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1
Content available Trajectory planning of the humanoid manipulator
Kacprzak C., Pająk G.
International Journal of Applied Mechanics and Engineering
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2019
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Vol. 24, no. 3
591--602
EN
The paper presents a method of planning a collision-free trajectory for a humanoid manipulator mounted on a rail system. The task of the robot is to move its end-effectors from the current position to the given final location in the workspace. The method is based on a redundancy resolution at the velocity level. In addition to this primary task, secondary objectives are also taken into account. The motion of the robot is planned in order to maximize a manipulability measure in purpose of avoiding manipulator singularities. State inequality constraints resulting from collision avoidance conditions are also considered. A computer example involving a humanoid manipulator operating in a three dimensional task space is also presented.
2
Content available Planning of collision-free trajectory for mobile manipulators
Pająk G.
International Journal of Applied Mechanics and Engineering
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2013
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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.
3
Content available remote Planning of sub-optimal collision-free trajectory for redundant manipulators
Pająk G., Pająk I.
International Journal of Applied Mechanics and Engineering
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2012
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Vol. 17, no. 4
1223-1235
EN
A method of planning sub-optimal trajectory for a redundant manipulator working in the environment including obstacles is presented. The robot's task is to move the tool from a given initial to final position in the workspace. The motion of the manipulator is planned in order to minimize a manipulability measure for the purpose of avoiding manipulator singularities. The method is based on using the penalty function approach and a redundancy resolution at the acceleration level. The collision avoidance is accomplished by locally perturbing the manipulator motion in the neighborhoods of the obstacles. The proposed method allows real time computations. A computer example involving 4 DOF PUMA-like manipulator operating in three dimensional task space is also presented.
4
Content available remote The robot toolbox for matlab
Pająk G., Pająk I.
International Journal of Applied Mechanics and Engineering
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2011
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Vol. 16, no 3
809-820
EN
In the paper, a Matlab toolbox for modeling and simulation manipulators described by Denavit-Hartenberg parameters is presented. This package can be used to realistic visualization of robot motion necessary in research, didactic process or during design of a production cell. Available functions render it possible to show a realistic model of a mechanism easily based on DH parameters only. The toolbox also provides a set of tools for creating any polyhedrons and functions to manipulate them in 3D space. Using those objects it is possible to create the appearance of the manipulator and its workspace. Functions implementing classical methods of trajectory planning in configuration space allow calculation of manipulator trajectory which can be shown as an animation. The main functions and computer examples illustrating the features of this toolbox are presented.
5
Content available remote Planning of a collision-free trajectory for multiple manipulators
Pająk G., Pająk I.
International Journal of Applied Mechanics and Engineering
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2011
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Vol. 16, no 2
475-486
EN
In this paper, a global method is presented in order to solve the task of trajectories generation for multiple manipulators operating in the common workspace including moving obstacles. The task of manipulators is to follow by their end effectors the geometric paths given in a task space. The dynamics of the manipulators is taken into consideration. The constraints imposed on controls and state inequality constraints resulting from collision avoidance of a moving obstacle with manipulator links are considered. A final time of the task performance is not fixed. This task is solved based on the calculus of variations. A computer example involving two planar redundant manipulators of three revolute kinematic pairs is presented.
6
Content available remote Collision-free sub-optimal trajectory planning of the redundant manipulators
Pająk G., Pająk I.
International Journal of Applied Mechanics and Engineering
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2010
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Vol. 15, no 3
799-810
EN
The paper presents a method of planning a sub-optimal collision-free trajectory for a redundant manipulator. The path of the end-effector is defined as a curve that can be parameterized by any scaling parameter. The method is based on penalty function approach and a redundancy resolution at the acceleration level. Constraints connected with the existence of mechanical limits for manipulator configuration and control constraints have been considered. The motion of the manipulator is planned in order to minimize a manipulability measure for the purpose of avoiding manipulator singularities. A computer example involving 4 a DOF PUMA-like manipulator operating in a three dimensional task space is also presented.
7
Content available remote Sub-optimal trajectory planning of the redundant manipulators
Pająk G., Pająk I.
International Journal of Applied Mechanics and Engineering
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2009
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Vol. 14, no 1
251-260
EN
The paper presents a method of planning a sub-optimal trajectory for a redundant manipulator subject to control constraints. The method is based on using the penalty function approach and scaling the robot dynamic equations to satisfy actuator constraints and allows real time computations. A computer example involving a spatial redundant manipulator of four revolute kinematics pairs is also presented.
8
Content available remote Formation of phytoplankton in the first years of existence of the water supplying reservoir (Southern Poland) against the background of increased eutrophication process
Pająk G.
Oceanological and Hydrobiological Studies
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2003
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Vol. 32, No. 4
5-77
EN
The aim of the investigations was a recognition of the complex of physico-chemical parameters affecting the dynamics and structure of phytoplankton. The taxonomical composition, abundance and biomass of nano- and phytoplankton has been determined. In the development of the reservoir four stages were distinguished. In stage I of the reservoir filling, the temperature and pH value of water as well as the level of PO4-P, had a decisive influence on the process of phytoplankton formation. A sudden change in the damming ordinate in stage II of the reservoir studies contributed to the development of nanoplanktonic diatoms, and the refilling of the reservoir ( stage III) caused an abundant development of green algae. After the reservoir had been filled (stage IV) the planktonic forms of cryptophytes group dominated. The initial dominance of taxons had no influence on its structure after a four-year searching. A very similar pattern of proportionally altering phytoplankton communities in the investigated basins (BM and BD) suggests that both the depth and availability of nutrient compounds were not the limiting factors in the initial period of functioning of the Dobczyce Reservoir.
9
Content available remote Planowanie bezkolizyjnej trajektorii manipulatora przy ograniczeniach na sterowania
Pająk G.
Studia z Automatyki i Informatyki
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2001
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T. 26
147-158
PL
W pracy zastosowano metodę globalnego rozkładu redundancji do rozwiązania zadania manipulatora w przypadku, gdy ścieżka chwytaka jest krzywą sparametryzowaną, a manipulator pracuje w przestrzeni roboczej z przeszkodami. Końcowy czas wykonania tego zadania nie był ustalony. Ponadto wzięto pod uwagę dynamikę manipulatora. Uwzględnione zostały ograniczenia na sterowania przyłożone do siłowników poszczególnych par kinematycznych. Znane dotychczas metody zajmują się takim zadaniem dla manipulatorów nieredundantnych lub dla redundantnych, gdy współrzędne uogólnione manipulatora są dane funkcjami długości ścieżki. Stanowi to istotne ograniczenie w praktycznym zastosowaniu tych metod. Prezentowane rozwiązanie jest pozbawione tych wad, a przeprowadzone symulacje komputerowe potwierdzają jego efektywność.
EN
In the paper, a global method of redundancy resolution has been used to solve the manipulation task. The path of the end-effector is a parametrized curve and there are obstacles in the workspace. The final time of task execution is not fixed. Additionally, the dynamic of the manipulator has been taken into consideration. The constraints imposed on control signals exerted to the servomotors have been taken into account. There are methods known for such task for non-redundant or redundant manipulators when the manipulator generalized coordinates are parametrized by the path length. It is an essential limitation in practical application of these methods. The presented solution is devoid of defects, and the investigated computer simulation confirm is effectiveness.
10
Content available remote Planowanie suboptymalnych trajektorii manipulatorów redundantnych
Pająk I., Pająk G.
Management
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2000
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Vol. 4, no 2
229-238
PL
W opracowaniu przedstawiono metodę planowania bezkolizyjnych trajektorii dla manipulatorów redundantnych. Zadanie to rozwiązano wykorzystując metody wewnętrznych funkcji kary oraz skalowania równań dynamiki manipulatora. Zaproponowana metoda rozwiązania jest efektywna obliczeniowo. Do opracowania dołączony został przykład planowania trajektorii trójczłonowego manipulatora planarnego pracującego w przestrzeni roboczej zawierającej przeszkody.
EN
A method of planning sub-optimal collision-free motion for redundant manipulator is presented. It is based on using penalty function approach and scaling the robot dynamic equation to satisfy actuator constraints. The proposed method allows real time computations. A computer example involving a planar redundant manipulator of three revolute kinematics pairs which operates in a work space with obstacles, is also presented.
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