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1

Adaptive impedance control of robot manipulators with parametric uncertainty for constrained path-tracking

Bonilla I., Mendoza M., Campos-Delgado D. U., Hernández-Alfaro D. E.

International Journal of Applied Mathematics and Computer Science

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2018

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Vol. 28, no. 2

363--374

EN

The main impedance control schemes in the task space require accurate knowledge of the kinematics and dynamics of the robotic system to be controlled. In order to eliminate this dependence and preserve the structure of this kind of algorithms, this paper presents an adaptive impedance control approach to robot manipulators with kinematic and dynamic parametric uncertainty. The proposed scheme is an inverse dynamics control law that leads to the closed-loop system having a PD structure whose equilibrium point converges asymptotically to zero according to the formal stability analysis in the Lyapunov sense. In addition, the general structure of the scheme is composed of continuous functions and includes the modeling of most of the physical phenomena present in the dynamics of the robotic system. The main feature of this control scheme is that it allows precise path tracking in both free and constrained spaces (if the robot is in contact with the environment). The proper behavior of the closed-loop system is validated using a two degree-of-freedom robotic arm. For this benchmark good results were obtained and the control objective was achieved despite neglecting non modeled dynamics, such as viscous and Coulomb friction.

2

A fast evaluation of initial configurations in repeatable inverse kinematics for redundant manipulators

Duleba I., Karcz-Duleba I., Mielczarek A.

International Journal of Applied Mathematics and Computer Science

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2018

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Vol. 28, no. 3

483--492

EN

A repeatable inverse kinematic task in robot manipulators consists in finding a loop (cyclic trajectory) in a configuration space, which corresponds to a given loop in a task space. In the robotic literature, an entry configuration to the trajectory is fixed and given by a user. In this paper the assumption is released and a new, indirect method is introduced to find entry configurations generating short trajectories. The method avoids a computationally expensive evaluation of (infinite) many entry configurations for redundant manipulators (for each of them, repeatable inverse kinematics should be run). Some fast-to-compute functions are proposed to evaluate entry configurations and their correlations with resulting lengths of trajectories are computed. It appears that only an original function, based on characteristics of a manipulability subellipsoid, properly distinguishes entry configurations that generate short trajectories. This function can be used either to choose one from a few possible entry configurations or as an optimized function to compute the best initial configuration.

3

Saturating stiffness control of robot manipulators with bounded inputs

Rodríguez-Liñán M. C., Mendoza M., Bonilla I., Chávez-Olivares C. A.

International Journal of Applied Mathematics and Computer Science

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2017

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Vol. 27, no. 1

79--90

EN

A saturating stiffness control scheme for robot manipulators with bounded torque inputs is proposed. The control law is assumed to be a PD-type controller, and the corresponding Lyapunov stability analysis of the closed-loop equilibrium point is presented. The interaction between the robot manipulator and the environment is modeled as spring-like contact forces. The proper behavior of the closed-loop system is validated using a three degree-of-freedom robotic arm.

4

Robust force/position control based on mechatronic solution

Osypiuk R., Tarasiejski L., Domek S.

Advances in Manufacturing Science and Technology

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2007

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Vol. 31, nr 3

27-43

EN

Application of a mechatronic system to improve the effectiveness of the position/force control for industrial manipulators is discussed in the paper. Owing to high stiffness of the kinematic chain and variable environment stiffness, there is a need to employ advanced control systems in order to provide stable force control. The concept proposed and presented in the paper is meant for use with a 6DOF platform, however preliminary tests have been performed on a 1DOF system.

PL

Dokonano analizy zastosowania mechatronicznego systemu w celu poprawy efektywności sterowania położeniem i siłą dla manipulatorów przemysłowych. Duża sztywność łańcucha kinematycznego oraz zmienna sztywność otoczenia powodują konieczność stosowania zaawansowanych systemów dla zapewnienia stabilnego przebiegu procesu regulacji siły. Proponowano i omówiono hipotezę z użyciem platformy 6DOF. Wstępny eksperyment praktyczny wykonano dla systemu z jednym stopniem swobody.

5

A variable structure observer for the control of robot manipulators

Abdessameud A., Khelfi M. F.

International Journal of Applied Mathematics and Computer Science

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2006

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Vol. 16, no 2

189-196

EN

This paper deals with the application of a variable structure observer developed for a class of nonlinear systems to solve the trajectory tracking problem for rigid robot manipulators. The analyzed approach to observer design proposes a simple design methodology for systems having completely observable linear parts and bounded nonlinearities and/or uncertainties. This observer is basically the conventional Luenberger observer with an additional switching term that is used to guarantee robustness against modeling errors and system uncertainties. To solve the tracking problem, we use a control law developed for robot manipulators in the full information case. The closed loop system is shown to be globally asymptotically stable based on Lyapunov arguments. Simulation results on a 3-DOF robot manipulator show the asymptotic convergence of the vectors of observation and tracking errors.

6

Problems of the balancing of industrial robots manipulators

Wawrzecki J.

Mechanics and Mechanical Engineering

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2001

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Vol. 5, nr 2

147-154

EN

The paper deals with certain problems of balancing that occur in manipulators, i.e. kinematic units of industrial robots constituting open kinematic chains of many degrees of freedom. Publications in this field testify to the need of research on the balancing of such mechanisms.