Dynamic modeling and design optimization of a 3-DOF spherical parallel manipulator

This paper deals with the dynamic modeling and design optimization of a three Degree-of-Freedom spherical parallel manipulator. Using the method of Lagrange multipliers, the equations of motion of the manipulator are derived by considering its motion characteristics, namely, all the components rotating about the center of rotation. Using the derived dynamic model, a multiobjective optimization problem is formulated to optimize the structural and geometric parameters of the spherical parallel manipulator. The proposed approach is illustrated with the design optimization of an unlimited-roll spherical parallel manipulator with a main objective to minimize the mechanism mass in order to enhance both kinematic and dynamic performances.     

Dynamic modeling and redundant force optimization of a 2-DOF parallel kinematic machine with kinematic redundancy

High precision is still one of the challenges when parallel kinematic machines are applied to advanced equipment. In this paper, a novel planar 2-DOF parallel kinematic machine with kinematic redundancy is proposed and a method for redundant force optimization is presented to improve the precision of the machine. The inverse kinematics is derived, and the dynamic model is modeled with the Newton–Euler method. The deformations of the kinematic chains are calculated and their relationship with kinematic error of the machine is established. Then the size and direction of the redundant force acting on the platform are optimized to minimize the position error of the machine. The dynamic performance of the kinematically redundant machine is simulated and compared with its two corresponding counterparts, one is redundantly actuated and the other is non-redundant. The proposed kinematically redundant machine possesses the highest position precision during the motion process and is applied to develop a precision planar mobile platform as an application example. The method is general and suitable for the dynamic modeling and redundant force optimization of other redundant parallel kinematic machines.     

2-DOF绳索驱动并联机构轨迹跟踪控制

基于PD控制和前馈控制方法,对2-DOF的绳索驱动并联机构的空间运动控制问题进行研究.首先,基于拉格朗日方程建立系统的空间运动数学模型.为了保证所有绳索在机构的工作空间范围内始终处于张紧状态,绳索内力原则被应用于所提的控制方法中.然后,基于李雅普诺夫稳定性理论,给出闭环系统的稳定性证明.最后,为了检验所提控制策略的正确性,给出仿真和实验结果.仿真和实验结果的近似一致性证明了所提控制策略的有效性和合理性.     

Kinematic calibration of a 2-DOF translational parallel manipulator

Two types of kinematic calibration method for a 2-DOF (degrees of freedom) translational parallel manipulator are proposed using different error models. A calibration experiment is performed on both methods using an Absolute Laser Tracker and the results are compared. Two error models of the 2-DOF translational parallel manipulator are established using differential method and linear perturbation method, respectively. The two error models are solved using both the least squares method and linear equations. The results for the two different calibration methods show that the error model based on differential method is more effective in improving the accuracy of the 2-DOF translational parallel manipulator. Overall, the absolute position error of the 2-DOF translational parallel manipulator is significantly reduced to 0.13?mm from 0.93?mm after kinematic calibration.     

Analytical modeling and simulation of a 2-DOF drive and 1-DOF sense gyro-accelerometer

In this paper, we present a new analytical model for frequency as well as transient analysis of a 3-DOF gyro-accelerometer system having 2-DOF in drive and 1-DOF in sense direction respectively. The model constructs lumped parameter differential equations by vector analysis associated with each degree of freedom that comprises Coriolis action, Euler’s action and action due to external acceleration along with biasing counterparts. These coupled differential equations are then solved explicitly in the frequency domain by taking their Laplace transforms. Based on these formulations, a thorough system analysis has been carried out keeping in view the various parameters and issues related to the device design. Furthermore, a discriminating scheme for time varying angular rate and linear acceleration by combining the structural model of a gyro-accelerometer with the demodulation and filtering processes to investigate frequency response of a micro gyro-accelerometer has also been presented by taking into account the presently derived settled transient solution of sense mode response. Finally we have verified the present model with MATLAB Simulink, showing their excellent agreement with each other.     

Dynamic formulation of a planar 3-DOF parallel manipulator with actuation redundancy

In this paper, based on the conventional Newton–Euler approach, a simplification method is proposed to derive the dynamic formulation of a planar 3-DOF parallel manipulator with actuation redundancy. Closed-form solutions are developed for the inverse kinematics. Based on the kinematics, the Newton–Euler approach in simplification form is used to derive the inverse dynamic model of the redundant parallel manipulator. Then, the driving force optimization is performed by minimizing an objective function which is the square of the sum of four driving forces. The dynamic simulations are done for the parallel manipulator with both the redundant and non-redundant actuations. The result shows that the dynamic characteristics of the manipulator in the redundant case are better than that in the non-redundancy. The redundantly actuated parallel manipulator was incorporated into a 4-DOF hybrid machine tool which includes a feed worktable.     

Numerical calculation of the base inertial parameters of robots

This article presents a new approach to the problem of determining the minimum set of inertial parameters of robots. The calculation is based on numerical QR and SVD factorizations and on the scaling procedure of matrices. It proceeds in three steps:

• eliminate standard inertial parameters which have no effect on the dynamic model,
• determine the number of base parameters,

and

• determine a set of base parameters by regrouping some standard parameters to some others in linear relations.

Different models, linear in the inertial parameters are used: a complete dynamic model, a simplified dynamic model, and an energy model. The method is general, it can be applied to open loop, or graph-structured robots. The algorithms are easy to implement. An application for the PUMA 560 robot is given.     

Tolerance design of a 2-DOF overconstrained translational parallel robot

This paper deals with the tolerance design of a two-degree-of-freedom translational parallel robot module for high-speed pick-and-place operations. The module is an overconstrained parallel mechanism using two sets of parallelograms in each limb. A probabilistic model of the uncompensatable pose error is formulated, together with a compatibility condition to ensure the mobility of the robot. Based upon this model, optimization of the tolerances of the geometric source errors and joint clearances is conducted, subject to a set of appropriate constraints. Simulation and experimental results are given to demonstrate the effectiveness of this approach.     

6-DOF并联机器人工作空间边界分析与判定算法

6-DOF并联机器人的工作空间是控制过程研究的主要问题之一,所谓活动空间的边界分析,即指各液压缸活动过程中相互不能发生碰撞,如果碰撞发生,则该点即为边界点.对6-DOF并联机器人的机构和工作原理进行了介绍,给出了对于工作空间边界分析必要的位置算法,根据机构的特点与机器人的运动特性对6-DOF并联机器人的工作空间边界进行了细致的分析并给出了可操作的运动边界判定算法.实现了对液压缸碰撞的判定.     

Dynamic analysis and driving force optimization of a 5-DOF parallel manipulator with redundant actuation

Redundant actuation can improve the performance and ability of parallel manipulator. In order to deal with coordination and distribution of the driving force of the parallel manipulator with redundant actuation and to realize the control strategy based on dynamics, on the basis of the original 5UPS/PRPU parallel manipulator, it increases a drive for the middle PRPU passive constraint branch to make it a redundant actuation branch. It introduces configurations’ redundant types and compositions of 5UPS/PRPU parallel manipulator with redundant actuation, illustrates that the mechanism is redundant actuation from the perspective of degree of freedom and establishes a dynamic model based on Lagrangian method. On the basis of the weighted optimization principle of driving torque, it optimizes the driving torque of the parallel manipulator and calculates the driving force of the redundant driving chain with cutting force. It carries out the simulation by using ADAMS software and proves validity of dynamic model. Finally it detects the dynamic performance of the parallel manipulator by processing experiment of parallel manipulator with redundant actuation and its non-redundant counterpart.     

Adaptive quaternion control of a 3-DOF inertial stabilised platforms

ABSTRACT

Inertial stabilised platforms are increasingly popular with a large range of products available mainstream. Most items are controlled using popular algorithms that sometimes do not offer best achievable performances. Present paper proposes an advanced control which aims at improving these latter. The exposed solution is based on quaternion representation and self-adapts to the characteristics of the payload it tries to stabilise. Proposed control law ensures the stability of the system whatever the required orientation path is. Although only simulation has been performed to check the performances of such control, results look very promising compared to non-adaptive controls and may help to construct more polyvalent and efficient gimbals which would further facilitate their expansion. Proposed control law can also be applied, as is, to every system that shares the same quaternion-based rotational dynamics.     

Analytical determination of the workspace of symmetrical spherical parallel mechanisms

This paper presents a methodology for the analytical determination and representation of the workspace boundaries of symmetrical spherical parallel mechanisms (SPMs). The methodology is based on an intuitive orientation representation which, while not well known, has proven to be very useful for the analysis of symmetrical parallel mechanisms. The latter, previously introduced as "tilt-and-torsion angles," are briefly described. Then, relatively simple analytical expressions are found for the workspace boundaries of general symmetrical SPMs. Next, using these expressions and a simple numerical procedure, a fast algorithm is proposed for representing the so-called constant-torsion workspace. Finally, several examples are provided.     

Supplier behavior modeling and winner determination using parallel MDP

Behavioral uncertainty of a supplier is a major challenge to a buyer operating in e-procurement setting. Modeling suppliers’ behavior from past transactions, estimation of possible future performance and integrating this knowledge with the winner determination process can bring a new dimension to procurement process automation. We propose a states-space model to capture the uncertainty involved in long-term supplier behavior. The states represent the performance level of a supplier. This behavioral aspect is then integrated with the winner determination process of a multi-attribute reverse auction for efficient supplier selection using parallel MDP. We also propose an implementation framework to collect the feedback on supplier, generate an aggregate performance score and integrate it with the winner determination process. The performance aggregation and winner determination with help of Markov decision process effectively uses the past performance information. In addition, it updates performance information in regular invervals and allevates the problem of maintaining a long history. We compare the MDP-based selection with that of performance score-based selection through a simulation experiment. It is observed that our scheme gives better buyer utility, selects best suppliers and fetches better quality product. The benefits realized through these attributes to the buyer increases the efficiency of the MDP-based selection process.     

Robust nonlinear control of a planar 2-DOF parallel manipulator with redundant actuation

A new robust nonlinear controller is presented and applied to a planar 2-DOF parallel manipulator with redundant actuation. The robust nonlinear controller is designed by combining the nonlinear PD (NPD) control with the robust dynamics compensation. The NPD control is used to eliminate the trajectory disturbances, unmodeled dynamics and nonlinear friction, and the robust control is used to restrain the model uncertainties of the parallel manipulator. The proposed controller is proven to guarantee the uniform ultimate boundedness of the closed-loop system by the Lyapunov theory. The trajectory tracking experiment with the robust nonlinear controller is implemented on an actual planar 2-DOF parallel manipulator with redundant actuation. The experimental results are compared with the augmented PD (APD) controller, and the proposed controller shows much better trajectory tracking accuracy.     

Dynamic modeling and robust control of a 3-PRC translational parallel kinematic machine

The dynamic modeling and robust control for a three-prismatic-revolute-cylindrical (3-PRC) parallel kinematic machine (PKM) with translational motion have been investigated in this paper. By introducing a mass distribution factor, the simplified dynamic equations have been derived via the virtual work principle and validated on a virtual prototype with the ADAMS software package. Based upon the established model, three dynamics controllers have been attempted on the 3-PRC PKM. The intuitive co-simulations with the combination of MATLAB/Simulink and ADAMS show that the control performance of neither inverse dynamics control nor robust inverse dynamics control is satisfactory in the presence of parametric uncertainties in PKM dynamics. On the contrary, the controller based on the passivity-based robust control scheme is more suitable for tracking control of the PKM in terms of both control performances and controller design procedures. The results presented in the paper provide a sound base for both the mechanical system design and control system design of a 3-PRC PKM.     

Design of a 3-DOF tripod electro-pneumatic parallel manipulator

The objective of the research project was to design and construct a 3DOF tripod-type electro-pneumatic parallel manipulator that could be used for pick-and-place tasks in municipal waste recycling facilities. The fundamental requirement was that the manipulator be simple and cheap to construct, operate and maintain as well as robust and resistant to damage. The forward and inverse kinematic problem as well as working space and strength analysis issues were used for construction of manipulator. The prototype was tested using different payloads and velocities to establish its positioning accuracy and repeatability. The robot behavior was controlled with a commercially available industrial controller, which was reported insufficient for point-to-point operations required during solid waste handling. Conclusions have been drawn on how to optimize the robot structure and control.     

Dynamics and elasto-dynamics optimization of a 2-DOF planar parallel pick-and-place robot with flexible links

Dynamic modeling and analysis of a 2-DOF translational parallel robot with flexible links for high-speed pick-and-place operation is presented in this paper. Optimization is implemented with the goal to improve the dynamic accuracy of the end-effector at high speed. The governing equations of flexible links within the robot are formulated in the floating reference frame using Euler–Lagrange method, leading to a global FEM model being generated using the KED (Kineto-Elasto-Dynamics) technique. The dynamic characteristics of the robot are then investigated by model analysis. A numerical dynamic index is proposed to identity the range of natural frequency when the robot reaches different configurations. The comparisons are made between the optimized and original designs in terms of dynamic stress and response.     

Closed-form forward kinematics solutions of a 4-DOF parallel robot

It is well known that the forward kinematics of parallel robots is a very difficult problem. Closed-form forward kinematics solutions have been reported only to a few special classes of parallel robots. This paper presents closed-form forward kinematics solutions of a 4-DOF parallel robot H4. A 16th order polynomial in a single variable is derived to solve the forward kinematics of the H4. The 16 roots of the polynomial lead to at most 16 different forward kinematics solutions. A numerical verification is also presented.