High-speed Parallel Manipulator Research Articles

Complete Kinematics/Dynamics Modeling and Performance Analysis of a Novel SCARA Parallel Manipulator Based on Screw Theory

Abstract In this paper, a novel Selective Compliance Assembly Robot Arm (SCARA) high-speed parallel manipulator that can realize three-translation and one-rotation motion is proposed, and an accurate dynamic modeling methodology is investigated. The mechanism is composed of four limbs with a double parallelogram structure and a single moving platform. The high bearing capacity and high dynamic response of the novel mechanism make it a viable alternative choice for this kind of automation equipment. The degree-of-freedom (DOF) of the mechanism is analyzed by the screw theory. At the same time, the velocity mapping model of the mechanism is established by the twist screw and the actuated Jacobian matrix. Then, the acceleration mapping model of the mechanism, including the generalized kinematic pairs, is established by reduced acceleration state, the modified Lie screw, and the acceleration Hessian matrix. On this basis, the complete dynamic model with a compact form of the mechanism is deduced by the combination of screw theory and virtual work principle, and the correctness of the developed model is verified by multibody simulation software. Finally, considering the inertial characteristics of the mechanism, the dynamic performance distribution in the reachable workspace of the mechanism is analyzed by the Joint-Reflected Inertia (JRI) index and Coefficient of Variation of joint-space Inertia (CVI) index, and some areas are selected as the task workspace using the above index to guarantee good dynamic performance.

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.

Time-energy-jerk optimal trajectory planning for high-speed parallel manipulator based on quantum-behaved particle swarm optimization algorithm and quintic B-spline

This paper presents a technique for multi-node trajectory planning for high-speed parallel manipulators that optimizes the execution time, energy consumption and jerk (the time derivative of the acceleration of the manipulator joints) to improve working efficiency, decrease energy consumption, dampen vibration and ensure mechanism protection. Initially, an improved quintic B-spline interpolation model is proposed, incorporating additional jerk boundary constraints to dampen residual vibrations at the start and end of the trajectory. Subsequently, the time-energy-jerk optimization model is formulated, with the maximum angular velocity, acceleration, and jerk serving as constraints. The normalized parameter of the B-spline curve is considered to divide the whole model into two submodels. In the first submodel, the satisfaction function is proposed to convert energy and jerk indices into one comprehensive objective for optimization with the quantum-behaved particle swarm optimization (QPSO) algorithm. Time parameters are to be decided as decision variables, regardless of kinematic constraints and execution time. In the second submodel, the optimal time parameters obtained in the first submodel are used as input arguments, and the optimal execution time is determined with respect to the kinematic constraints. The simulation results on a planar parallel manipulator show that the proposed method achieves an efficient trajectory, which is energy-saving and possesses reduced vibration. Application of the comprehensive trajectory generated by the proposed method, rather than the classical method, enhances the maximum productivity of the fast pick-and-place operation to 155 picks per minute from 97 picks/min. This improvement is accomplished by using less energy and reducing vibration.

A new fast nonlinear model predictive control of parallel manipulators: Design and experiments

High-speed parallel manipulators are characterized by fast sampling rates and challenges owing to the presence of constraints, high nonlinearities, uncertainties, and fast dynamics. The development of a reliable nonlinear model predictive control (NMPC) approach for this type of robotic systems is challenging because of the complex dynamics that involves high computational burden. To address this control problem, this paper proposes a new fast NMPC strategy applied to high-speed parallel robots. Based on (i) a parameterization technique, (ii) a fast gradient solver, (iii) a proportional integral derivative (PID) control term, (iv) a nonlinear dynamic model, and (v) an artificial neural network (ANN) model, two fast NMPC frameworks were developed to reduce the computational cost of the classical NMPC and address online implementation. In this study, we focus on improving the performance of the standard predictive control strategy outside of the range of its classical applicability by developing a fast NMPC controller for high-speed parallel kinematic manipulators (PKMs). Numerical simulations and real-time experimental results were presented and discussed to validate the relevance of the proposed controllers. Experiments were conducted on a four-degree-of-freedom (4-DOF) PKM called VELOCE developed in our laboratory. The results show that the proposed solution outperforms the original scheme in terms of real-time tracking performance.

Study on modeling and dynamic performance of a planar flexible parallel manipulator based on finite element method.

The application of a high-speed parallel manipulator necessitates the adoption of a lightweight design to reduce dead weight. However, this increases the elastic deformation of certain components, affecting the dynamic performance of the system. This study examined a 2-DOF planar flexible parallel manipulator. A dynamic model of the parallel manipulator composed of fully flexible links was established using a floating reference coordinate system and a combination of the finite element and augmented Lagrange multiplier methods. A dynamic analysis of the simplified model under three driving torque modes showed that the axial deformation was less than the transverse deformation by three orders of magnitude. Further, the kinematic and dynamic performance of the redundant drive was significantly better than that of the non-redundant drive, and the vibration was well suppressed in the redundant drive mode. In addition, the comprehensive performance of driving Mode 2 was better than that of the other two modes. Finally, the validity of the dynamic model was verified by modeling via Adams. The modular modeling method is conducive to the extension to other models and programming. Furthermore, the dynamic model of the established fully flexible link system can aid in optimizing the lightweight design and dynamic performance of the parallel manipulator.

Dynamic Modeling and Torque Feedforward based Optimal Fuzzy PD control of a High-Speed Parallel Manipulator

Dynamic modeling and control of high-speed parallel manipulators are of importance due to their industrial applications deployed in production lines. However, there are still a number of open problems, such as the development of a precise dynamic model to be used in the model-based control design. This paper presents a four-limb parallel manipulator with Schönflies motion and its simplified dynamic modeling process. Then, in order to fix the issue that computed torque method control (CTC) will spend a lot of time to calculate dynamic parameters in real-time, offline torque feedforward-based PD (TFPD) control law is adopted in the control system. At the same time, fuzzy logic is also used to tune the gains of PD controller to adapt to the variation of external disturbance and compensate the un-modeled uncertainty. Additionally, bottom widths of membership functions of fuzzy controller are optimized by bat algorithm. Finally, three controllers of CTC, TFPD and bat algorithm-based torque feedforwad fuzzy PD controller (BA-TFFPD) are compared in trajectory tracking simulation. Fro the result, compared with TFPD and CTC, BA-TFFPD can lead faster transient response and lower tracking error, which prove the validity of BA-TFFPD.

Dynamic Modeling and Torque Feedforward based Optimal Fuzzy PD control of a High-Speed Parallel Manipulator

Dynamic modeling and control of high-speed parallel manipulators are of importance due to their industrial applications deployed in production lines. However, there are still a number of open problems, such as the development of a precise dynamic model to be used in the model-based control design. This paper presents a four-limb parallel manipulator with Schonflies motion and its simplified dynamic modeling process. Then, in order to fix the issue that computed torque method control (CTC) will spend a lot of time to calculate dynamic parameters in real-time, offline torque feedforward-based PD (TFPD) control law is adopted in the control system. At the same time, fuzzy logic is also used to tune the gains of PD controller to adapt to the variation of external disturbance and compensate the un-modeled uncertainty. Additionally, bottom widths of membership functions of fuzzy controller are optimized by bat algorithm. Finally, three controllers of CTC, TFPD and bat algorithm-based torque feedforwad fuzzy PD controller (BA-TFFPD) are compared in trajectory tracking simulation. Fro the result, compared with TFPD and CTC, BA-TFFPD can lead faster transient response and lower tracking error, which prove the validity of BA-TFFPD.

RETRACTED: Reducing energy consumption via trajectory planning method for delta high-speed parallel manipulator

This paper selects delta high-speed parallel robot with three degrees of freedom as the research object. The trajectory planning strategies of Cartesian space and angular displacement, angular velocity and angular acceleration of three joints in high-speed handling are studied. Firstly, the critical trajectory points starting point and end point, and points for obstacle avoidance height are set up, and then according to the inverse kinematics model of the robot, a point-to-point “door” type moving trajectory is established, and the mapping relationship between the motion characteristics of the operating space and the motion characteristics of the joint space is established by using the 4-3-4 degree polynomial motion law in the operating space. However, aiming at the higher energy consumption of 4-3-4 degree polynomial interpolation caused by longer the trajectory, and difficult control of obstacle avoidance height, one key point is added. Thereby, the motion rules are interpolated by 4-3-3-4 degree polynomial interpolation, and the mapping relationship between the motion characteristics of the operating space and the motion characteristics of the joint space is established. Two trajectory planning methods are simultaneously simulated under the same keys points and the same trajectory time range. The motion characteristics of the joint rotation angle of the parallel robot between polynomial interpolations are respectively compared. The results show that the trajectory planning method based on 4-3-3-4 degree polynomial interpolation in joint space has obvious advantages in improving the running state of the delta parallel robot and reducing the energy consumption of the system.

An improved PSO algorithm for time-optimal trajectory planning of Delta robot in intelligent packaging

With the advancement of the times, robotics technology is also developing rapidly. Some large enterprises in China use robots to work in manufacturing and handling positions, and also make robots more and more widely used. This paper focuses on the trajectory planning strategy for three-degree-of-freedom high-speed parallel manipulator of Delta robot in Cartesian space under high-speed operation handling, the point-to-point “door” type handling operation trajectory under the condition of ensuring control accuracy and increasing productivity in intelligent packaging is established based on the inverse kinematics model of the manipulator. The 4–3–3-4 degree polynomial interpolation is presented to control height of obstacle avoidance and trajectory length, on this basis, the mapping relationship between the motion features in operation space and those in joint space is established. Taking into account the complexity of trajectory optimization due to multiple constraints, in order to reduce the difficulty of trajectory optimization, it is necessary to ensure smoothness and constrains of angular displacement, angular velocity and angular acceleration of each joint in space, an improved particle swarm optimization algorithm is proposed to optimize trajectory running time of the 4–3–3-4 degree polynomial interpolation. The simulation results by using Matlab indicate that the accurate and stable time-optimal trajectory planning of 4–3–3-4 degree polynomial interpolation can be achieved by means of the improved particle swarm optimization algorithm. Compared with other trajectory planning algorithms, the proposed algorithm is easier to implement, which not only improves the local convergence of particle swarm optimization algorithm, achieves the time optimal trajectory planning of Delta robot, but also realizes the controllability of obstacle avoidance height, therefore which realizes the fast, accurate and safe operation in intelligent packaging.

Integrated optimal design of a high-speed planar parallel manipulator

To obtain excellent comprehensive performances of the planar parallel manipulator for the high-speed application, an integrated optimal design method, which integrated dimensional synthesis, motors/reducers selection, and control parameters tuning, is proposed, and the 3RRR parallel manipulator was taken as the example. The kinematic and dynamic performances of condition number, velocity index, acceleration capability, and low-order frequency are taken into accounts for the dimensional synthesis. Then, to match motors/reducers parameters and keep an economical cost, the constraint equations and the parameters library are built, and the cost is chosen as one of the optimization objectives. Also, to get high tracking accuracy, the dynamic forward plus proportional–derivative control scheme is introduced, and the tracking error is chosen as one of the optimization objectives. Hence, the optimization model including dimensional synthesis, motors/reducers selection and controller parameters tuning is established, which is solved by the genetic algorithm II (NSGA-II). The result shows that comprehensive performances can be effectively promoted through the proposed integrated optimal design, and the prototype was constructed according to the Pareto-optimal front.

Dynamic performance analysis of the X4 high-speed pick-and-place parallel robot

With the closed-loop structure, parallel manipulators possess some inherent advantages, such as high stiffness, enhanced dynamics, and compact structure. As a result, parallel manipulators gradually gain wide application. In the great variety of parallel manipulators, a kind of high-speed parallel robot, the limb of which is composed of active pendulum and passive parallelogram, gets popular and has realized industrial application firstly. Dynamic performance is the core of the high-speed parallel manipulator, which is usually illustrated through dynamic performance analysis with the aid of the index. Thus, developing reasonable dynamic performance indices is of great theoretical and practical significance for the high-speed parallel manipulator. In this paper, the Coefficient of Variation of joint-space Inertia (CVI) index is proposed to illustrate the acceleration consistency of each limb of the parallel manipulator. By taking the X4 high-speed pick-and-place parallel manipulator as object, the dynamic model and joint-space inertia matrix is established, and the dynamic performance analysis is carried out with the proposed CVI index and the existing Joint-Reflected Inertia (JRI) index. Simulation results illustrate changes of the dynamic performance of the X4 parallel manipulator, and reveal that the JRI index is well complemented with the CVI index. Finally, the workspace with good dynamic performance is discussed. This paper provides a new approach for dynamic analysis and optimal design of high-speed parallel manipulator. Limb Jacobian matrices of the X4 manipulator are given.Dynamic model and inertia matrix of the X4 manipulator are deduced.The CVI index is proposed to evaluate the dynamic performance.Dynamic performance of the X4 mahipulator is analyzed with indices.The workspace with good dynamic performance is disscussed.

Modal Analysis of High-Speed Parallel Manipulator with Flexible Links

The modal analysis was carried out to investigate the proposed improved curvature based finite element method (ICFE) for parallel manipulator with flexible links. The flexible link was discretizatied with ICFE first, and with the proposed rigid-flexible coupling technique, the flexible displacement of the moving platform and passive links was obtained, then through Lagrange equation, the structural model was derived. At last, to investigate the accuracy and efficiency of the ICFE and rigid-flexible coupling technique, modal analysis of ICFE model with different nodes and comparison studies with CFE and the ABAQUS model was carried out.

Optimum design of a novel redundantly actuated parallel manipulator with multiple actuation modes for high kinematic and dynamic performance

A novel redundantly actuated parallel manipulator with multiple potential actuation modes is proposed in this paper to conquer the drawbacks of the traditional planar 5R parallel manipulator. Firstly, some feasible topology configurations are presented and then an optimum scheme was achieved through some selection criteria. Kinematic analysis indicates that the redundant actuation modes have remarkable advantage over the non-redundant actuation modes because the redundant actuation ones can completely conquer the type II singularities within the theoretical reachable workspace. To investigate the dynamics, the Lagrangian formulation is employed to establish the uniformly dynamic model of the proposed parallel manipulator with multiple actuation modes. Based upon the dynamic model, two global dynamic performance indices are proposed for minimization by taking into accounts both inertia and centrifugal/Coriolis effects. Finally, the dynamic dimensional synthesis is performed subject to geometric constraints and some kinematic performance constraints. By using this approach, the designer can obtain a set of optimum dimensional parameters satisfying both the kinematic and dynamic performance. This approach can be extended to the optimum design for other high-speed parallel manipulators, especially for the ones with multiple actuation modes.

The Combined Simulation of High-Speed Parallel Manipulator Based on MATLAB, SolidWorks and ADAMS

This paper mainly focuses on the modeling and simulation of a three-DOF high-speed parallel robot which is widely used in the design of an enterprise vials testing equipment. For high-speed parallel manipulator rapid modeling and collaborative simulation, we study the two methods. One approach is to transfer the 3D SOLIDWORKS model into MATLAB/ SIMULINK model. Another method is to convert the three-dimensional model of SOLIDWORKS models into ADAMS. ADAMS and SIMULINK work together as a simulation platform. The results show that the two methods could provide the efficient and significant simulation platform to research the control strategy of High-speed parallel manipulator.

An efficient dynamic modelling approach for high-speed planar parallel manipulator with flexible links

An efficient dynamic modelling approach was presented for planar parallel manipulator with flexible links. To increase the accuracy of the model, an improved curvature-based finite element method (ICFE) was developed for discretisation of the flexible links. Then, a novel approach for analysis of the coupling between rigid-body motion and flexible-body motion was proposed, and compared to the regular geometrical method, the proposed method was accurate and easy to implement. With the aforementioned proposed methods, the Kane equation was integrated to formulate the dynamic model of a 3RRR planar parallel manipulator. Finally, comparison studies were performed to validate the proposed ICFE and the integrated dynamic modelling method. Compared to the regular curvature-based finite element method (CFE), the ICFE exhibits improved accuracy with equivalent degrees of freedom. Additionally, the proposed integrated dynamic model shows a good agreement with the Abaqus model. Therefore, it was concluded that the proposed dynamic modelling method herein was efficient and accurate for parallel manipulators with flexible links, demonstrating reasonable potentials for model based control.

Controller Design Based on Mechatronic Model

The dissertation deals with some key issues relevant to the controller design and digital design method for a newly patented high-speed parallel manipulator. Meanwhile, a Virtual Prototyping based co-simulation platform is also established according to the ADAMS and Matlab/Simulink software. In order to promote the ability that the manipulator traces the prescribed trajectory, a model based computed torque controller is described in detail, and a neural network algorithm is also used to optimize controller parameters real-timely under the consideration of systematic nonlinear, modeling error and outer disturbance. The neural network based computed torque controller increases the robustness of system dramatically.

Dynamic Dimensional Synthesis of a 4-DOF High-speed Parallel Manipulator

Dynamic Dimensional Synthesis of a 4-DOF High-speed Parallel Manipulator

Design and experimental evaluation of a dynamically balanced redundant planar 4-RRR parallel manipulator

Shaking forces and shaking moments in high-speed parallel manipulators are a significant cause of base vibrations. These vibrations can be eliminated by designing the manipulator to be shaking-force balanced and shaking-moment balanced. In this article an approach for the design and evaluation of high-speed dynamically balanced parallel manipulators is presented and applied to a comparative experimental investigation of a balanced and unbalanced DUAL-V planar 4-RRR parallel manipulator. For precise simulation of the manipulator motion, the inverse dynamic model of the manipulator is derived and validated. Experiments show that the balanced manipulator has up to 97% lower shaking forces and up to a 96% lower shaking moment. For small inaccuracies of the counter-masses or for a small unbalanced payload on the platform, base vibrations may be considerable for high-speed manipulation, however their values remain significantly low as compared to the unbalanced manipulator. For the balanced manipulator the actuator torques are about 1.6 times higher and the bearing forces are about 71% lower as compared to the unbalanced manipulator.

Digital platform-based multi-domain virtual prototype simulation on a high-speed parallel manipulator

SUMMARYThis paper presents how to build an all-digital co-simulation platform of a mechtronic system so as to reduce the burden and error of system modeling. In the construction of a platform, a driving system, including a motor, a pulse-width modulation (PWM) and a controller, is simulated using Matlab/Simulink. The behavior of the mechanism is analyzed using the ADAMS software. By the proper interface function for the real-time communication between two parts of the models, a virtual working environment is established. Finally, a proportional integral derivative (PID) controller verifies the validity of the digital platform.

Kineto-static analysis of a novel high-speed parallel manipulator with rigid-flexible coupled links

A novel high-speed parallel kinematic machine (PKM) named Delta-S parallel manipulator is proposed, which consists of a fixed base connected to a moving platform through three limbs with identical topology. Each limb is composed of one driving arm and one follower arm, herein, the latter includes two strings and one middle rod, all located in a same plane. Compared with similar manipulators with uniform parameters, the novel and unique topology as well as the addition of two strings of Delta-S manipulator can remove the clearance of the spherical joints, reduce the inertial load of components further, improve the positioning accuracy and dynamic performance, and so on. In order to formulate the kineto-static model of Delta-S manipulator, the kineto-static analyses and models of the driving arm, the generalized follower and the moving platform can be carried out by the D’ALEMBERT principle. For the sake of obtaining the force analytic results of strings, the deformation compatibility condition of strings and the middle rod are determined. Furthermore, in virtue of the assumption of small deformation and the linear superposition principle, the minimal pre-tightening force of the strings is calculated. The main results include that the loads of the strings and the middle rod must be larger than “zero” and the pre-tightening force over the workspace must be larger than the minimal pre-tightening force at any time within the workspace, which lay the foundation for the dynamic analysis and the prototype manufacture of the Delta-S manipulator.