Kinematic analysis of a novel 3-DOF actuation redundant parallel manipulator using artificial intelligence approach

Kinematic analysis is one of the key issues in the research domain of parallel kinematic manipulators. It includes inverse kinematics and forward kinematics. Contrary to a serial manipulator, the inverse kinematics of a parallel manipulator is usually simple and straightforward. However, forward kinematic mapping of a parallel manipulator involves highly coupled nonlinear equations. Therefore, it is more difficult to solve the forward kinematics problem of parallel robots. In this paper, a novel three degrees-of-freedom (DOFs) actuation redundant parallel manipulator is introduced. Different intelligent approaches, which include the Multilayer Perceptron (MLP) neural network, Radial Basis Functions (RBF) neural network, and Support Vector Machine (SVM), are applied to investigate the forward kinematic problem of the robot. Simulation is conducted and the accuracy of the models set up by the different methods is compared in detail. The advantages and the disadvantages of each method are analyzed. It is concluded that ν-SVM with a linear kernel function has the best performance to estimate the forward kinematic mapping of a parallel manipulator.     

Structures and characteristics of parallel manipulators

Parallel structures have remarkable characteristics such as high precision, high load capacity, high rigidity and high speed. Therefore, they have received a lot of attention as alternative structures for robot manipulators. This paper reviews the recent results on properties of the parallel manipulator. First, the basics of the link mechanism, which is necessary to understand the structure of the parallel manipulator, is summarized before the structure of the parallel manipulator is defined. Then, the parallel manipulator is compared with the serial manipulator. The singular point of the parallel manipulator and the optimum design of the structure of the parallel manipulator are also discussed.     

A new inverse kinematics algorithm for binary manipulators with many actuators

In this paper we present a new, and extremely fast, algorithm for the inverse kinematics of discretely actuated manipulator arms with many degrees of freedom. Our only assumption is that the arm is macroscopically serial in structure, meaning that the overall structure is a serial cascade of units with each unit having either a serial or parallel kinematic structure. Our algorithm builds on previous works in which the authors and coworkers have used the workspace density function in a breadthfirst search for solving the inverse kinematics problem. The novelty of the method presented here is that only the 'mean' of this workspace density function is used. Hence the requirement of storing a sampled version of the workspace density function (which is a function on a six-dimensional space in the case of a spatial manipulator) is circumvented. We illustrate the technique with both planar revolute and variable-geometry-truss manipulators, and briefly describe a new manipulator design for which this algorithm is applicable.     

Cable-Direct-Driven Robot (CDDR) with Passive SCARA Support: Theory and Simulation

This article presents a new planar translational cable-direct-driven robot (CDDR) with actuation redundancy and supported against loading normal to the motion plane with a passive planar two-degree-of-freedom SCARA-type (Selective Compliance Assembly Robot Arm) serial manipulator. This allows the robot to resist cable sag without being supported on the motion plane. The proposed robot architecture may assure high payload-to-weight ratio, resistance to forces normal to the plane of motion, and a potentially large workspace. Another benefit is that the passive SCARA has structure to provide end-effector moment resistance, which is not possible with many proposed translational CDDRs. Moreover, the passive robot can also serve as an independent Cartesian metrology system. This article derives the kinematics and dynamics models for the proposed hybrid serial/parallel architecture. Additionally it proposes a dynamic Cartesian controller always ensuring positive cable tensions while minimizing the sum of all the torques exerted by the actuators. Simulation examples are also presented to demonstrate the novel CDDR concept, dynamics, and controller.Category (7) – System Modelling/Simulation/Control/Computer–Aided Design/Robot Control/Teleoperation/Moving Robots     

Inverse Kinematics of Binary Manipulators Using a Continuum Model

Binary actuators have only two discrete states, both of which are stable without feedback. As a result, manipulators with binary actuators have a finite number of states. The major benefits of binary actuation are that extensive feedback control is not required, reliability and task repeatability are very high, and two-state actuators are generally very inexpensive, resulting in low cost robotic mechanisms. These manipulators have great potential for use in both the manufacturing and service sectors, where the cost of high performance robotic manipulators is often difficult to justify. The most difficult challenge with a binary manipulator is to achieve relatively continuous end-effector trajectories given the discrete nature of binary actuation. Since the number of configurations attainable by binary manipulators grows exponentially in the number of actuated degrees of freedom, calculation of inverse kinematics by direct enumeration of joint states and calculation of forward kinematics is not feasible in the highly actuated case. This paper presents an efficient method for performing binary manipulator inverse kinematics and trajectory planning based on having the binary manipulator shape adhere closely to a time-varying curve. In this way the configuration of the arm does not exhibit drastic changes as the end effector follows a discrete trajectory.     

Near Time-Optimal Control of Redundant Manipulators along a Specified Path with Jerks Constraint

A time-optimal control scheme for a general type of closed-chain manipulator is proposed. The considered manipulator is composed of multiple serial manipulators that are connected to each other and single manipulators may be kinematically redundant. Also, the limit on the actuator torques and actuator jerks are considered. The jerk constraints create a smooth trajectory for reducing strain on robot actuators and satisfy torque limitations of industrial actuators. Inclusion of the jerk constraints increases the traversal time, hence, a method is introduced to optimize this time. To this end, a simple method to find switching points is investigated.     

Cartesian path generation of robot manipulators using continuous genetic algorithms

In this paper, the authors describe a novel technique based on continuous genetic algorithms (CGAs) to solve the path generation problem for robot manipulators. We consider the following scenario: given the desired Cartesian path of the end-effector of the manipulator in a free-of-obstacles workspace, off-line smooth geometric paths in the joint space of the manipulator are obtained. The inverse kinematics problem is formulated as an optimization problem based on the concept of the minimization of the accumulative path deviation and is then solved using CGAs where smooth curves are used for representing the required geometric paths in the joint space through out the evolution process. In general, CGA uses smooth operators and avoids sharp jumps in the parameter values. This novel approach possesses several distinct advantages: first, it can be applied to any general serial manipulator with positional degrees of freedom that might not have any derived closed-form solution for its inverse kinematics. Second, to the authors’ knowledge, it is the first singularity-free path generation algorithm that can be applied at the path update rate of the manipulator. Third, extremely high accuracy can be achieved along the generated path almost similar to analytical solutions, if available. Fourth, the proposed approach can be adopted to any general serial manipulator including both nonredundant and redundant systems. Fifth, when applied on parallel computers, the real time implementation is possible due to the implicit parallel nature of genetic algorithms. The generality and efficiency of the proposed algorithm are demonstrated through simulations that include 2R and 3R planar manipulators, PUMA manipulator, and a general 6R serial manipulator.     

Simultaneous kinematic calibration,localization, and mapping (SKCLAM) for industrial robot manipulators†

Recently, the demand for more accurate, productive, and economical robot manipulators is increasing in the robotics industry. However, a manipulator will produce kinematic errors during production. Thus low-cost kinematic calibration is demanded. Moreover, environmental mapping is also demanded to plan the motions of the manipulator. In this paper, we proposed a simultaneous kinematic calibration, localization, and mapping (SKCLAM) method, which can simultaneously calibrate the kinematic parameters of an industrial robot manipulator using a commercial RGB-D camera attached to its end effector to reconstruct its surroundings. In our method, the kinematic calibration is achieved with feature detection and epipolor geometry. Synthetic and real data experiments were conducted to verify the SKCLAM method. We succeeded in reducing the kinematic errors of the manipulator and reconstructing dense 3D maps of the workspace in the experiments.     

Kinematics analysis of a hybrid manipulator for computer controlled ultra-precision freeform polishing

As one of the final processing steps of precision machining, polishing process is a very key decision for surface quality. This paper presents a novel hybrid manipulator for computer controlled ultra-precision (CCUP) freeform polishing. The hybrid manipulator is composed of a three degree-of-freedom (DOF) parallel module, a two DOF serial module and a turntable providing a redundant DOF. The parallel module gives the workpiece three translations without rotations. The serial module holds the polishing tool and gives it no translations on the polishing contact area due to its particular mechanical design. A detailed kinematics model is established for analyzing the kinematics of the parallel module and the serial module, respectively. For the parallel module, the inverse kinematics, the forward kinematics, the Jacobian matrix, the workspace and the dexterity distribution are analyzed systematically. Workspaces are also investigated for varying structural parameters. For the serial module, the inverse kinematics, the forward kinematics, the workspace and the precession motion analysis are carried out. An example of saddle surface finishing with this manipulator is given and the movement of actuators with respect to this shape is analyzed theoretically. These analysis results illustrate that the proposed hybrid manipulator is a very suitable machine structure for CCUP freeform polishing.     

An efficient method for inverse dynamics of manipulators based on the virtual work principle

The computational efficiency of inverse dynamics of a manipulator is important to the real-time control of the system. For serial manipulators, the recursive Newton-Euler method has been proven to be the most efficient. However, for more general manipulators, such as serial manipulators with closed kinematic loops or parallel manipulators, it must be modified accordingly and the resultant computational efficiency is degraded. This article presents a computationally efficient scheme based on the virtual work principle for inverse dynamics of general manipulators. The present method uses a forward recursive scheme to compute velocities and accelerations, the Newton-Euler equation to calculate inertia forces/torque, and the virtual work principle to formulate the dynamic equations of motion. This method is equally effective for serial and parallel manipulators. For serial manipulators, its computational efficiency is comparable to the recursive Newton-Euler method. For parallel manipulators or serial manipulators with closed kinematic loops, it is more efficient than the existing methods. As an example, the computations of inverse dynamics (including inverse kinematics) of a general Stewart platform require only 842 multiplications, 511 additions, and 12 square roots.     

A novel XY-Theta precision table and a geometric procedure for its kinematic calibration

Spatial precision positioning devices are often based on parallel robots, but when it comes to planar positioning, the well-known serial architecture is virtually the only solution available to industry. Problems with parallel robots are that most are coupled, more difficult to control than serial robots, and have a small workspace. In this paper, new parallel robot is proposed, which can deliver accurate movements, is partially decoupled and has a relatively large workspace. The novelty of this parallel robot lies in its ability to achieve the decoupled state by employing legs of a different kinematic structure. The robot repeatability is evaluated using a CMM and so are the actual lead errors of its actuators. A simple geometric method is proposed for directly identifying the actual base and mobile reference frames, two actuator's offsets and one distance parameter, using a measurement arm from FARO Technologies. While this method is certainly not the most efficient one, it yields a satisfactory improvement of the robot accuracy without the need for any background in robot calibration. An experimental validation shows that the position accuracy achieved after calibration is better than 0.339 mm within a workspace of approximately 150 mm×200 mm.     

A new approach to improve absolute positioning accuracy of robot manipulators

This article describes a new calibration system for robot manipulators which improves their absolute positioning accuracy by using parameter-estimation algorithms based on the Newton method. When 3D position data of the specified points on a manipulator and the joint encoder values are input to the calibration system, the system estimates the offset values of joint encoders, link lengths, and position and orientation of the manipulator base coordinate system with respect to the world coordinate system which is difficult to obtain by conventional calibration methods. This calibration system can be applied to various manipulator types by just changing the basic kinematic equations. The system employs an algebraic programming system called REDUCE to automatically reduce the manipulator kinematic equation and partial differential calculus in the Newton method. For efficiency, first only the arm part with three degrees of freedom and then the hand part are calibrated. The experimental results demonstrate the effectiveness of this system by reducing the robot's absolute positioning errors to the order of repeatability errors.     

A New Algorithm for Measuring and Optimizing the Manipulability Index

The estimation of the performance characteristics of robot manipulators is crucial in robot application and design. Furthermore, studying the manipulability index for every point within the workspace of any serial manipulator is considered an important problem. Such studies are required for designing trajectories to avoid singular configurations. In this paper, a new method for measuring the manipulability index is proposed, and then some simulations are performed on different industrial manipulators such as the Puma 560 manipulator, a six DOF manipulator and the Mitsubishi Movemaster manipulator.     

Analysis of duality-based interconnected kinematics of planar serial and parallel manipulators using screw theory

In this paper, a method has been proposed to analyze the planar architectures of serial and parallel manipulators, based on the duality associated with their interconnected kinematics. The interconnected kinematics states that model of one architecture can be derived from the kinematic model of the other, using screw theory approach. The performance of the initial and the derived manipulators was evaluated with three criteria: isotropy, maximum force transmission ratio and local transmission index. Without loss of generality, the serial manipulator derived from parallel has better isotropy, while the parallel manipulator derived from serial can be designed to have better force and power transmission.

     

Kinematics and dynamics analyses of a parallel manipulator with three active legs and one passive leg by a virtual serial mechanism

A novel CAD variation geometry approach and a virtual serial mechanism approach are proposed for analyzing the kinematics and dynamics of a parallel manipulator with three SPS-type active legs and one PU-type constrained passive leg. First, a simulation mechanism of this parallel manipulator is created, and some kinematic characteristics are analyzed. Second, the inverse formulae for solving pose and Jocabian matrix are derived, and workspace and singularity are determined. Third, a virtual serial mechanism is created, and the analytic formulae for solving active forces and constrained wrench of these parallel manipulators are derived. The analytic results are verified by using its simulation mechanism.     

Cable-direct-driven-robot (CDDR) with a 3-link passive serial support

Cable-direct-driven-robots (CDDRs) provided with a passive serial support represent an interesting and rising evolution of planar cable robots. The paper is devoted to present and analyze a novel CDDR robot. The robot consists in a fully actuated CDDR supported against loading normal to the motion plane with a 3-link passive planar serial manipulator. This hybrid structure combines positive features of both parallel and serial architectures, and prevents out-of-plane movements without the necessity for the robot to be supported on the motion plane. The adoption of a 3-link serial manipulator ensures a greater workspace area compared with similar structures that adopt a smaller number of links, and improves specific characteristics of their dynamics. Nevertheless undesired oscillations may occur since the serial manipulator is underconstrained. For this reason damping elements are inserted in the structure. Simulation examples are presented to demonstrate the novel CDDR concept and its dynamics. In addition, a strategy to select proper values of damping coefficients is presented.     

Determination of the orientation workspace of parallel manipulators

An important step during the design of a parallel manipulators is the determination of its workspace. For a 6-d.o.f. parallel manipulator workspace limitations are due to the bounded range of their linear actuators, mechanical limits on their passive joints and links interference. The computation of the workspace of a parallel manipulator is far more complex than for a serial link manipulator as its translation ability is dependent upon the orientation of the end-effector.We present in this paper an algorithm enabling to compute the possible rotation of the end-effector around a fixed point. This algorithm enables to take into account all the constraints limiting the workspace. Various examples are presented.     

Method for kinematic calibration of stewart platforms

A Stewart platform is a six degrees of freedom parallel manipulator composed of six variable-length legs connecting a fixed base to a movable plate. Like all parallel manipulators, Stewart platforms offer high force/torque capability and high structural rigidity in exchange for small workspace and reduced dexterity. Because the solution for parallel manipulators' forward kinematics is in general much harder than their inverse kinematics, a typical control strategy for such manipulators is to specify the plate's pose in world coordinates and then solve the individual leg lengths. The accuracy of the robot critically depends on accurate knowledge of the device's kinematic parameters. This article focuses on the accuracy improvement of Stewart platforms by means of calibration. Calibration of Stewart platforms consists of construction of a kinematic model, measurement of the position and orientation of the platform in a reference coordinate frame, identification of the kinematic parameters, and accuracy compensation. A measurement procedure proposed in this article allows a great simplification of the kinematic identification. The idea is to keep the length of the particular leg, whose parameters are to be identified, fixed while the other legs change their lengths during the measurement phase. By that, redundant parameters can be eliminated systematically in the identification phase. The method also shows the estimation of each leg's parameters separately because the measurement equations are fully decoupled, which results in a drastical reduction of the computational effort in the parameter identification. Simulation results assess the performance of the proposed approach. © 1993 John Wiley & Sons, Inc.     

Certified solving of the forward kinematics problem with an exact algebraic method for the general parallel manipulator

This article introduces an exact method to solve the forward kinematics problem (FKP) specifically applied to spatial parallel manipulators. The majority can modeled by the 6-6 parallel manipulator. This manipulator is a hexapod made up of a fixed base and a mobile platform attached to six kinematics chains with linear (prismatic) actuators located between two ball or Cardan joints. In order to implement algebraic methods, the parallel manipulator kinematics will be formulated as polynomial equations systems where the equation number is equal to the unknown numbers. One position-based kinematics model will be identified to solve the difficult FKP. The selected proven algebraic method implements Gröbner bases and constructs an equivalent univariate polynomial system. The exact resolution of this last system determines the real solution which exactly corresponds to the manipulator postures. The FKP resolution of the general 6-6 parallel manipulator outputs 40 complex solutions. We provide several examples of various hexapod types yielding eight real solutions. This algebraic method is exact and computes certified results.     

Prediction of geometric errors of robot manipulators with Particle Swarm Optimisation method

This paper reports on the prediction of the expected positioning errors of robot manipulators due to the errors in their geometric parameters. A Swarm Intelligence (SI) based algorithm, which is known as Particle Swarm Optimization (PSO), has been used to generate error estimation functions. The experimental system used is a Motoman SK120 manipulator. The error estimation functions are based on the robot position data provided by a high precision laser measurement system. The functions have been verified for three test trajectories, which contain various configurations of the manipulator. The experimental results demonstrate that the positioning errors of robot manipulators can be effectively predicted using some constant coefficient polynomials whose coefficients are determined by employing the PSO algorithm. It must be emphasized that once the estimation functions are obtained, there may be no need of any further experimental data in order to determine the expected positioning errors for a subsequent use in the error correction process.