Parallel Robot Manipulator Research Articles

Structural synthesis of fully-isotropic translational parallel robots via theory of linear transformations

Abstract The paper presents a new structural synthesis approach of fully-isotropic translational parallel robotic manipulators (TPMs) based on the theory of linear transformations. A TPM is a 3-DOF (degree of freedom) parallel mechanism whose output link, called platform, can achieve three independent orthogonal translational motions with respect to the fixed base. The manipulators presented in this paper have three legs connecting the moving platform and the base (fixed platform). Only one kinematic pair per leg is actuated by a linear motor situated on the fixed base. A one-to-one correspondence exists between the actuated joint space and the operational space of the moving platform. The Jacobian matrix of fully-isotropic TPMs presented in this paper is the identity 3 × 3 diagonal matrix throughout the entire workspace. The synthesis method proposed in this paper allows us to obtain all structural solutions of fully-isotropic TPMs in a systematic manner. Overconstrained/isostatic solutions with elementary/complex and identical/different legs are obtained. Fully-isotropic TPMs have the advantage of simple command and important energy-saving due to the fact that, for a unidirectional translation, only one motor works as in a serial translational manipulator.

Smart Actuator Positioning and Displacement Transmissibility in Serial and Parallel Robot Manipulators for Performance Enhancement

A method is presented for the evaluation of the transmissibility of displacement from smart (active) actuators integrated in the structure of robot manipulators to the manipulator joint and end-effector displacements. The method is based on studying the characteristics of the Jacobian of the mapping function between the two displacements for a given position of the robot manipulator. The developed method provides a tool for the determination of the positioning of smart actuators to provide maximum effectiveness in eliminating high harmonics of the joint or the end-effector motion. In robots with serial and parallel kinematics chains containing nonprismatic joints, due to the associated kinematics nonlinearity, if the joint motions were synthesized with low harmonic trajectories, the end-effector trajectory would still contain high harmonics of the joint motions. Alternatively, if the end-effector motion were synthesized with low harmonic components, due to the inverse kinematics nonlinearity, the actuated joint trajectories would contain a significant high harmonic component. As a result, the operating speed and tracking precision are degraded. By integrating smart materials based actuators in the structure of robot manipulators to provide small amplitude and high frequency motions, the high harmonic component of the actuated joint and/or the end-effector motions can be significantly reduced, thereby making it possible to achieve higher operating speed and tracking precision.

On the Load Inertia Parameter Estimation of a Class of Parallel Robots

This paper presents a systematic load identification procedure for a class of parallel robot manipulators. It is considered as a regular dynamic robot identification problem since the load is rigidly fixed on the robot-platform. The challenge is that the estimation must be based only on the measurements obtained through sensors in the robot actuators. The load identification procedure is exemplified by experimental studies with a calibrated test load using periodic robot excitation.

Error attenuation in the control of a parallel robot manipulator using a dual-model-based structure

Parallel structure robots have been receiving growing attention from both academia and industry in recent years. This is due to their advantages over serial structure robots, such as high stiffness, high motion accuracy and a high load-structure ratio. Control of parallel robots, however, produces difficulties to control engineers due to the modelling errors arising from the highly non-linear and complex structures. This paper proposes a dual-model-based structure for error attenuation in the trajectory-tracking control of a parallel robot manipulator. In this design, a conventional model-based control algorithm employing an estimated robot dynamic model is first implemented in the inner loop of the control structure. Then, in order to reduce the unwanted effects caused by modelling erros, another model-based structure, developed based on the concept of the internal model control, is appended in the outer loop of the control structure as a compensator. A combination of these two model-based components results in a novel dual-model-based structure for parallel robot control. Sensitivity analyses show that the effects due to modelling errors and external disturbances can be significantly reduced by applying this new control structure without relying on a high-gain control solution. The effectiveness of this control design is successfully demonstrated by numerical studies on a planar parallel robot with 2 degrees of freedom.

Kinematics analysis of an offset 3-UPU translational parallel robotic manipulator

The parallel robotic manipulator has attracted many researchers’ attention and it also has growing applications to different areas. This paper proposes a 3-UPU (universal–prismatic–universal) translational parallel robotic manipulator with an equal offset in its six universal joints, based on the zero offset 3-UPU parallel manipulator. The kinematics of the new manipulator is analyzed and its inverse and forward kinematics solutions are provided. The conclusion is that its forward kinematics has 16 solutions instead of two in the zero offset manipulator.

Dynamics analysis and learning control for 3-PRPS platform

Employing a mathematical model to represent the dynamics of robot manipulators is a extremely difficult and complicated task. This study presents the dynamic analysis of parallel robot manipulators. The dynamic equations are first formulated in Cartesian space and then transformed into the joint space. Once the dynamic equations are derived, the D-type learning control algorithm is proposed to reduce position-tracking errors. The convergence conditions are also derived to ensure stability of the control systems. Moreover, a PC based, 3-PRPS platform control system is constructed to closely examine the effects of the D-type learning controller.

Development of Robot Control and Measurement for Unknown Geometric Surface Grinding

This paper introduces the control and measurement of a double parallel robot manipulator applied for unknown geometric surface grinding. A measurement system is developed to recognize a grinding path by a vision camera and to observe a grinding load by a current sensor. With the measured fusion information, an intelligent controller identifies the unknown geometric surface and moves the robot along the grinding path with a constant grinding load.

Robotic Measurement and Control for Chiropractic Research

The precision and programmability of robotic manipulators makes them suitable for biomechanics research, particularly when an experimental procedure must be accurately repeated multiple times. This paper describes a robotic system used to investigate biomechanical mechanisms of stroke in humans. A parallel robot manipulator is used to reproduce chiropractic manipulations on animal subjects using a 3‐D vision system. An algorithm for calibrating the system is proposed and tested on the robot. An iterative learning control scheme is then introduced to improve positional accuracy. Experimental results demonstrate that the calibration procedure and learning scheme are both effective.

The Kinematics and the Full Minimal Dynamic Model of a 6-DOF Parallel Robot Manipulator

In this paper we present a particular architecture of parallel robots which has six-degrees-of-freedom (6-DOF) with only three limbs. The particular properties of the geometric and kinematic models with respect to that of a classical parallel robot are presented. We show that inverse problems have an analytical solution. However, to solve the direct problems, an efficient numerical procedure which needs to inverse only a 3 × 3 passive Jacobian matrix is proposed. In a second step, dynamic equations are derived using the Lagrangian formalism where the joint variables are passive and active joint coordinates. Based on the geometrical properties of the robot, the equations of motion are derived in terms of only nine coordinates related by three kinematic constraints instead of 18 joint coordinates. The computational cost of the dynamic model obtained is reduced by using a minimum set of base inertial parameters.

Extreme reaches and reachable workspace analysis of general parallel robotic manipulators

Extreme reaches and reachable workspace analysis of general parallel robotic manipulators

Extreme reaches and reachable workspace analysis of general parallel robotic manipulators

Extreme reaches and reachable workspace analysis of general parallel robotic manipulators

Use of the cylindroid for the singularity analysis of rank 3 robot manipulators

Conventional methods for evolving the degrees-of-freedom, degrees-of-constraint, and/or singularity conditions of robot manipulators specifies a rank analysis of the Jacobian matrix. For serial-chain robot manipulators, these conventional practices have worked quite well. However, for parallel robot manipulators, these conventional practices lead to analytic complications and results that are difficult to physically interpret. This manuscript explores use of the cylindroid, coupled with its analytic expression in the principal coordinate system, for the singularity analysis of rank 3 robot manipulators. For 3R serial-chains, we illustrate two major points: (1) the cylindroid provides explicit solutions in the singularity analysis and (2) the cylindroid is quite efficient for developing 3R serial-chains that maintain rank 3 throughout the entire workspace. For 3F force-producing parallel-chains, we show the cylindroid can aid the solution process by simplifying the constitutive equations.

On the velocity and acceleration snalyses of general parallel robotic manipulators

AbstractThis article presents a unified method for the velocity and acceleration analyses of general parallel robotic manipulators. In this method, the governing velocity and acceleration equations of the robot are formulated in the joint space by considering it as a tree‐type mechanism subjected to Cartesian velocity and acceleration constraints. The procedures for solving the direct and the inverse analysis problems are established based on the generalized coordinate partitioning technique and the full pivoting Gaussian elimination method. These procedures take into account the overconstrained kinematic loops and redundant joints, and are applicable to either fully parallel robots or hybrid series‐parallel robots without any modifications. In addition, a set of generalized recursive formulas for computing the forward Cartesian velocity and acceleration transformations are developed. These formulas are also useful for efficient evaluating the complex nonlinear terms of the governing acceleration equations. © 1995 John Wiley & Sons, Inc.

Optimal control of a flexible parallel link robotic manipulator

The parallel link robotic manipulator consists of a base platform fixed in space or attached to the end-effector of another robot, a mobile platform, and six linear actuators (pistons) that link the two platforms together. The load carrying parts of the actuators are considered to be flexible (deformable) and modeled as mass-spring-damper elements. The nonlinear dynamic equations of the manipulator have been rigorously derived. No attempt has been made to linearize the plant or the measurements. The observer and the control law are derived based on the optimal control theory. The control gain matrix and the estimate gain matrix are obtained by solving the algebraic Riccati equations. The state excitation white noises and the observation white noises are included in the plant and the measurements, respectively. The dynamic equations of the observer are solved analytically and exactly. The feasibility of real-time control is demonstrated by the computer simulation results which are presented here.

Dynamic analysis and control of a stewart platform manipulator

AbstractThe Stewart platform is a six‐axis parallel robot manipulator with a force‐to‐weight ratio and positioning accuracy far exceeding that of a conventional serial‐link arm. Its stiffness and accuracy approach that of a machine tool yet its workspace dexterity approaches that of a conventional manipulator. In this article, we study the dynamic equations of the Stewart platform manipulator. Our derivation is closed to that of Nguyen and Pooran because the dynamics are not explicitly given but are in a step‐by‐step algorithm. However, we give some insight into the structure and properties of these equations: We obtain compact expressions of some coefficients. These expressions should be interesting from a control point of view. A stiffness control scheme is designed for milling application. Some path‐planning notions are discussed that take into account singularity positions and the required task. The objective is to make the milling station into a semiautonomous robotic tool needing some operator interaction but having some intelligence of its own. It should interface naturally with part delivery and other higher‐level tasks.

On the numerical kinematic analysis of general parallel robotic manipulators

A systematic two-part approach for the numerical kinematic analysis of general parallel robotic manipulators, is presented. The first part deals with structural analysis. Based on graph theory and the depth first search algorithm, a method for identifying and orienting the dependent kinematic loops of the robot is developed. This method not only facilitates the assignment of the local coordinate systems attached to the robot, but also arranges them in the correct order to allow efficient recursive coordinate transformation. The second part deals with displacement analysis. A set of recursion formulas is developed for computing the forward coordinate transformations, and these formulas are then adopted in a two-phase computational algorithm to obtain the numerical solutions to the direct and inverse kinematics problems. The two-phase algorithm developed is not only insensitive to the initial approximation of the solution vector, but also converges rapidly. It is also useful for finding multiple solutions for the robot as well as for continuous trajectory planning, as shown by the numerical examples presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A binary-decision/transputer network for the control of a planar three degree of freedom parallel robotic manipulator

A BINARY-DECISION/TRANSPUTER NETWORK FOR THE CONTROL OF A PLANAR THREE DEGREE OF FREEDOM PARALLEL ROBOTIC MANIPULATOR E. Harms 1, S. Kounias 2, L. J. Vroomen 2 and P. J. Zsombor-Murray 2 1 Electrical Engineering Department Technical University Eindhoven, The Netherlands 2 Department of Mechanical Engineering and McGill Research Centre for Intelligent Machines, McGiI[ University 817 Sherbrooke Street W., Montreal, Canada H3A 2K8

Two-dimensional model and algorithm analysis for a class of iterative learning control systems

The iterative learning control system (ILCS) has attracted considerable research interest in recent years. However the theoretical results on some fundamental properties of the ILCS have not yet been established. One of the common drawbacks shared by current approaches is lack of a suitable mathematical model which can clearly describe both the dynamics of the control system itself and the behaviour of the learning process as well. In this paper, a class of iterative learning control systems is analysed from the point of view of two-dimensional (2-D) system theory. The 2-D model for a class of ILCS is established in the form of‘Roessor's model’, based on which a general type of learning controller is proposed. Analysis of the 2-D error equation shows that the 2-D asymptotic stability of the 2-D model guarantees the learning convergence of an ILCS. Design criteria for a learning controller is also suggested. The learning gain matrices are obtained from a recursive 2-D identifier using the input and output of the controlled plant in previous operations; the model transformation method is discussed. An example of applying the proposed learning control method to a parallel link robotic manipulator is given.

Learning control of a parallel-link direct-drive robot manipulator

A learning control method for a parallel link direct-drive robot manipulator is introduced. The acceleration error is used to correct the motion of the direct-drive motors. A theoretical method, which estimates the convergence condition of the learning control process based on the limit condition of a geometric series, is proposed. The validity of the proposed theory is proved through a computer simulation, and the method is applied to the practical system of a parallel link direct-drive robot manipulator. The convergence condition of a learning control system can be quantitatively estimated by the divergent index which is defined in this study.

A Stewart Platform- Based Manipulator: General Theory and Practical Construction

The Stewart Platform is one example of a parallel connection robot manipulator. This paper summarizes work that has been done at Oregon State University over the past several years on this topic. The work has fallen into two general areas: theoretical consideration of the generalized Stewart Platform and practical considerations for building a working machine. Both of these areas are covered in this paper. The theoretical part of the paper discusses the following four problems: 1. Given the position and orientation of the end effector, what are the actuator coordinates? 2. Given the velocity, position, and orientation of the end effector, what are the actuator velocities? 3. Given the forces exerted on the end effector by the external world and the accelerations of the end effèc tor, what are the forces at the actuators? 4. What are the singular configurations of the manipu lator? For the Stewart Platform, the singular configu rations are positions where the end effector gains one or more degrees of freedom. After the theoretical problems have been solved, there are still a group of practical problems to be tackled when a real machine is built. How can the general configuration be sim plified to make the solution of the equations practical? Once a configuration is decided upon, what are the construction considerations for building a real machine? What is the range of motion of the end effector? What are the necessary ranges of motion of the joints? What are the implications of the singularities of the Stewart Platform and what are some practical ways of solving the problems they cause? In the process of doing this research, three machines were built and a computer simulation was written and used. The most recent machine and the computer simulation will be described in this paper.