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1

Application of direct and inverse kinematics and dynamics in motion planning of manipulator links

Delyová Ingrid, Hroncová Darina, Frankovský Peter, Sivák Peter, Kostka Ján, Neumann Vojtech

International Journal of Applied Mechanics and Engineering

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2023

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Vol. 28, no. 3

53--64

EN

For the synthesis of manipulators and robots, an accurate analysis of the movements of the individual links is essential. This thesis deals with motion planning of the effector of a multi-linked manipulator. An important topic in this area is the orientation and position of links and kinematic pairs in space. In particular, attention should be paid to the position of their endpoint as well as other significant points. Trajectory planning allows the manipulator to perform complex tasks, such as picking and placing objects or following a particular path in space. Overall, trajectory planning of a multibody manipulator involves a combination of direct and inverse kinematics calculations, as well as control theory and optimization techniques. It is an important process enabling manipulators to perform complex tasks such as assembly, handling and inspection. In the design of robot kinematic structures, simulation programs are currently used for their kinematic and dynamic analysis. The proposed manipulator was first solved by inverse kinematics problem in Matlab. Subsequently, the trajectories of the end-effector were determined in Matlab by a direct kinematics problem. In Simulink, using the SimMechanics library, the inverse problem of dynamics was used to determine the trajectories of the moments.

2

Multi-Robot Coverage with Reeb Graph Clusteringand Optimized Sweeping Patterns

Szklarski Jacek Tomasz

Computer Assisted Methods in Engineering and Science

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2022

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Vol. 29, no. 4

379--395

EN

In order to perform mapping, inspecting, searching, painting, cleaning, and other similartasks, mobile robots have to act according to a coverage plan. Finding a trajectory thata robot should follow requires an appropriate coverage path planning (CPP) algorithmand is a non-trivial problem, especially if a cooperating group of robots is considered. Wepropose that the multi-robot CPP can be solved by: decomposing the input occupancygrid map into cells, generating a corresponding Reeb graph, clustering the graph intoNrclusters, and solving the associated equality generalized traveling salesman problemin order to obtain optimal back-and-forth sweeping patterns on the clusters. This laststep has been proven to be one of the most efficient ways to find trajectories for a singlerobot [5]. The discussed approach is motivated by a specific application: industrial cleaningof large warehouses byNrautonomic mobile cleaners (the cleaning radius of a robot ismuch smaller than the area to be cleaned). The total time required for cleaning is to beminimized. By means of statistical analysis, using an extensive, realistic set of syntheticmaps, it is shown that the proposed algorithm meets the criteria for applying it in theproduction process.

3

FDA* : a focused single‐query grid based path planning algorithm

Boumediene Mouad, Lamine Mehennaoui Lamine, Lachouri Abderazzak

Journal of Automation Mobile Robotics and Intelligent Systems

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2021

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Vol. 15, No. 3

37--43

EN

Square grid representations of the state‐space are a commonly used tool in path planning. With applications in a variety of disciplines, including robotics, computational biology, game development, and beyond. However, in large‐scale and/or high dimensional environments the creation and manipulation of such structures become too expensive, especially in applications when an accurate representation is needed. In this paper, we present a method for reducing the cost of single‐query grid‐based path planning, by focusing the search to a smaller subset, that contains the optimal solution. This subset is represented by a hyperrectangle, the location, and dimensions of which are calculated departing from an initial feasible path found by a fast search using the RRT* algorithm. We also present an implementation of this focused discretization method called FDA*, a resolution optimal algorithm, where the A* algorithm is employed in searching the resulting graph for an optimal solution. We also demonstrate through simulation results, that the FDA* algorithm uses less memory and has a shorter run‐time compared to the classic A* and thus other graph‐based planning algorithms, and at the same time, the resulting path cost is less than that of regular RRT based algorithms.

4

Motion planning of planar and redundant underwater serial link manipulator based on minimization of energy consumption

Kumar Virendra, Sen Soumen, Roy Shibendu Shekhar

Archive of Mechanical Engineering

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2021

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LXVIII, nr 4

415--434

EN

The article describes motion planning of an underwater redundant manipulator with revolute joints moving in a plane under gravity and in the presence of obstacles. The proposed motion planning algorithm is based on minimization of the total energy in overcoming the hydrodynamic as well as dynamic forces acting on the manipulator while moving underwater and at the same time, avoiding both singularities and obstacle. The obstacle is considered as a point object. A recursive Lagrangian dynamics algorithm is formulated for the planar geometry to evaluate joint torques during the motion of serial link redundant manipulator fully submerged underwater. In turn the energy consumed in following a task trajectory is computed. The presence of redundancy in joint space of the manipulator facilitates selecting the optimal sequence of configurations as well as the required joint motion rates with minimum energy consumed among all possible configurations and rates. The effectiveness of the proposed motion planning algorithm is shown by applying it on a 3 degrees-of-freedom planar redundant manipulator fully submerged underwater and avoiding a point obstacle. The results establish that energy spent against overcoming loading resulted from hydrodynamic interactions majorly decides the optimal trajectory to follow in accomplishing an underwater task.

5

Hand guiding a virtual robot using a force sensor

Gregor Radovan, Babinec Andrej, Duchoň František, Dobiš Michal

Acta Mechanica et Automatica

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2021

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Vol. 15, no. 3

177--186

EN

The research behind this paper arose out of a need to use an open-source system that enables hand guiding of the robot effector using a force sensor. The paper deals with some existing solutions, including the solution based on the open-source framework Robot Operating System (ROS), in which the built-in motion planner MoveIt is used. The proposed concept of a hand-guiding system utilizes the output of the force–torque sensor mounted at the robot effector to obtain the desired motion, which is thereafter used for planning consequential motion trajectories. Some advantages and disadvantages of the built-in planner are discussed, and then the custom motion planning solution is proposed to overcome the identified drawbacks. Our planning algorithm uses polynomial interpolation and is suitable for continuous replanning of the consequential motion trajectories, which is necessary because the output from the sensor changes due to the hand action during robot motion. The resulting system is verified using a virtual robot in the ROS environment, which acts on the real Optoforce force–torque sensor HEX-70-CE-2000N. Furthermore, the workspace and the motion of the robot are restricted to a greater extent to achieve more realistic simulation.

6

Multiquery motion planning in uncertain spaces: Incremental adaptive randomized roadmaps

Khaksar Weria, Uddin Md Zia, Torresen Jim

International Journal of Applied Mathematics and Computer Science

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2019

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Vol. 29, no. 4

641--654

EN

Sampling-based motion planning is a powerful tool in solving the motion planning problem for a variety of different robotic platforms. As its application domains grow, more complicated planning problems arise that challenge the functionality of these planners. One of the main challenges in the implementation of a sampling-based planner is its weak performance when reacting to uncertainty in robot motion, obstacles motion, and sensing noise. In this paper, a multi-query sampling-based planner is presented based on the optimal probabilistic roadmaps algorithm that employs a hybrid sample classification and graph adjustment strategy to handle diverse types of planning uncertainty such as sensing noise, unknown static and dynamic obstacles and an inaccurate environment map in a discrete-time system. The proposed method starts by storing the collision-free generated samples in a matrix-grid structure. Using the resulting grid structure makes it computationally cheap to search and find samples in a specific region. As soon as the robot senses an obstacle during the execution of the initial plan, the occupied grid cells are detected, relevant samples are selected, and in-collision vertices are removed within the vision range of the robot. Furthermore, a second layer of nodes connected to the current direct neighbors are checked against collision, which gives the planner more time to react to uncertainty before getting too close to an obstacle. The simulation results for problems with various sources of uncertainty show a significant improvement compared with similar algorithms in terms of the failure rate, the processing time and the minimum distance from obstacles. The planner is also successfully implemented and tested on a TurtleBot in four different scenarios with uncertainty.

7

An Algorithm in the Process of Planning of Safety Pathway – A Collision-Free Pathway of a Robot

Daneshjo Naqib, Olexová Cecilia, Králik Marián, Danishjoo Enayat

Advances in Science and Technology. Research Journal

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2019

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Vol. 13, no 3

16--23

EN

The paper was based on research tasks in the field of robotics. It approaches solving the collision states of a robot while operating equipment and applies the knowledge in the CATIA system environment. Motion Planning is of paramount importance in robotics, where a goal is to determine a collision-free, unobstructed path for a robot that works in an environment which contains obstacles. An obstacle can be an object that is found in the robot’s workspace.

8

Motion planning for nonholonomic systems with earlier destination reaching

Ratajczak A.

Archives of Control Sciences

|

2018

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Vol. 28, No. 2

269--283

EN

The motion planning problem consists in finding a control function which drives the system to a desired point. The motion planning algorithm derived with an endogenous configuration space approach assumes that the motion takes place in an arbitrary chosen time horizon. This work introduces a modification to the motion planning algorithm which allows to reach the destination point in time, which is shorter than the assumed time horizon. The algorithm derivation relies on the endogenous configuration space approach and the continuation (homotopy) method. To achieve the earlier destination reaching a new formulation of the task map and the task Jacobian are introduced. The efficiency of the new algorithm is depicted with simulation results.

9

Stability Controller on the Atlas Robot Example

Wasielica M.

Pomiary Automatyka Robotyka

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2017

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R. 21, nr 2

65--70

EN

The paper presents the gait framework for a biped robot on the Atlas robot example. The method utilizes inverted pendulum model and static stability controller with correction from IMU sensor. A straight-forward balance control strategy based on ankle joints control is proposed. The controller which stabilizes the robot during execution of the planned path is described. To show the efficiency of the proposed method the results obtained in the Virtual Robotics Challenge environment (Gazebo) are provided.

PL

Artykuł przedstawia system generowania chodu dla robotów dwunożnych na przykładzie robota Atlas. Metoda wykorzystuje model odwróconego wahadła oraz statyczny kontroler stabilności wraz z korekcją z sensora IMU. Zaproponowano prostą metodę utrzymywania równowagi w oparciu o sterowanie ruchami stóp robota. Opisano też kontroler stabilizujący robota podczas pokonywania zaplanowanej ścieżki. Zweryfikowano działanie zaproponowanych metod na robocie Atlas w symulatorze Virtual Robotics Challenge (Gazebo).

10

Manipulation and path planning for KUKA (LWR/ LBR 4+) robot in a simulated and real environment

Jitendra T. P., Doss A. S. A., Ramon J. A. C.

Journal of Automation Mobile Robotics and Intelligent Systems

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2017

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Vol. 11, No. 3

15--21

EN

Robotics has accomplished its greatest triumph to date in the world of industrial manufacturing and academia. This work aims to perform path planning using a KUKA (LWR/ LBR 4+) robot platform as well as a simulator to grasp the object. This whole implementation will be carried out in a ROS environment with Ubuntu (Linux) as an operating platform. The KUKA (LWR/ LBR 4+) has 7 degrees of freedom with several joints and linkages. It uses KR C2 LR as the main hardware controller. The robot gets visual information of an object by Microsoft Kinnect RGB-D camera and carries out necessary actions to clasp the object using a shadow hand and Barrett hand. The simulation and manipulation of robot gantry is performed by using C++ and python as a programming language. The bilateral robot platform and main PC hub are linked together by using Ethernet cable. The obtained results from the current research are found to be satisfactory and can be proven beneficial for researcher as a reference.

11

Vehicle navigation in populated areas using predictive control with environmental uncertainty handling

Skrzypczyk K., Mellado M.

Archives of Control Sciences

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2017

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Vol. 27, no. 2

351--359

EN

This paper addresses the problem of navigating an autonomous vehicle using environmental dynamics prediction. The usefulness of the Game Against Nature formalism adapted to modelling environmental prediction uncertainty is discussed. The possibility of the control law synthesis on the basis of strategies against Nature is presented. The properties and effectiveness of the approach presented are verified by simulations carried out in MATLAB.

12

On dynamically consistent Jacobian inverse for non-holonomic robotic systems

Ratajczak J., Tchoń K.

Archives of Control Sciences

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2017

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Vol. 27, no. 4

555--573

EN

This paper presents the dynamically consistent Jacobian inverse for non-holonomic robotic system, and its application to solving the motion planning problem. The system’s kinematics are represented by a driftless control system, and defined in terms of its input-output map in accordance with the endogenous configuration space approach. The dynamically consistent Jacobian inverse (DCJI) has been introduced by means of a Riemannian metric in the endogenous configuration space, exploiting the reduced inertia matrix of the system’s dynamics. The consistency condition is formulated as the commutativity property of a diagram of maps. Singular configurations of DCJI are studied, and shown to coincide with the kinematic singularities. A parametric form of DCJI is derived, and used for solving example motion planning problems for the trident snake mobile robot. Some advantages in performance of DCJI in comparison to the Jacobian pseudoinverse are discovered.

13

Gry przeciwko naturze jako narzędzie modelowania niepewności predykcji w zagadnieniu planowania bezkolizyjnego ruchu pojazdu

Skrzypczyk K.

Zeszyty Naukowe. Organizacja i Zarządzanie / Politechnika Śląska

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2016

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z. 88

277--288

PL

W pracy przedyskutowano przydatność modelu gier przeciwko naturze do modelowania niepewności predykcji stanu otoczenia sterowanego pojazdu. Pokazano możliwość syntezy prawa sterowania realizującego bezkolizyjny ruch pojazdu w dynamicznym środowisku na bazie strategii gry przeciwko naturze. Działanie oraz efektywność proponowanego podejścia zweryfikowano za pomocą symulacji przeprowadzonych w środowisku MATLAB.

EN

This paper addresses the problem of collision free motion planning of a vehicle in a dynamical environment. The usefulness of the game against nature for modeling environmental prediction uncertainty was discussed. The possibility of the control law synthesis on the basis of strategies against nature was presented. The properties and effectiveness of the approach presented were verified by simulations carried out in MATLAB.

14

Sterowanie predykcyjne platformą Rex z wykorzystaniem estymacji z przesuwanym horyzontem

Juszkiewicz Ł.

Prace Naukowe Politechniki Warszawskiej. Elektronika

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2016

|

z. 195, t. 2

563--572

PL

Przedmiotem pracy jest praktyczne rozwiązanie zadania śledzenia trajektorii przez czterokołową platformę mobilną ze sprzężonymi kołami przy pomocy algorytmu sterowania predykcyjnego z wykorzystaniem estymacji z przesuwanym horyzontem. Przedstawiony został model dynamiki platformy przy założeniu poślizgów bocznych wszystkich kół oraz braku poślizgów wzdłużnych. Oba algorytmy zostały zaimplementowane przy użyciu pakietu ACADO i włączone w system sterowania platformy. Przeprowadzone zostały badania eksperymentalne, weryfikujące ich działanie. Wykazały one praktyczną zbieżność trajektorii realizowanej przez platformę do trajektorii zadanej.

EN

The paper presents practical implementation of model predictive control and moving horizon estimation in case of four wheel mobile platform with coupled wheels. Dynamics equations of the platform moving with lateral slips are presented. The ACADO package has been used for implementation of algorithms, which performance was experimentaly verified.

15

Platforma mobilna Rex : parametryczne i nieparametryczne planowanie ruchu

Zadarnowska K., Gut D.

Prace Naukowe Politechniki Warszawskiej. Elektronika

|

2016

|

z. 195, t. 2

573--584

PL

Przedmiotem pracy jest zadanie planowania ruchu czterokołowej platformy mobilnej ze sprzężonymi kołami bocznymi poruszającej się w obecności poślizgów poprzecznych i wzdłużnych kół. Przedstawiono równania ruchu platformy. W oparciu o metodę endogenicznej przestrzeni konfiguracyjnej zaproponowano parametryczny i nieparametryczny jakobianowy algorytm planowania ruchu. Działanie algorytmu zilustrowano na przykładzie zadania parkowania równoległego platformy Rex.

EN

A motion planning problem of a skid-steering, 4-wheel mobile platform with coupled wheels is considered. A dynamics model of the mobile platform Rex is derived. Parametric and nonparametric Jacobian motion planning algorithms are designed and applied to a parking problem of the platform. Theoretical concepts are illustrated with computer simulations.

16

Planowanie ruchu układów nieholonomicznych z wcześniejszym osiąganiem celu

Ratajczak A.

Prace Naukowe Politechniki Warszawskiej. Elektronika

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2016

|

z. 195, t. 2

585--594

PL

Zadanie planowania ruchu polega na wyznaczeniu funkcji sterującej, która doprowadzi układ do zadanego punktu końcowego w zadanym czasie. Niniejsza praca przedstawia modyfikację algorytmu planowania ruchu, która umożliwia osiągnięcie punktu docelowego w czasie krótszym niż założony horyzont czasowy. Wyprowadzenie algorytmu wykorzystuje ideę endogenicznej przestrzeni konfiguracyjnej, a jego konstrukcja bazuje na algorytmie z priorytetowaniem zadań dodatkowych. Efektywność przedstawionego podejścia jest zobrazowana wynikami symulacyjnymi.

EN

The motion planning problem consists in finding a control function which drives the system to desired point in a prescribed time interval. This work introduces an motion planning algorithm modification which allows to reach the destination in time which is shorter than the assumed time horizon. The algorithm derivation relies on the endogenous configurations pace approach, and the algorithm construction bases on the task-priority motion planning algorithm. The new algorithm efficiency is depicted with simulation results.

17

Nowe jakobianowe algorytmy planowania ruchu robotów nieholonomicznych

Tchoń K., Ratajczak J.

Prace Naukowe Politechniki Warszawskiej. Elektronika

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2016

|

z. 195, t. 2

541--552

PL

Praca przedstawia dwa algorytmy planowania ruchu robotów nieholonomicznych oparte na pojęciu lagranżowskiej i dynamicznie zgodnej odwrotności jakobianu. Do opisu układu nieholonomicznego wykorzystano metodę endogenicznej przestrzeni konfiguracyjnej. Oba algorytmy są oparte na odwrotnościach jakobianu uzyskanych jako rozwiązanie pewnego zadania sterowania optymalnego w układzie liniowym, zależnym od czasu. Działanie algorytmów planowania zilustrowano na przykładzie zadania planowania ruchu robota mobilnego typu trójkątny smok.

EN

This work presents two motion planning algorithms for non-holonomic robots based on the concepts of Lagrangian and dynamically consistent Jacobian inverse. New Jacobian inverses have been designed as solutions of a certain optimal control problem in a linear control system defining the Jacobian of the non-holonomic system. Performance of the algorithms is illustrated by a motion planning problem of the trident snake robot.

18

Algorytmy eksploracji i znajdowania ścieżki w labiryncie w robotach Micromouse

Wlazło D., Ogonowski M., Chmielniak A.

Prace Naukowe Politechniki Warszawskiej. Elektronika

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2016

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z. 195, t. 2

607--616

PL

Niewielkie roboty mobilne są bardzo dobrym polem do testowania procesów zachodzących w większych konstrukcjach. W artykule przedstawiono algorytmy eksploracji i znajdowania ścieżki robota typu Micromouse. Wskazano ich mocne i słabe strony oraz możliwości poprawy ich działania. Pokazano robota, którego zbudowano w celu implementacji różnych wersji algorytmów. Przeprowadzono badania testowe algorytmów i porównano ich działanie.

EN

Small mobile robots are a very good area for testing processes occuring in larger structures. The article presents the maze solving algorithms for micrornouse robots. Their strengths and weaknesses are pointed out. The paper presents opportunities to improve some of them. The robot designed for implementing different versions of the algorithms is shown. The algorithms were tested and compared.

19

Modeling and control of a skid-steering mobile platform with coupled side wheels

Tchoń K., Zadarnowska K., Juszkiewicz Ł., Arent K.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2015

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Vol. 63, nr 3

807--818

EN

This study is devoted to the modeling and control of a 4-wheel, skid-steering mobile platform with coupled side wheels, subject to lateral and longitudinal slips. The dynamics equations of the platform are derived, and 16 variants of motion distinguished. For the variant of motion allowing for all possible slips of the wheels two control problems are addressed: the motion planning problem and the trajectory tracking problem. The former problem is solved by means of a Jacobian motion planning algorithm based on the Endogenous Configuration Space Approach and, complementarily, using the Optimal Control Approach. The Nonlinear Model Predictive Control is applied to the latter problem. Performance of these control algorithms is illustrated by a sort of the parking problem. Significant robustness of the predictive control algorithm against the model uncertainty is revealed.

20

Dynamic Path Planning with Regular Triangulations

Brož P., Zemek M., Kolingerová I., Szkandera J.

Machine Graphics and Vision

|

2014

|

Vol. 23, No. 3/4

119--142

EN

Path planning is a well known problem that has been extensively studied in many scientific disciplines. In general, it defines a task of finding a path between two given spots in an abstract environment so that the path satisfies certain criterion of optimality. Although there are many methods solving this objective, they usually assume the examined space does not change in runtime. Modern applications, however, do not have to meet these requirements, especially in case of virtual reality or computer games. Therefore, we propose a general model for real-time path planning in dynamic environment where the obstacles can nondeterministically appear, disappear, change the position, orientation or even shape. The model uses a triangulation for dynamic space subdivision among bounding spheres of the obstacles and a heuristic algorithm to repair an already found path after any change of the scene. The presented solution is the first one using regular triangulation. At the price of the suboptimal result, it provides an efficient and fast way to plan a path with the maximal clearance among the moving and changing obstacles. In comparison to raster based techniques and methods using the Delaunay triangulation (Voronoi diagram), it requires less time to preprocess and generates paths with a larger clearance.