Redundant Parallel Manipulator Research Articles

Dynamic response investigation of high-speed structural redundant parallel manipulator considering multiple spatial revolute joints with radial and axial clearances

In order to grasp dynamic characteristics of the kind of high-speed structural redundant parallel manipulator in actual work, the dynamic response of a novel high-speed structural redundant parallel manipulator considering multiple spatial revolute joints with radial and axial clearances is studied. Firstly, the dynamic model of the novel high-speed parallel manipulator considering the multiple spatial revolute clearance joints is developed and verified. Then, the influences of different factors on dynamic characteristics of parallel manipulator are explored respectively. This paper contributes to explore the effect of revolute joints clearance on total property of the manipulator.

Inverse kinematics and singularity analysis of a redundant parallel robot

The 3C (computer, communications, consumer electronics) industry belongs to labor-intensive and the requirements of the 3C industry are precisely high. The parallel robot is a good choice to replace human labor to manufacture these products. This paper presents a new 3- redundant parallel mechanism for 3C manufacturing. Firstly, some advantages of redundant parallel robots in the current industrial demand are discussed. Then, the inverse kinematics of the redundant parallel manipulator is analyzed according to the closed-loop equation, the inverse displacement problem is solved. The machine is simple and low cost, and as a less freedom robot, it has a higher precision than the traditional robot and has a broad prospect for 3C manufacturing. Finally, the Jacobian matrix of the redundant parallel manipulator was calculated and established by the inverse kinematics formula, and three kinds of the singularity of the mechanism were analyzed by the Jacobian matrix, which are the forward singularity, reverse singularity, mixed singularity respectively.

Torque Optimization Method of a 3-DOF Redundant Parallel Manipulator Based on Actuator Torque Range

Abstract The small actuator torque range brings advantages for the high-accuracy control of a manipulator. By taking the minimum actuator torque range into account, this paper proposes a novel torque optimization method of a 3-DOF redundantly actuated parallel manipulator for friction stir welding. The dynamic model of the 3-DOF redundant parallel manipulator with four kinematic chains is derived by using the principle of virtual work. The solution of the dynamics is not unique, and the range of four actuator torques constitutes a 4D generalized rectangle. A torque optimization method that minimizes the actuator torque range is presented by determining the generalized 4D rectangle with minimum side length. The proposed optimization method is a global solution corresponding to one trajectory of the moving platform, and it is compared with the least square method which is a local solution corresponding to one pose of the moving platform.

Model-based joint and task space control strategies for a kinematically redundant parallel manipulator

AbstractOne alternative to overcome the presence of singularities within Parallel Manipulators’ workspace is kinematic redundancy. This design alternative can be realized by adding an extra active joint to a kinematic chain. Due to this addition, the IKM presents an infinite number of solutions requiring a redundancy resolution scheme. Moreover, Parallel Manipulators’ control may require complex strategies due to their coupled and complex dynamic and kinematic relations. In this work, a model-free, a joint space computed torque, and a hybrid joint-task-space computed torque control strategies are experimentally compared for a kinematically redundant parallel manipulator. The latter is a novel strategy that requires the measurement of the end-effector’s pose, which is performed by an eye-to-hand limited frame rate camera. The impact of up to three kinematic redundancy levels is also experimentally evaluated using prepositioning and ongoing positioning redundancy resolution schemes. The data are assessed by evaluating a prescribed trajectory executed using a planar kinematically redundant parallel manipulator. These results indicate that kinematic redundancy can not only be used as an alternative design for reducing the presence of singular regions, as claimed in the literature, but also be used along with model-based control strategies for improving dynamic performance and accuracy of parallel manipulators.

Reliable redundancy resolution strategies for kinematically redundant parallel manipulators

The reconfiguration capability given by the use of kinematic redundancy can be an alternative for enlarging the useable workspace of parallel manipulators. However, the inverse kinematic model of a kinematically redundant parallel manipulator presents an infinite number of solutions requiring redundancy resolution strategies. These decision-maker strategies are responsible for keeping the manipulator away from singular configurations, which is considered a failure. However, singular regions might be affected by uncertainties. Therefore, every possible solution for the kinematic model presents a probability of failure according to the system’s uncertainties. In this work, the probability of failure is assessed using the Monte Carlo Simulation and surrogate models. Reliable redundancy resolution strategies using these surrogate models are proposed and numerical results considering geometrical uncertainties demonstrate the proposal’s applicability.

Global Finite Time Active Disturbance Rejection Control for Parallel Manipulators With Unknown Bounded Uncertainties

In this article, a global finite-time active disturbance rejection control (ADRC) scheme is proposed for tracking control of redundant parallel manipulators with unknown bounded uncertainties. This approach combines an ADRC and a global finite-time control for high accuracy trajectory tracking control. Based on the nonsingular fast terminal sliding mode control, the proposed approach can remove the condition in the original ADRC that the derivative of the uncertainties is required to be bounded. The extended state observer is employed to handle the real-time estimation of the total uncertainty. It can be found that the proposed scheme not only can converge fast to the semi-global finite-time stable equilibrium but also can have superior tracking control performance. In summary, compared to existing approaches, the proposed scheme can have several advantages, such as uncertainty rejection, easy implementation, robustness, chattering-free, high precision, and no need for prior knowledge of bounded uncertainties. The simulation results validate the effectiveness of the proposed method.

Stability Analysis of a Visual PID Controller Applied to a Planar Parallel Robot

This work analyses the stability of a standard PID controller fed by measurements provided by a vision system, and applied to a planar parallel redundant manipulator for constant set point tracking. The stability analysis considers uncertainty in the Jacobian matrix associated to the manipulator active joints, and constant disturbances perturbing these joints. The disturbances appear as time-varying at the visual level. Asymptotic stability of the closed loop system is proven using a Strict Lyapunov Function. The above allows directly applying the Lyapunov second method without resorting on the LaSalle-Krassovsky invariance theorem. The analysis also provides an upper bound on the allowable uncertainty in the Jacobian matrix. Experiments on a laboratory prototype permit evaluating the performance of a PID controller applied to a planar parallel robot.

Adaptive finite‐time neural network control for redundant parallel manipulators

AbstractThis paper reports our study of an adaptive finite‐time neural network control scheme for redundant parallel manipulators. The proposed controller is based on fully tuned radial basis function neural networks (RBFNs), nonsingular fast terminal sliding mode control (NFTSMC), and nonlinearities in output feedback. RBFNs with a fully online update on the output weights and both the centers and variances of Gaussian functions are used to estimate system uncertainties and disturbances. The proposed approach possesses several advantages over other existing approaches like robustness, rapid response, nonsingularity, higher precision, finite‐time convergence, and better tracking control performance. The stability of the parallel manipulators is ensured by the Lyapunov theory. Finally, simulation results validate the effectiveness of the proposed methodology.

Structural synthesis of a class of kinematically redundant parallel manipulators based on modified G–K criterion and RDOF criterion

Based on the modified Grübler–Kutzbach (G–K) criterion and relative degrees of freedom (RDOF) criterion, a novel method is proposed for structural synthesis of a class of kinematically redundant parallel manipulators (KR-PMs) with spherical joints attached to a moving platform. First, a formula that can be used to calculate the number of kinematic joints not limited to basic joints is proposed, which is affected by the number of links including fixed base, links with multi-node, compound hinges, and the INTERNAL independent loops in parallel manipulators. Furthermore, the sum degrees of all the kinematic joints possesses a direct relationship with the number of kinematic joints, the number of spherical joints, and the type combination of spherical joints attached to the moving platform. Then, the relationship between the mobility M and the RDOF with intermediate variables is derived based on modified G-K criterion and RDOF criterion, which is the base of the proposed synthesis procedure. Next, the proposed synthesis procedure is performed with the synthesis conditions RDOF = 3 or 4, and some typical KR-PMs are obtained. Finally, the condition for proper selection of actuators for KR-PM is revealed. And the reasons for large configuration randomness of the synthesized KR-PMs are discussed.

Adaptive Chattering Free Neural Network Based Sliding Mode Control for Trajectory Tracking of Redundant Parallel Manipulators

AbstractIn this paper, an adaptive chattering free neural network‐based sliding mode control (ACFN‐SMC) method is proposed for tracking trajectories of redundant parallel manipulators. ACFN‐SMC combines adaptive chattering free radial basis function neural networks (RBFN), sliding mode control with online updating the robust term parameters, and a nonlinear compensation item for reducing tracking errors. The stability of the closed‐loop system with modeling uncertainties, frictional uncertainties, and external disturbances is ensured by using the Lyapunov method. The proposed controller has a simple structure and little computation time while securing dynamic performance with expected quality in tracking trajectories of redundant parallel manipulators. In addition, the ACFN‐SMC strategy does not need to know the upper bound of any uncertainties. From the simulation results, it is evident that the proposed control strategy not only has significantly higher robustness capability for uncertainties but also can achieve better chattering elimination when compared with those using existing intelligent control schemes.

The effect of the number of degrees of kinematic redundancy on the actuation forces of a planar parallel manipulator

This paper proposes a two-step optimization procedure for resolving the actuation forces of a kinematically redundant planar parallel manipulator following a specified trajectory. Simulation results compare the performance of the manipulator when different degrees of kinematic redundancy are used. It is seen that the required forces are generally lower when there are more degrees of kinematic redundancy; however, more mechanical energy is required. In some cases, fewer degrees of kinematic redundancy can produce similar results from a force point of view, while requiring less energy. Furthermore, the importance of correctly choosing an initial configuration is presented. The proposed method finds an optimal initial configuration by considering a performance index along the entire trajectory. The evolution of the singularity loci as the manipulator moves along the trajectory demonstrates why certain initial configurations should not be used, even if they are optimal at the initial pose.

Numerical and experimental evaluation of the dynamic performance of kinematically redundant parallel manipulators

Parallel manipulators present high load capacity and rigidity, among other advantages, when compared to the serial manipulators. Due to their kinematic architecture, their parts are lighter. This characteristic may be an asset for designing high dynamic performance manipulators. However, parallel manipulators suffer from singularities in their workspace. This drawback can be circumvented by the use of kinematic redundancies. Due to the presence of these redundancies, the inverse kinematic problem presents an infinite number of solutions. The selection of a single solution among the possible ones is denoted as redundancy resolution. In this manuscript, the impact of several levels of kinematic redundancy on the dynamic performance of a planar parallel manipulator, the 3PRRR, is numerically and experimentally investigated. The kinematic redundancy of this manipulator can be added by the actuation of the active prismatic joints (P). Two redundancy resolution schemes are proposed using a multiobjective optimization problem. Based on the numerical and experimental results, one can conclude that the use of a proper redundancy resolution scheme can considerably reduce the maximum required torque to perform a predefined task.

On the Solutions of Interval Systems for Under-Constrained and Redundant Parallel Manipulators

For under-constrained and redundant parallel manipulators, the actuator inputs are studied with bounded variations in parameters and data. Problem is formulated within the context of force analysis. Discrete and analytical methods for interval linear systems are presented, categorized, and implemented to identify the solution set, as well as the minimum 2-norm least-squares solution set. The notions of parameter dependency and solution subsets are considered. The hyperplanes that bound the solution in each orthant characterize the solution set of manipulators. While the parameterized form of the interval entries of the Jacobian matrix and wrench produce the minimum 2-norm least-squares solution for the under-constrained and over-constrained systems of real matrices and vectors within the interval Jacobian matrix and wrench vector, respectively. Example manipulators are used to present the application of methods for identifying the solution and minimum norm solution sets for actuator forces/torques.

A novel approach for 2-degrees of freedom redundant parallel manipulator dynamics

A novel Udwadia–Kalaba approach for redundant parallel manipulator dynamics is presented in this article. This methodology is explicit and simple which is suitable for systems with holonomic or non...

Singularity analysis of a class of kinematically redundant parallel Schönflies motion generators

This paper provides an analysis of the singularities of a class of kinematically redundant parallel manipulators. The studied mechanisms are capable of spatial translations in addition to rotation around an axis with constant orientation. Such motion is classified as Schönflies motion and is of high importance for industrial applications. The studied mechanisms include a manipulated platform composed of two platform sections, which are connected by a passive joint. The mechanisms include five actuated kinematic chains of a specific type, where three kinematic chains are connected to one platform section and two to the other section. Several novel mechanisms in this class are introduced and the singularities of all introduced variants are analyzed utilizing screw theory. In particular, all configurations leading to a redundant passive motion (RPM) singularity are determined. In such configurations, at least one of the passive joints in the mechanism may have a non-zero velocity while the velocity of the tool and all actuated joints are zero. For the studied mechanisms, such configurations correspond to the system of wrenches acting on the platform section including the tool has full rank while the wrench system acting on the other platform section is rank deficient.

An introduction to utilising the redundancy of a kinematically redundant parallel manipulator to operate a gripper

Although parallel manipulators provide several benefits compared to similar-sized serial manipulators, they typically exhibit a limited rotational workspace. One approach to designing a parallel manipulator with infinite range of tool rotation around one axis is to introduce kinematic redundancy. This is typically achieved by extending a non-redundant mechanism with an additional actuator and a supplemental degree of freedom, while the degrees of freedom of the tool platform remain the same. The main drawback of this approach is the cost of the additional actuator. In this paper, we discuss the possibility of harvesting the motion in the additional degree of freedom to operate a gripper. The benefits of the proposed idea include saving the cost of a gripper actuator and reducing the mass of the manipulated platform. Additionally, the requirement to provide the manipulated platform with compressed air or electric power is removed. Several variants of a kinematically redundant manipulated platform with five degrees of freedom are introduced along with conceptual mechanical designs for transforming the redundant platform motion into the opening and closing of a gripper.

Trajectory planning of kinematically redundant parallel manipulators by using multiple working modes

A method for joint trajectory planning of kinematically redundant parallel manipulators is presented in this paper. The method is based on the use of feasibility maps that allow the graphical assessment of postures related to the different working modes of the manipulator. Thus, in such maps suitable trajectories are found in order to improve the performance of the manipulator and to avoid parallel singularities. When the desired path cannot be achieved by using only one working mode of the manipulator without crossing parallel singularities then, by applying the approach proposed here, a number of working modes could be chosen and combined to complete the whole path. The method can be applied to parallel manipulators with one degree of kinematic redundancy, whose legs allow the changing of working modes. The efficiency of this method is shown in a case study with a 3-RRR parallel manipulator (note that this manipulator becomes kinematically redundant if the orientation of the mobile platform is not specified for a desired task), in which postures associated to four working modes are employed in such a way that parallel singularities can be avoided. The obtained joint trajectories are applied to an experimental prototype to successfully execute the desired task.

A Measure for Evaluation of Maximum Acceleration of Redundant and Nonredundant Parallel Manipulators

The paper deals with the evaluation of acceleration of redundant and nonredundant parallel manipulators. The dynamic model of three degrees-of-freedom (3DOF) parallel manipulator is derived by using the virtual work principle. Based on the dynamic model, a measure is proposed for the acceleration evaluation of the redundant parallel manipulator and its nonredundant counterpart. The measure is designed on the basis of the maximum acceleration of the mobile platform when one actuated joint force is unit and other actuated joint forces are less than or equal to a unit force. The measure for evaluation of acceleration can be used to evaluate the acceleration of both redundant parallel manipulators and nonredundant parallel manipulators. Furthermore, the acceleration of the 4-PSS-PU parallel manipulator and its nonredundant counterpart are compared.

Optimum design of a 4-PSS-PU redundant parallel manipulator based on kinematics and dynamics

This paper presents an optimum design of a 4-PSS-PU redundant parallel manipulator by taking the workspace, conditioning performance, and acceleration into account. On the basis of rank of the Jacobian matrix, a method to directly find out the workspace is presented, rather than the search method. Based on the dynamic model, a maximum acceleration index is defined. The corresponding atlases of these performance indices are represented graphically in the established design space. Based on these atlases, the optimum design is performed and the optimum region is determined. It is expected to realize the high acceleration of parallel manipulators by using the optimum method.

Integrated Stiffness Analysis of Redundant Parallel Manipulator Based on Finite Element Method

An integrated stiffness model is established for a Planar Parallel Manipulator (PPM) with actuation redundancy based on Finite Element Method (FEM), and the static stiffness, dynamitic stiffness and moving stiffness of the PPM are analyzed according to the integrated stiffness model. Firstly, a dynamic model of flexible plane beam element is created as a basic unit for branches. Secondly, each branch is assembled in generalized coordinates, and the integrated stiffness model of the PPM is established. Then calculation and simulation for the static stiffness, dynamitic stiffness and moving stiffness are carried out. The results show that the static stiffness and dynamitic stiffness are related with the position and posture of the PPM. The moving stiffness shows that the elastic deformations cause the oscillation of the PPM. In this paper, three stiffness models are unified in the integrated stiffness model, which improves the efficiency of the stiffness calculation and mechanism design.