Finding the general solution of partial differential equations (PDEs) is essential for controller design in newly developed methods. Interconnection and damping assignment passivity-based control (IDA-PBC) is one of such methods in which the solution to corresponding PDEs which are called matching equations is needed to apply it in practice. In this paper, these matching equations are transformed to corresponding Pfaffian differential equations. Furthermore, it is shown that upon satisfaction of the integrability condition, the solution to the corresponding third-order Pfaffian differential equation may be obtained quite easily. The method is applied to the PDEs of IDA-PBC in some benchmark systems such as Magnetic levitation system, Pendubot, and underactuated cable-driven robot to verify its applicability.

In underactuated robots (URs) with closed kinematic chains, the task space configuration variables are coupled through complex dynamics. In this paper, the regulation control of a 3-DOF underactuated cable-driven parallel robot is investigated by using the interconnection and damping assignment passivity based control (IDA-PBC) approach which is designed based on the solution of some challenging partial differential equations (PDEs). Additionally, as cables can only pull, positive tension in cables shall also be taken into account. Here, the corresponding PDE for controller design is solved by transforming the PDE into some Pfaffian differential equations. Then, boundedness of control efforts are ensured via suitable modification of the gains. Furthermore, an adaptation law for the mass of the robot is designed and the system stability is investigated through Lyapunov direct method. The efficiency of the …

Cable-driven parallel robots with redundant actuators are faced with the problem of loose cables, especially when the robot is deployable and controlled within the joint space. This paper aims to addresses this shortcoming by proposing a suitable robust controller which requires no expensive positioning sensors such as laser trackers. The robot’s embedded force sensors are used alongside a new sliding surface for the robust controller to avoid loose cables even in the presence of kinematic and dynamic uncertainties. Therefore, conventional joint-space controllers are modified to become applicable for cable-driven robots, while assuring positive cable tensions. Implementation results on the ARAS suspended cable-driven parallel robot illustrate the effectiveness of the proposed control architecture and the feasibility of stable solutions.

Despite model-based approaches are capable of providing acceptable performance, but they require complex dynamics modeling, which make them difficult to apply. To overcome this problem, a time-delay learning-based controller as a model-free approach is proposed for fully-constrained cable-driven parallel robots (CDPRs) considering the positive cable force constraints and actuator limitations. The proposed method uses the memory of control effort as a learning element to linearize the system. In addition, using a saturation function in control law has provided the opportunity to ensure all the cables are bounded and remain in tension, to guarantee both the positive cable forces and actuator limitation. Moreover, in the proposed method, we are able to eliminate the requirement of measurement of the task variables, which is very costly by using expensive external positioning measurement systems. Finally, a …

One of the most challenging issues in adaptive control of robot manipulators with kinematic uncertainties is the requirement of inverse Jacobian matrix in regressor form. This requirement is inevitable in the case of the control of parallel robots, whose dynamics formulation are derived in the task space. In this paper, an adaptive controller is proposed for parallel robots based on representation of Jacobian matrix in regressor form with asymptotic trajectory tracking.

One of the most challenging issues in adaptive control of robot manipulators with kinematic uncertainties is requirement of the inverse of Jacobian matrix in regressor form. This requirement is inevitable in the case of the control of parallel robots, whose dynamic equations are written directly in the task space. In this paper, an adaptive controller is designed for parallel robots based on representation of Jacobian matrix in regressor form, such that asymptotic trajectory tracking is ensured. The main idea is separation of determinant and adjugate of Jacobian matrix and then organize new regressor forms. Simulation and experimental results on a 2--DOF R\underline{P}R and 3--DOF redundant cable driven robot, verify promising performance of the proposed methods.

In this paper, Large-scale deployable cable-driven robots face a lack of kinematic precision, and the cable dynamics impose considerable challenges in terms of controller design. The problem’s complexity increases because a deployable robot may not exploit expensive and highly accurate of measurement devices.

The attitude control of a quadrotor is a fundamental problem, which has a pivotal role in a quadrotor stabilization and control. What makes this problem more challenging is the presence of uncertainty such as unmodelled dynamics and unknown parameters. In this paper, to cope with uncertainty, an control approach is adopted for a real quadrotor

Despite the intense development of cable-driven robot in recent years, they have not yet been
vastly utilized in their potential applications because of difficulties in their performing accurate
installation and calibration. This paper aims to present a suitable control method, relieving the
limitation of accurate calibration and installation requirement in the suspended cable-driven
parallel robot. In this paper, kinematics and dynamics uncertainties are investigated and based
on their bounds, a robust controller is proposed. The main innovation of this article is providing
a new control method to cost reduction by eliminating accurate measurement tools such as a
camera in position control of a deployable cable-driven robot. Using this approach, reducing
costs in building a robot and increasing the speed of installation and calibration is achieved.
Another problem investigated in this paper is the problem of joint space controllers applied
to redundant cable-driven parallel robots, namely the loosened redundant cable. To solve this
problem, the embedded force sensor and a new sliding surface for the controller is proposed. In
fact, in this paper, the conventional joint-space controllers are modified to become applicable
to the control of cable-driven robots. Finally, by conducting some experiments using ARAS
suspended cable-driven parallel robot, the proposed algorithms are verified and it is shown
that there are feasible solutions for stable robot maneuvers.

Increasing the speed and precision of operation in
cable robots is crucial due to the flexibility of cables. On the other hand, due to the frequent dynamical uncertainties present in
cable robots, providing a robust control method is necessary. The
performance of the fast terminal sliding mode (FTSM) controller
has been investigated in various systems, which ensures that
the state of the system is rapidly converged to the equilibrium
point at a finite time. In this paper, the FTSM controller has
been developed in such a way to be able to track the optimal robot path in the presence of dynamic uncertainties at different operating speeds. The main innovation of this paper is to provide
an adaptive robust control method for controlling cable robots and analyzing the stability of the closed-loop control system
based on the Lyapunov stability theory. In order to demonstrate
the effectiveness of the proposed controller, simulation results,
as well as experimental implementation on ARAS–CAM, a four
cable suspended robot with three degrees of freedom, has been
investigated and it is shown that the proposed controller can
provide suitable tracking performance in practice.

Despite of bing intensively developed, cable driven parallel manipulators are not yet vastly used due to their requirements for accurate assembly and installation. The main goal of this paper is to propose a suitable control method by which the robot could be suitably controlled without the requirement for undergoing any accurate calibration process. Here this robot is called deployable cable driven manipulator, in which the positions of the cable attachment points are not accurately known. This uncertainty in measurements will affect many parameters in the kinematic model especially the Jacobian matrix which is used as a force distributer in the Cartesian-space control strategies. In this paper in order to overcome this problem, a robust dynamic sliding mode controller is proposed. Then robust stability of the closed-loop system is analyzed through the Lyapunov direct method and by accordingly appropriate controller gain selection is performed. In order to illustrate the performance of the proposed controller, the robot is simulated in ADAMS software and it is shown that a suitable controller performance could be achieved.

In this paper, forward kinematic derivation of a deployable suspended cable robot (DSCR) is investigated. Since the positions of the cable attachment points in this robot are not accurately available, the forward kinematics of the robot would not provide an accurate estimate for the end effector position. This paper proposes two methods to improve the accuracy of the forward kinematic solutions. First, an analysis on parameter sensitivity is presented and effective parameters are extracted. Then, based on these parameters and by using the redundant equations of the DSCR, a new set of equations for forward kinematic analysis are derived. The second method proposed in this paper is based on a geometrical analysis of kinematic uncertainty bounds. Finally, using the simulation results the effectiveness of the proposed methods is verified by illustrating the significant accuracy improvement in the obtained end effector positions.

In this paper robust PID control of fully-constrained cable driven parallel manipulators with elastic cables is studied in detail. In dynamic analysis, it is assumed that the dominant dynamics of cable can be approximated by linear axial spring. To develop the idea of control for cable robots with elastic cables, a robust PID control for cable driven robots with ideal rigid cables is firstly designed and then, this controller is modified for the robots with elastic cables. To overcome vibrations caused by inevitable elasticity of cables, a composite control law is proposed based on singular perturbation theory. The proposed control algorithm includes robust PID control for corresponding rigid model and a corrective term. Using the proposed control algorithm the dynamics of the cable driven robot is divided into slow and fast subsystems. Then, based on the results of singular perturbation theory, stability analysis of the total system is performed. Finally, the effectiveness of the proposed control law is investigated through several simulations on a planar cable driven robot.

In this paper robust PID control of fully-constrained cable driven parallel manipulators with elastic cables is studied in detail. In dynamic analysis, it is assumed that the dominant dynamics of cable can be approximated by linear axial spring. To develop the idea of control for cable robots with elastic cables, a robust PID control for cable driven robots with ideal rigid cables is firstly designed and then, this controller is modified for the robots with elastic cables. To overcome vibrations caused by inevitable elasticity of cables, a composite control law is proposed based on singular perturbation theory. The proposed control algorithm includes robust PID control for corresponding rigid model and a corrective term. Using the proposed control algorithm the dynamics of the cable driven robot is divided into slow and fast subsystems. Then, based on the results of singular perturbation theory, stability analysis of the total system is performed. Finally, the effectiveness of the proposed control law is investigated through several simulations on a planar cable driven robot.

In this paper, adaptive robust control of fully constrained cable-driven parallel robots with elastic cables is studied in detail. A composite controller is proposed for the system under the assumption of linear axial spring model as the dominant dynamics of the cables and in presence of model uncertainties. The proposed controller which is designed based on the singular perturbation theory, consists of two main parts. An adaptive robust controller is designed to counteract the unstructured and parametric uncertainties of the robot and a fast control term which is added to control the longitudinal vibrations of the cables. Moreover, to ensure that all cables remain in tension, the proposed control algorithm benefits from internal force concept. Using the results of the singular perturbation theory, the stability of the overall closed-loop system is analyzed through Lyapunov second method, and finally, the effectiveness of the proposed control algorithm is verified through some simulations on a planar cable-driven parallel robot.

In this paper, adaptive robust control (ARC) of fully-constrained cable driven parallel robots is studied in detail. Since kinematic and dynamic models of the robot are partly structurally unknown in practice, in this paper an adaptive robust sliding mode controller is proposed based on the adaptation of the upper bound of the uncertainties. This approach does not require pre-knowledge of the uncertainties upper bounds and linear regression form of kinematic and dynamic models. Moreover, to ensure that all cables remain in tension, proposed control algorithm benefit the internal force concept in its structure. The proposed controller not only keeps all cables under tension for the whole workspace of the robot, it is chattering-free, computationally simple and it does not require measurement of the end-effector acceleration. The stability of the closed-loop system with proposed control algorithm is analyzed through Lyapunov second method and it is shown that the tracking error will remain uniformly ultimately bounded (UUB). Finally, the effectiveness of the proposed control algorithm is examined through some experiments on a planar cable driven parallel robot and it is shown that the proposed controller is able to provide suitable tracking performance in practice.

This paper addresses the design and implementation of adaptive control on a planar cable-driven parallel robot with uncertainties in dynamic and kinematic parameters. To develop the idea, firstly, adaptation is performed on dynamic parameters and it is shown that the controller is stable despite the kinematic uncertainties. Then, internal force term is linearly separated into a regressor matrix in addition to a kinematic parameter vector that contains estimation error. In the next step to improve the controller performance, adaptation is performed on both the dynamic and kinematic parameters. It is shown that the performance of the proposed controller is improved by correction in the internal forces. The proposed controller not only keeps all cables in tension for the whole workspace of the robot, it is computationally simple and it does not require measurement of the end-effector acceleration as well. Finally, the effectiveness of the proposed control algorithm is examined through some experiments on KNTU planar cable-driven parallel robot and it is shown that the proposed control algorithm is able to provide suitable performance in practice.

Spherical Parallel Robot (SPR) is a complex but widely used type of manipulators that performs only rotational motion. Dynamic analysis of SPR has a vital role in mechanical design, model-based controller, identification and fault detection of such robots. Complexity of SPR kinematic structure makes traditional dynamic modeling methods such as Newton-Euler, virtual work and Lagrange formulations a prohibitive task. In this paper a new procedure for deriving closed form dynamics of general SPR using Gibbs-Appell method is presented. The proposed method does not require any recursive computation or symbolic manipulation and dynamic matrices of the robot is directly derived in an explicit form. By using the proposed method, closed form dynamic formulation of a general 3DOF SPR, known as agile wrist, is obtained and it is verified for an arbitrary trajectory. The unique feature of the method presented in this paper, makes it promising to be used for other parallel manipulators.

In this paper, control of fully-constrained parallel cable robots with elastic cables is studied in detail. In the modeling process, longitudinal vibration of cables is considered as their dominant dynamics, and the governing equations of motion are rewritten to the standard form of singular perturbation. The proposed composite controller consists of two main components. A rigid controller is designed based on the slow or rigid model of the system and a corrective term is added to guarantee asymptotic stability of the fast dynamics. Then, by using Tikhonov theorem, slow and fast variables are separated and incorporated into the stability analysis of the overall closed-loop system, and a set of sufficient conditions for the stability of the total system is derived. Finally, the effectiveness of the proposed control law is verified through simulations.

In this paper, control of fully-constrained parallel cable robots with elastic cables is studied in detail. In the modeling process, longitudinal vibration of cables is considered as their dominant dynamics, and the governing equations of motion are rewritten to the standard form of singular perturbation. The proposed composite controller consists of two main components. A rigid controller is designed based on the slow or rigid model of the system and a corrective term is added to guarantee asymptotic stability of the fast dynamics. Then, by using Tikhonov theorem, slow and fast variables are separated and incorporated into the stability analysis of the overall closed-loop system, and a set of sufficient conditions for the stability of the total system is derived. Finally, the effectiveness of the proposed control law is verified through simulations.

In this paper robust PID control of fully-constrained cable-driven robots with elastic cables is studied in detail. To develop the idea, a robust PID control for cable-driven robots with ideal rigid cables is firstly designed and then, this controller is extended for the robots with elastic cables. To overcome vibrations caused by inevitable elasticity of cables, a composite control law is proposed based on singular perturbation theory. The proposed control algorithm includes robust PID control for corresponding rigid model and a corrective term. Using the proposed control algorithm the dynamics of the cable-driven robot is divided into slow and fast subsystems. Then, based on the results of singular perturbation theory, stability analysis of the total system is performed. Finally, the effectiveness of the proposed control law is investigated through several simulations on a planar cable-driven robot.

In this paper, some new kinematic performance indices are proposed and examined on four planar cable driven parallel manipulators. The main kinematic indices are based on kinematic sensitivity and controllable workspace of the robot. Interval analysis is adopted as a mathematical framework to compute feasible kinematic sensitivity and worst kinematic sensitivity indices. For determining the feasible kinematic sensitivity, the controllable workspace is combined with the desired kinematic sensitivity property. The area of the foregoing region and the worst kinematic sensitivity corresponding to it are introduced as practical design indices. Then four typical design of planar cable robot are examined by the following performance measures, and one of such designs are selected and implemented in practice.

In this paper dynamic analysis and experimental performance of robust PID control for fully-constrained cable driven robots are studied in detail. Since in this class of manipulators cables should remain in tension for all maneuvers through their whole workspace, feedback control of such robots becomes more challenging than conventional parallel robots. To ensure that all the cables remain in tension, a corrective term is used in the proposed PID control scheme. In design of PID control it is assumed that there exist bounded norm uncertainties in Jacobian matrix and in all dynamics matrices. Then a robust PID controller is proposed to overcome partial knowledge of robot, and to guarantee boundedness of tracking errors. Finally, the effectiveness of the proposed PID algorithm is examined through experiments and it is shown that the proposed control structure is able to provide suitable performance in practice.

Workspace analysis is always a crucial issue in robotic manipulator design. This paper introduces a set of newly defined fundamental wrenches that opens new horizons to physical interpretation of controllable workspace of a general cable-driven redundant parallel manipulator. Based on this set of fundamental wrenches, a novel tool is presented to determine configurations of cable-driven redundant parallel manipulator that belong to the controllable workspace. Analytical expressions of such workspace boundaries are obtained in an implicit form and a rigorous mathematical proof is provided for this method. Finally, the proposed method is implemented on a spatial cable-driven manipulator of interest.

Workspace analysis is one of the most important issues in robotic manipulator design. This paper introduces a set of newly defined fundamental wrenches that opens new horizons for physical interpretation of controllable workspace of cable driven redundant parallel manipulators. Moreover, an analytical method is proposed to specify the controllable workspace of general redundant cabledriven parallel manipulators based on this set of fundamental wrenches. In the proposed method, an analytic approach based on linear algebra is employed to derive the boundary of controllable workspace. Finally, the proposed method is illustrated through spatial example.

In this paper modeling and control of cable driven redundant parallel manipulators with flexible cables, are studied in detail. Based on new results, in fully constrained cable robots, cables can be modeled as axial linear springs. Considering this assumption the system dynamics formulation is developed using Lagrange approach. Since in this class of robots, all the cables should remain in tension for the whole workspace, the notion of internal forces are introduced and incorporated in the proposed control algorithm. The control algorithm is developed in cable coordinates in which the internal forces play an important role. Finally, asymptotic stability of the closed loop system is analyzed through Lyapunov theorem, and the performance of the proposed algorithm is studied by simulations

The kinematic sensitivity is a unit-consistent measure that has been recently proposed as a mechanism performance index to compare robot architectures. This paper presents a robust geometric approach for computing this index for the case of planar parallel mechanisms. The physical meaning of the kinematic sensitivity is investigated through different combinations of the Euclidean and infinity norms and by means of several illustrative examples. Finally, this paper opens some avenues to the dimensional synthesis of parallel mechanisms by exploring the meaning of the global kinematic sensitivity index.

In this paper modelling and control of cable-driven redundant parallel manipulators (CDRPM) with flexible cables are studied in detail. In this type of manipulators the cables should remain in tension in the whole workspace. New research results have shown that in fully constrained CDRPM cable can be modelled as an axial spring. Based on this fact a new model of this type of robot is studied. Furthermore, internal forces are introduced and incorporated in the proposed control algorithm. This control algorithm is formed in cable length coordinates in which the internal forces play an important role. Finally, the closed loop system is proved to be stable, through Lyapunov analysis, and the performance of the proposed algorithm is studied through simulation.

This paper deals with the optimization of 3-RPR planar parallel mechanisms based on different per-formance indices including kinematic sensitivity, stiffness, workspace and singularity. The optimization is imple-mented in sequence using first a single objective tech-nique, differential evolution, and then resorting to a multi-objective optimization concept, the so-called nondomi-nated sorting genetic algorithm-II. The results revealed that the optimality of the mechanism under study is scale-independent for the considered optimization objectives. Moreover, based on the scale invariance property of the main objectives, it follows that different kinetoestatic ob-jective functions must be scale invariant. The relations for the kinetoestatic objective expressions as functions of mech-anism scale are derived and to circumvent the problem of unit inconsistency the rotational and translational parts of these objectives are considered separately. To overcome the problem of inconsistent objectives in optimization al-gorithm, a Pareto-based multi-objective approach is used which preserves the scale invariance property.

In this paper, redundancy resolution of a cable-driven parallel manipulator is performed through an analytic-iterative scheme. The redundancy resolution scheme is formulated as a convex optimization problem with inequality constraints that are imposed by manipulator structure and cable dynamics. The Karush-Kuhn-Tucker theorem is used to analyze the optimization problem and to draw an analytic-iterative solution for it. Subsequently, a tractable and iterative search algorithm is proposed to implement the redundancy resolution of such redundant manipulators. Furthermore, it is shown through simulations that the worst case and average elapsed time that is required to implement the proposed redundancy resolution scheme in a closed-loop implementation is considerably less than that of other numerical optimization methods.

This paper investigates an important kinematic property, the constant-orientation workspace, of five-degree-of-freedom parallel mechanisms generating the 3T2R motion and comprising five identical limbs of the P RUR type. The general mechanism originates from the type synthesis performed for symmetrical 5-DOF parallel mechanism. In this study, the emphasis is placed on the determination of constant-orientation workspace using geometrical interpretation of the so-called vertex space, i.e., motion generated by a limb for a given orientation, rather than relying on classical recipes, such as discretization methods. For the sake of better understanding a CAD model is also provided for the vertex space. The constructive geometric approach presented in this paper provides some insight into the architecture optimization. Moreover, this approach facilitates the computation of the evolution of the volume of the constant-orientation workspace for different orientations of the end-effector.

This paper presents an approach to the control of the KNTU CDRPM using an integrated control scheme. The goal in this approach is achieving accurate trajectory tracking while assuring positive tension in the cables. By the proposed controller, the inherent nonlinear behavior of the cable and the target tracking errors are simultaneously compensated. In this paper asymptotic stability analysis of the close loop system is studied in detail. Moreover, it is shown that the integrated control strategy reduces the tracking error by 80% compared to that of a single loop controller in the considered manipulator. The closed-loop performance of the control topology is analyzed by a simulation study that is performed on the manipulator. The simulation study verifies that the proposed controller is not only promising to be implemented on the KNTU CDRPM, but also being suitable for other cable driven manipulators.

Dynamic analysis of parallel manipulators plays a vital role in the design and control of such manipulators. Closed-chain kinematic structure affects the dynamics formulations by several constraints. Therefore, especially for higher degrees of freedom manipulators, manipulation of implicit and bulky dynamics formulation looses the tractability of the analysis. In this paper, a methodology and some simplification tools are introduced to achieve explicit dynamics formulation for parallel manipulators. This methodology is applied for the dynamics analysis of the most celebrated parallel manipulator, namely Stewart-Gough platform. By avoiding any recursive or component-wise derivations, the resulting dynamics formulation provides more insight for designers, and can be much easier used in any model-based control of such manipulators. In order to verify the resulting dynamics equations, Lagrange method is used to derive and compare the manipulator mass matrix. This methodology can be further used to formulate the explicit dynamics of other parallel manipulators.Dynamic analysis of parallel manipulators plays a vital role in the design and control of such manipulators. Closed-chain kinematic structure affects the dynamics formulations by several constraints. Therefore, especially for higher degrees of freedom manipulators, manipulation of implicit and bulky dynamics formulation looses the tractability of the analysis. In this paper, a methodology and some simplification tools are introduced to achieve explicit dynamics formulation for parallel manipulators. This methodology is applied for the dynamics analysis of the most celebrated parallel manipulator, namely Stewart-Gough platform. By avoiding any recursive or component-wise derivations, the resulting dynamics formulation provides more insight for designers, and can be much easier used in any model-based control of such manipulators. In order to verify the resulting dynamics equations, Lagrange method is used to derive and compare the manipulator mass matrix. This methodology can be further used to formulate the explicit dynamics of other parallel manipulators.

Workspace analysis is one of the most important issues in robotic manipulator design. This paper introduces a systematic method of analysis the wrench feasible workspace for general redundant cable-driven parallel manipulators. In this method, wrench feasible workspace is formulated in term of linear matrix inequalities and projective method is used for solving them. This method is one of the most efficient interior-point methods with a polynomial-time complexity. Moreover, the notion of dexterous workspace is defined, which can be determined for redundant cable driven manipulators exerting a worst case external wrench at the end effector. A detailed case study of the wrench feasible workspace and dexterous workspace determination are included for a six DOF, eight actuated cable-driven redundant parallel manipulator.

The challenging control problem of the cable driven redundant manipulators is due to the complexity of its dynamic and the required stringent performance for the its promising applications. This paper presents an approach to the control of the KNTU CDRPM using an adaptive cascade control scheme. The goal in this approach is achieving accurate trajectory tracking while assuring positive tension in the cables. The cascade control topology uses two loops, namely the internal and external loops. The inherent nonlinear behavior of the cable manipulator is controlled by the internal loop, while the external loop can effectively reduce the target tracking errors of the end-effector in the presence of disturbance force/torques. The cascade strategy reduces the tracking error by 80% compared to that of a single loop controller in the KNTU CDRPM. Moreover, adaptation of the cascade controller gains can significantly improve the overall tracking performance. The closed-loop performance of various control topologies are analyzed by a simulation study that is performed on the KNTU CDRPM. Since, the dynamic equations of this parallel manipulator is implicit in its general form, special integration routines are used for integration. The simulation study verifies that the proposed controller is not only promising to be implemented on the KNTU CDRPM, but also being suitable for other cable driven manipulators.

In this paper the dynamic analysis of a macro–micro parallel manipulator is studied in detail. The manipulator architecture is a simplified planar version adopted from the structure of the Large Adaptive Reflector (LAR), the Canadian design of next-generation giant radio telescopes. In this structure it is proposed to use two parallel redundant manipulators at the macro and micro level, both actuated by cables. In this paper, the governing dynamic equation of motion of such a structure is derived using the Newton–Euler formulation. Next, the dynamic equations of the system are used in the open-loop inverse dynamics simulations, as well as closed-loop forward dynamics simulations. In the open-loop dynamic simulations it is observed that the inertial forces of the limbs contribute only 10% of the dynamic forces required to generate a typical trajectory and, moreover, the total dynamic forces contribute only 10% of the experimentally measured disturbance forces. Furthermore, in the closed-loop simulations using decentralized PD controllers at the macro and micro levels, it is shown that the macro–micro structure results in a 10 times more accurate positioning than that in the first stage of the macro–micro structure. This convincing result promotes the use of the macro–micro structure for LAR application.

In this paper the dynamic analysis of a cable-driven parallel manipulator is studied in detail. The manipulator architecture is a simplified planar version adopted from the structure of large adaptive reflector (LAR), the Canadian design of next generation giant radio telescopes. This structure consists of a parallel redundant manipulator actuated by long cables. The dynamic equations of this structure are nonlinear and implicit. Long cables, large amounts of impelling forces and high accelerations raise more concern about the elasticity of cables during dynamic analysis, which has been neglected in the preceding works. In this paper, the kinematic analysis of such manipulator is illustrated first. Then the nonlinear dynamic of such mechanism is derived using Newton-Euler formulation. Next a simple model for cable dynamics containing elastic and damping behavior is proposed. The proposed model neither ignores longitude elasticity properties of cable nor makes dynamic formulations heavily complicated like previous researches. Finally, manipulator dynamic with cable dynamic is derived, and the cable elasticity effects are compared in a simulation study. The results show significant role of elasticity in a cable-driven parallel manipulator such as the one used in LAR mechanism.

This paper is devoted to the control of a cable driven redundant parallel manipulator, which is a challenging problem due the optimal resolution of its inherent redundancy. Additionally to complicated forward kinematics, having a wide workspace makes it difficult to directly measure the pose of the end-effector. The goal of the controller is trajectory tracking in a large and singular free workspace, and to guarantee that the cables are always under tension. A control topology is proposed in this paper which is capable to fulfill the stringent positioning requirements for these type of manipulators. Closed-loop performance of various control topologies are compared by simulation of the closed-loop dynamics of the KNTU CDRPM, while the equations of parallel manipulator dynamics are implicit in structure and only special integration routines can be used for their integration. It is shown that the proposed joint space controller is capable to satisfy the required tracking performance, despite the inherent limitation of task space pose measurement.

KNTU CDRPM is a cable driven redundant parallel manipulator, which is under investigation for possible implementation of large workspace applications. This newly developed manipulators have several advantages compared to the conventional parable mechanisms. In this paper, the governing dynamic equation of motion of such structure is derived using the Newton-Euler formulation. Next, the dynamic equations of the system are used in simulations. It is shown that on the contrary to serial manipulators, dynamic equations of motion of cable-driven parallel manipulators can be only represented implicitly, and only special integration routines can be used for their simulations. In order to verify the accuracy and integrity of the derived dynamic equations, open- and closed-loop simulations for the system is performed and analyzed. Also, the effects of mechanical assembly tolerances on the closed-loop control performance of a cable driven parallel robot are studied in detail, and the sensitivity analysis of the precision in the construction and assembly of the system on the closed-loop behavior of the KNTU CDRPM is performed.

In this paper the kinematic analysis of a macro-micro parallel manipulator is studied in detail. The manipulator architecture is a simplified planar version adopted from the structure of large adaptive reflector (LAR), the Canadian design of next generation giant radio telescopes. This structure is composed of two parallel and redundantly actuated manipulators at macro and micro level, which both are cable-driven. Inverse and forward kinematic analysis of this structure is presented in this paper. It is shown that unique closed form solution to the inverse kinematic problem of such structure exists. However, the forward kinematic solution is derived using numerical methods, and simulation results are reported to illustrate the integrity and accuracy of the solution.

In this paper the dynamic analysis of a macro–micro parallel manipulator is studied in detail. The manipulator architecture is a simplified planar version adopted from the structure of the Large Adaptive Reflector (LAR), the Canadian design of next-generation giant radio telescopes. In this structure it is proposed to use two parallel redundant manipulators at the macro and micro level, both actuated by cables. In this paper, the governing dynamic equation of motion of such a structure is derived using the Newton–Euler formulation. Next, the dynamic equations of the system are used in the open-loop inverse dynamics simulations, as well as closed-loop forward dynamics simulations. In the open-loop dynamic simulations it is observed that the inertial forces of the limbs contribute only 10% of the dynamic forces required to generate a typical trajectory and, moreover, the total dynamic forces contribute only 10% of the experimentally measured disturbance forces. Furthermore, in the closed-loop simulations using decentralized PD controllers at the macro and micro levels, it is shown that the macro–micro structure results in a 10 times more accurate positioning than that in the first stage of the macro–micro structure. This convincing result promotes the use of the macro–micro structure for LAR application.

In this paper, three numerical methods are presented to solve the forward kinematics of a three DOF actuator-redundant hydraulic parallel manipulator. It is known, that on the contrary to series manipulators, the forward kinematic map of parallel manipulators involves highly coupled nonlinear equations, whose closed-form solution derivation is a real challenge. This issue is of great importance noting that the forward kinematics solution is a key element in closed loop position control of parallel manipulators. The proposed methods, namely the Neural Network Estimation, the Quasi-closed Solution, and the Taylor series approximation, are using mainly numerical computations, with different ideas to solve the problem in hand. The latter two methods are proposed for the first time in literature to solve the forward kinematics of a parallel manipulator. These methods are compared in detail and the advantages or the disadvantages of each method in computing the forward kinematic map of the given mechanism is discussed. It is shown that a 4th order Taylor series approximation to the problem provides a good compromise for practical applications compared to that of other methods considered in this paper.

In this paper, kinematic modeling and singularity analysis of a three DOF redundant parallel manipulator has been elaborated in detail. It is known, that on the contrary to series manipulators, the forward kinematic map of parallel manipulators involves highly coupled nonlinear equations, whose closed-form solution derivation is a real challenge. This issue is of great importance noting that the forward kinematics solution is a key element in closed loop position control of parallel manipulators. Using the novel idea of kinematic chains recently developed for parallel manipulators, both inverse and forward kinematics of our parallel manipulator are fully developed, and a closed-form solution for the forward kinematic map of the parallel manipulator is derived. The closed form solution is also obtained in detail for the Jacobian of the mechanism and singularity analysis of the manipulator is performed based on the computed Jacobian.

In this paper, different approaches to solve the forward kinematics of a three DOF actuator redundant hydraulic parallel manipulator are presented. On the contrary to series manipulators, the forward kinematic map of parallel manipulators involves highly coupled nonlinear equations, which are almost impossible to solve analytically. The proposed methods are using neural networks identification with different structures to solve the problem. The accuracy of the results of each method is analyzed in detail and the advantages and the disadvantages of them in computing the forward kinematic map of the given mechanism is discussed in detail. It is concluded that ANFIS presents the best performance compared to MLP, RBF and PNN networks in this particular application.

In this paper, a quasi-closed solution method is presented to solve the forward kinematics of a three DOF actuator redundant hydraulic parallel manipulator. It is shown, that on the contrary to series manipulators, the forward kinematic map of the parallel manipulators involves highly coupled nonlinear equations, which are almost impossible to solve analytically. The proposed method uses a combination of analytical and numerical schemes to solve the problem. A simulation study is performed using a sample trajectory to identify the advantages and disadvantages of the proposed method in computing the forward kinematic map of the given mechanism. The results show that the proposed method provides us with a relatively fast solution and good tracking performance although being dependent on the initial conditions used in the solution process.

In this paper, three numerical methods are presented to solve the forward kinematics of a three DOF actuator-redundant hydraulic parallel manipulator. It is known, that on the contrary to series manipulators, the forward kinematic map of parallel manipulators involves highly coupled nonlinear equations, whose closed-form solution derivation is a real challenge. This issue is of great importance noting that the forward kinematics solution is a key element in closed loop position control of parallel manipulators. The proposed methods, namely the Neural Network Estimation, the Quasi-closed Solution, and the Taylor series approximation, are using mainly numerical computations, with different ideas to solve the problem in hand. The latter two methods are proposed for the first time in literature to solve the forward kinematics of a parallel manipulator. These methods are compared in detail and the advantages or the disadvantages of each method in computing the forward kinematic map of the given mechanism is discussed. It is shown that a 4th order Taylor series approximation to the problem provides a good compromise for practical applications compared to that of other methods considered in this paper.