This work offers the solution at the control feed-back level of the accurate trajectory tracking subject to finite-time convergence. Dynamic equations of a rigid robotic manipulator are assumed to be ...uncertain. Moreover, globally unbounded disturbances are allowed to act on the manipulator when tracking the trajectory. Based on the suitably defined non-singular terminal sliding vector variable and the Lyapunov stability theory, we propose a class of absolutely continuous robust controllers which seem to be effective in counteracting both uncertain dynamics and unbounded disturbances. The numerical simulation results carried out for a robotic manipulator consisting of two revolute kinematic pairs operating in a two-dimensional joint space illustrate performance of the proposed controllers.
This work addresses the problem of the accurate task space control subject to finite-time convergence. Dynamic equations of a rigid robotic manipulator are assumed to be uncertain. Moreover, globally ...unbounded disturbances are allowed to act on the manipulator when tracking the trajectory by the end-effector. Based on suitably defined task space non-singular terminal sliding vector variable and the Lyapunov stability theory, we derive a class of absolutely continuous Jacobian transpose robust controllers, which seem to be effective in counteracting uncertain dynamics, unbounded disturbances and (possible) kinematic and/or algorithmic singularities met on the end-effector trajectory. The numerical simulations carried out for a robotic manipulator of a SCARA type consisting of two revolute kinematic pairs and operating in a two-dimensional task space, illustrate performance of the proposed controllers.
This study proposes a new class of controllers for mobile manipulators subject to both undesirable forces exerted on the end-effector and unknown friction forces coming from joints directly driven by ...the actuators as well as undesirable forces resulting from the kinematic singularities appearing on the mechanism trajectory. Based on the suitably defined task space non-singular terminal sliding manifold (TSM) and the Lyapunov stability theory, we derive a class of estimated extended transposed Jacobian controllers which seem to be effective in counteracting the unstructured forces. Due to a redundant nature of the tasks to be accomplished, our controllers also a involve useful criterion function (energy consumption) in optimally tracking a desired trajectory. Moreover, in order to eliminate (or to alleviate) undesirable chattering effects the proposed control laws include second order sliding techniques. The numerical computations, which are carried out for a mobile manipulator consisting of a platform of (2, 0) type and a holonomic manipulator of two revolute kinematic pairs, illustrate the performance of the proposed controllers and simultaneously their minimizing properties. Numerical comparison with other control algorithms well-known in the literature is also given.
•We offer the solution of energy optimal robust control of mobile manipulators.•The mobile manipulator is subject to unknown external disturbance forces.•Controllers involve new non-singular TSM manifold to track desired trajectory.•The approach is based on utilizing the sliding techniques of the second order.•Our controllers tackle also singular configurations.
In this study, the solution to the kinematically optimal control problem of the mobile manipulators is proposed. Both dynamic equations are assumed to be uncertain, and globally unbounded ...disturbances are allowed to act on the mobile manipulator when tracking the trajectory by the end effector. We propose a computationally efficient class of cascaded control algorithms, which are based on an extended Jacobian transpose matrix. Our controllers involve two new non-singular terminal sliding mode manifolds defined by nonlinear integral equalities of both the second order with respect to the task space tracking error and the first order with respect to reduced mobile manipulator acceleration. Using the Lyapunov stability theory, we prove that the proposed Jacobian transpose cascaded control schemes are finite time stable provided that some practically reasonable assumptions are fulfilled during the mobile manipulator movement. The numerical examples carried out for mobile manipulators consisting of a non-holonomic platform of type (2, 0) and holonomic manipulators of 2 and 3 revolute kinematic pairs, which operate in two-dimensional and three-dimensional work spaces, respectively, illustrate both the trajectory tracking performance of the proposed control schemes and simultaneously their minimising property for some practically useful objective function.
This work offers the solution at the control feed-back level of the accurate positioning in a finite time of the end-effector whose mobile manipulator is subject to control and complex state ...constraints. We propose new forms of various terminal sliding modes (TSM’s) which result from the access to kinematic redundancy of the non-holonomic mechanical system. In order to incorporate control and state inequality constraints into trajectory generation law, both a suitably defined extended task error is introduced and exterior penalty function approach is utilized. In addition, to incorporate holonomic singularity avoidance condition, collision avoidance constraints for the whole mobile manipulator and its final velocity, a suitably defined projection term onto the null space of the extended Jacobian matrix has been introduced. Control limits are maintained by suitable choice of trajectory generator gains. The numerical simulation results carried out for a mobile manipulator consisting of a nonholonomic differentially steered wheeled mobile platform and a holonomic manipulator of two revolute kinematic pairs, operating both in a two-dimensional unconstrained work space and work space including the obstacles, illustrate performance of the proposed trajectory generators.
•A class of non-linear mobile manipulator trajectory generators is proposed.•The trajectory generation laws are shown to be finite-time stable.•Collision-free motion generators providing bounded controls are also offered.•The numerical simulations confirm theoretical results.
A new method to the planning of optimal motions of the non-holonomic systems is presented. It is based on a non-classical formulation of the Pontryagin Maximum Principle given in variational form, ...which handles efficiently various control and/or state-dependent constraints. They arise naturally due to both physical limits of the actuators of the non-holonomic systems and potential existence of obstacles in the workspace. The method proposed here provides continuous solutions in infinite-dimensional control space. It seems to be in contrast to majority of known optimization algorithms which project infinite-dimensional control space into finite-dimensional one and then apply techniques of linear and/or nonlinear programming, thus resulting only in near-optimal trajectories. Moreover, the offered control schemes do not require computation of inverse or pseudo-inverse of the Jacobian in the case of classic non-holonomic motion planning what also results in numerical stability of our approach. The performance of the proposed control strategies is illustrated through computer simulations for a chosen class of non-holonomic structures operating in both an obstacle-free workspace and a workspace including obstacles. Numerical comparison of our control scheme with the representative algorithms known from the literature is also given.
This paper addresses the problem of position control of mobile manipulators operating in the task space with state constraints. Motivated in part by the energy shaping and damping injection ...methodology, we first propose a class of non-linear model-based constraint task space regulators which, by the fulfilment of a reasonable condition, are shown both to be asymptotically stable and to provide an optimal solution at the desired end-effector location. This methodology is then generalized to a class of both parametrically uncertain kinematic and dynamic equations of the mobile manipulators. The position control problem in the presence of kinematic and dynamic uncertainties and (unknown) environment (obstacles) is solved herein based on the Lyapunov stability theory, the exterior penalty function approach and by using the sensory feed-back of the end-effector and the sensors, in which the mobile manipulator is equipped. Novel adaptive laws, extending the capability of the classic algorithms to deal with both holonomic and nonholonomic kinematic uncertainties and obstacles, are proposed.
•We offer the solution of constraint position control problem of mobile manipulators.•It is subject to state equality and/or inequality constraints.•Kinematics and dynamics of mobile manipulators are parametric uncertain.•We propose a class of asymptotically stable controllers to solve this control task.
This paper addresses the control problem in a task space of the redundant and/or non-redundant manipulators with both known and parametric unknown kinematics and dynamics. A computationally simple ...class of the inverse-free control algorithms is proposed for the end-effector trajectory tracking. These controllers use some suitably constructed non-singular matrix whose inverse estimates the product of the manipulator Jacobian by its transposition. Moreover, by introducing a suitably defined sliding vector and nonlinear errors of the parameters estimation, the new controllers generate bounded and continuous signals. Based on the Lyapunov stability theory, inverse-free control schemes proposed are shown to be asymptotically stable provided that some reasonable assumptions are fulfilled during the manipulator movement. The performance of the proposed control strategies is illustrated through computer simulations for a planar redundant manipulator of three revolute kinematic pairs which accomplishes trajectory tracking by the end-effector in a two-dimensional task space.
•A class of kinematic inverse-free nonlinear manipulator controllers is proposed.•The control laws are shown to be asymptotically stable.•Adaptive inverse-free controllers generating bounded controls are also offered.•The numerical simulations confirm theoretical results.
This paper addresses the kinematically optimal control problem of the mobile manipulators. Dynamic equations of the mobile manipulator are assumed to be uncertain. Moreover, globally unbounded ...disturbances are allowed to act on the mobile manipulator when tracking the trajectory by the end-effector. A computationally simple class of the Jacobian transpose control algorithms is proposed for the end-effector trajectory tracking. Such controllers apply a new non-singular Terminal Sliding Mode (TSM) manifold defined by a non-linear integral equality of the second order with respect to the task space tracking error. Based on the Lyapunov stability theory, the proposed Jacobian transpose control schemes are proved to be finite-time stable provided that some well-founded assumptions are fulfilled during the mobile manipulator movement. The performance of the proposed control strategies is illustrated through computer simulations for a mobile manipulator that attains trajectory tracking by the end-effector in a two-dimensional task space and simultaneously minimises some objective function.
This work offers the solution at the control feed-back level of the end-effector trajectory tracking problem for mobile manipulators subject to state equality and/or inequality constraints, suitably ...transformed into control dependent ones. Based on the Lyapunov stability theory, a class of controllers fulfilling the above constraints and generating a collision-free mobile manipulator trajectory with (instantaneous) minimal energy, is proposed. The problem of collision avoidance is solved here based on an exterior penalty function approach which results in continuous and bounded mobile manipulator controls even near boundaries of obstacles. The numerical simulation results carried out for a mobile manipulator consisting of a non-holonomic unicycle and a holonomic manipulator of two revolute kinematic pairs, operating both in a two-dimensional unconstrained task space and task space including the obstacles, illustrate the performance of the proposed controllers.
PDF
