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This paper addresses the problem of tracking a prescribed geometric path by the end effector of a kinematically redundant manipulator at the control loop level. The constraints imposed on the robot actuator controls are taken into account. The Lyapunov stability theory and/or the calculus of variations is used to derive the control scheme. Through the use of an exterior penalty function approach, an additional objective to be fulfilled by the robot, that is, collision avoidance of the manipulator links with obstacles, is ensured. The extensive computer simulation results illustrate the trajectory performance of the proposed control scheme for a geometric end effector path given in both an obstacle-free work space and a work space including obstacles. KEY WORDS—redundant manipulator, end-effector path, stability, collision avoidance 1

Trajectory tracking control of a mobile manipulator with an external force compensation

This paper considers the problem of the accurate task space finite-time control susceptible to both undesirable disturbance forces exerted on the end-effector and unknown friction forces coming from joints directly driven by the actuators as well as unstructured forces resulting from the kinematic singularities appearing on the mechanism trajectory. We obtain a class of estimated extended transposed Jacobian controllers which seem to successfully counteract the external disturbance forces on the basis of a suitably defined task-space non-singular terminal sliding manifold (TSM) and the Lyapunov stability theory. Moreover, in order to overcome (or to minimise) the undesirable chattering effects, the proposed robust control law involves the second-order sliding technique. The numerical simulations (closely related to an experiment) ran for a mobile manipulator consisting of a non-holononic platform of (2;0) type and a holonomic manipulator of two revolute kinematic pairs show the performance of the proposed controllers and make a comparison with other well-known control schemes

Sterowanie odporne śledzeniem trajektorii manipulatora kosmicznego w rozszerzonej przestrzeni zadaniowej

This study provides a new class of controllers for freeflying space manipulators subject to unknown undesirable disturbing forces exerted on the end-effector. Based on suitably defined taskspace non-singular terminal sliding manifold and the Lyapunov stability theory, we derive a class of estimated extended transposed Jacobian controllers which seem to be effective in counteracting the unstructured disturbing forces. The numerical computations which are carried out for a space manipulator consisting of a spacecraft propelled by eight thrusters and holonomic manipulator of three revolute kinematic pairs, illustrate the performance of the proposed controller.W pracy zaproponowano nową klasę sterowników dla manipulatorów kosmicznych przy uwzględnieniu nieznanych, niepożądanych sił zakłócających wywieranych na koniec efektora. W oparciu o odpowiednio zdefiniowane nieosobliwą, końcową rozmaitość ślizgową i teorię stabilności Lapunowa wyprowadzono klasę rozszerzonych estymowanych transponowanych sterowników Jakobianowych, ktore wydają się być efektywne w przeciwdziałaniu nieustrukturyzowanych sił zakłócających. Podejście zilustrowano również obliczeniami numerycznymi dla manipulatora kosmicznego składającego się z bazy napędzanej przez osiem pędników typu cold-gas i manipulatora holonomicznego o trzech parach kinematycznych obrotowych