszyński R.
Journal of Automation Mobile Robotics and Intelligent Systems
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2017
|
Vol. 11, No. 2
75--81
EN
To apply a spinning hemisphere as a mobile robot drive is an unconventional idea. Equipping a mobile robot with two such hemispheres brings to life a device with absolutely novel properties. In this paper we derive kinematics models of a mobile robot with two driving hemispheres, analyse shortly their properties, and adopt a control algorithm designed to follow a path. There are two kinematics models presented: the full model of the original system, and the model of the simplified system, equivalent to the original one. The second model is expressed in two different coordinate systems – the later allowing for the application of known control algorithms to drive the robot. The performance of the analysed algorithm is illustrated by computer simulations
10
Sterowanie VFO dla monocykla w zadaniu stwarzania ścieżki nieparametryzowanej
Michałek M. M.
Prace Naukowe Politechniki Warszawskiej. Elektronika
|
2016
|
z. 195, t. 2
489--498
PL
Metoda VFO (ang. Vector-Field(s)-Orientation), zaproponowana dla modelu monocykla w pracy [7], pozwala na rozwiązanie dwóch klasycznych zadań sterowania - śledzenia trajektorii oraz sterowania do punktu - w zunifikowany sposób poprzez odpowiednią (re)definicję postaci tzw. pola wektorowego zbieżności. Do tej poty, nie istniała wersja sterownika VFO dla ostatniego z klasycznych zadań sterowania, a mianowicie dla zadania odtwarzania ścieżki. Niniejszy artykuł wypełnia tę lukę przedstawiając nową propozycję konstrukcji pola zbieżności dla problemu odtwarzania ścieżki wykorzystując koncepcję krzywej poziomicowej. Zastosowanie tej koncepcji pozwala na ominięcie zasadniczych ograniczeń związanych ze standardowym podejściem wykorzystującym opis ścieżki parametryzowany jej krzywoliniową długością. W pracy przedstawiono projekt reguły sterowania, analizę stabilności układu zamkniętego oraz wyniki symulacyjne działania sterownika dla modelu monocykla.
EN
The VFO (Vector- Field(s)-Orientation) method, proposed for the unicycle in the previous publications, allows one to solve two classical control tasks - trajectory tracking and set-point control - in a unified manner by re-definition of the so-called convergence vector field. However, the VFO control law was not available for the path following task so far. The paper fills this gap by introducing a novel form of the convergence vector field for the path-following problem utilizing the level curve approach. Thanks to this approach, one can avoid main limitations imposed by the standard methods which employs description of a reference path parametrized by a curvilinear abscissa.
11
Content available Following 3D paths by a manipulator
Mazur A., Płaskonka J., Kaczmarek M.
Archives of Control Sciences
|
2015
|
Vol. 25, no. 1
117--133
EN
In the paper a description of a manipulator relative to a desired three-dimensional path was presented. The path is parameterized orthogonally to the Serret-Frenet frame which is moving along the curve. For the path two different time parameterizations were chosen. The control law for the RTR manipulator which ensures realization of the task was specified. Theoretical considerations were illustrated by simulation results.
12
Content available Noise sensitivity of selected kinematic path following controllers for a unicycle
Libal U., Płaskonka J.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2014
|
Vol. 62, nr 1
3--13
EN
In the paper a path following problem for a wheeled mobile robot of (2,0) type has been considered. The kinematic model of the robot was derived with respect to the Serret-Frenet frame. Two kinematic control algorithms - Samson and Morin-Samson - have been tested taking into account their sensitivity to a white noise with a zero mean appearing in the one of state variables. The properties of path following errors have been analysed using statistical techniques. The conclusions related to an acceptable level of noise and a range of applicability of the presented algorithms have been reached.
13
Content available Collision-Free Trajectory Planning for Mobile Manipulators Subject to Control Constraints
Pajak G., Pajak I.
Archive of Mechanical Engineering
|
2014
|
Vol. LXI, nr 1
35--55
EN
A method of planning collision-free trajectory for a mobile manipulator tracking a line section path is presented. The reference trajectory of a mobile platform is not needed, mechanical and control constraints are taken into account. The method is based on a penalty function approach and a redundancy resolution at the acceleration level. Nonholonomic constraints in a Pfaffian form are explicitly incorporated to the control algorithm. The problem is shown to be equivalent to some point-to-point control problem whose solution may be easier determined. The motion of the mobile manipulator is planned in order to maximise the manipulability measure, thus to avoid manipulator singularities. A computer example involving a mobile manipulator consisting of a nonholonomic platform (2,0) class and a 3 DOF RPR type holonomic manipulator operating in a three-dimensional task space is also presented.
PL
W pracy opisano tok postępowania podczas budowy modeli symulacyjnych z wykorzystaniem programu SolidWorks i Matlab/Simulink. Tworzenie modelu symulacyjnego przebiega etapami, to znaczy najpierw opracowywany jest model geometryczny w programie SolidWorks, następnie dzięki możliwości wymiany danych, model CAD jest implementowany w środowisku obliczeniowym Matlab/Simulink. Modele SimMechanics pozwalają na śledzenie wielu parametrów, np. trajektorii, prędkości, czy przyspieszeń dowolnych elementów układu złożonego. W pracy, jako przykłady modeli symulacyjnych opracowanych zgodnie z zaprezentowana metoda, pokazano modele laboratoryjnego żurawia samochodowego oraz żurawia leśnego. Modele te umożliwiają wizualizacje zadanego - za pomocą wymuszeń kinematycznych - cyklu pracy.
14
Content available Motion planning for mobile surgery assistant
Pajak G., Pajak I.
Acta of Bioengineering and Biomechanics
|
2014
|
Vol. 16, no. 2
11--20
EN
The paper presents a method of motion planning for a mobile manipulator acting as a helper providing the necessary tools or a surgery assistant carrying out pre-planned procedures. Mobility of this system makes it possible to reach the position which will give optimal access to the operating field. The path of the end-effector, determined during operation pre-planning, is defined as a curve parameterized by any scaling parameter, the reference trajectory of a mobile platform is not needed. The motion of the mobile manipulator is planned in order to maximise the manipulability measure, thus to avoid manipulator singularities. The method is based on a penalty function approach and a redundancy resolution at the acceleration level. Constraints connected with the existence of mechanical limits for a given manipulator configuration, collision avoidance conditions and control constraints are considered. A computer example involving a mobile manipulator consisting of a nonholonomic platform (2,0) class and a 3 DOF RPR type holonomic manipulator operating in a three-dimensional task space is also presented.
15
Content available Planning of collision-free trajectory for mobile manipulators
Pająk G.
International Journal of Applied Mechanics and Engineering
|
2013
|
Vol. 18, no. 2
475--489
EN
A method of planning sub-optimal trajectory for a mobile manipulator working in the environment including obstacles is presented. The path of the end-effector is defined as a curve that can be parameterized by any scaling parameter, the reference trajectory of a mobile platform is not needed. Constraints connected with the existence of mechanical limits for a given manipulator configuration, collision avoidance conditions and control constraints are considered. The motion of the mobile manipulator is planned in order to maximize the manipulability measure, thus to avoid manipulator singularities. The method is based on a penalty function approach and a redundancy resolution at the acceleration level. A computer example involving a mobile manipulator consisting of a nonholonomic platform and a SCARA type holonomic manipulator operating in a two-dimensional task space is also presented.
16
Content available remote On path following control of nonholonomic mobile manipulators
Mazur A., Szakiel D.
International Journal of Applied Mathematics and Computer Science
|
2009
|
Vol. 19, no 4
561-574
EN
This paper describes the problem of designing control laws for path following robots, including two types of nonholonomic mobile manipulators. Due to a cascade structure of the motion equation, a backstepping procedure is used to achieve motion along a desired path. The control algorithm consists of two simultaneously working controllers: the kinematic controller, solving motion constraints, and the dynamic controller, preserving an appropriate coordination between both subsystems of a mobile manipulator, i.e. the mobile platform and the manipulating arm. A description of the nonholonomic subsystem relative to the desired path using the Frenet parametrization is the basis for formulating the path following problem and designing a kinematic control algorithm. In turn, the dynamic control algorithm is a modification of a passivity-based controller. Theoretical deliberations are illustrated with simulations.
17
Śledzenie ścieżki dla manipulatorów mobilnych z platformą typu (2,0)
Mazur A., Szakiel D.
Prace Naukowe Politechniki Warszawskiej. Elektronika
|
2008
|
z. 166, t. 2
439-452
PL
Śledzenie ścieżki dla manipulatorów mobilnych typu (nh, h) zostało zdekomponowane na śledzenie osobnych ścieżek dla każdego z podsystemów manipulatora mobilnego. Ponieważ platforma mobilna powinna poruszać się bez poślizgu kół, to ograniczenia nieholonomiczne pojawią się w modelu obiektu jako dodatkowe równania, czyli kinematyka. Aby podsystem nieholonomiczny spełniał ograniczenia podczas śledzenia ścieżki, należy użyć algorytmu kinematycznego Samsona, dedykowanego platformom klasy (2,0). Algorytm sterowania działający na poziomie dynamicznym jest modyfikacją algorytmu przedstawionego w [5].
EN
This paper has presented a solution to the path following problem for nonholonomic mobile manipulator of (nh, h) type. The control goal for the mobile platform was to follow along the desired flat curve without stopping the motion and the manipulator should move in such a way that its end-effector follows along the geometric path described in Cartesian coordinates and stops at the end of the desired path. As a kinematic control algorithm solving a task for the nonholonomic subsystem the Samson algorithm, dedicated platforms of (2,0) class, should be used. Dynamical control algorithm is a some modification of the algorithm introduced in [5].
18
Content available A stable homotopy approach to horizontal linear complementarity problems
Ralph D.
Control and Cybernetics
|
2002
|
Vol. 31, no 3
575-599
EN
We are interested in the solution of Horizontal Linear Complementarity Problems, HLCPs, that is complementarity problems with more variables than equations. Globally metrically regular HLCPs have nonempty solution sets that are stable with respect to "right-hand-side perturbations" of the data, hence are numerically attractive. The main purpose of the paper is to show how the stability on conditioning properties of globally metrically regular HLCPs are preserved by a homotopy framework for solving the HLCP that finds a "stable" direcaion at each iteration as a local minimizer of a strongly convex quadratic program with linear complementarity constraints, QPCC. Apart from intrinsic interest in numerical solution of HLCPs, this investigation has application in solving horizontal nonlinear complementarity problems and more broadly in the area of mathematical programs with complementarity constraints, MPCCs.
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