Parallel Kinematic Manipulator Research Articles

DESIGN OF A CONTROL SYSTEM WITH A PREDICTIVE MODEL FOR A TWO-DRIVE MANIPULATOR WITH A PARALLEL STRUCTURE

This work intends to contribute to the corpus of knowledge on parallel manipulators and their control by making the most use of Model Predictive Control. We aim to investigate parallel manipulator kinematics, dynamics, and control strategies in detail in order to open up opportunities for enhanced performance, flexibility, and precision in these robotic systems.

DESIGN OF A CONTROL SYSTEM WITH A PREDICTIVE MODEL FOR A TWO-DRIVE MANIPULATOR WITH A PARALLEL STRUCTURE

This work intends to contribute to the corpus of knowledge on parallel manipulators and their control by making the most use of Model Predictive Control. We aim to investigate parallel manipulator kinematics, dynamics, and control strategies in detail in order to open up opportunities for enhanced performance, flexibility, and precision in these robotic systems.

A Recursive Lie-Group Formulation for the Second-Order Time Derivatives of the Inverse Dynamics of Parallel Kinematic Manipulators

Series elastic actuators (SEA) were introduced for serial robotic arms. Their model-based trajectory tracking control requires the second time derivatives of the inverse dynamics solution, for which algorithms were proposed. Trajectory control of parallel kinematics manipulators (PKM) equipped with SEAs has not yet been pursued. Key element for this is the computationally efficient evaluation of the second time derivative of the inverse dynamics solution. This has not been presented in the literature, and is addressed in the present paper for the first time. The special topology of PKM is exploited reusing the recursive algorithms for evaluating the inverse dynamics of serial robots. A Lie group formulation is used and all relations are derived within this framework. Numerical results are presented for a 6- DOF Gough-Stewart platform (as part of an exoskeleton), and for a planar PKM when a flatness-based control scheme is applied.

Hybrid Position‐Compliance Control of Redundantly Actuated Parallel Kinematic Manipulators Equipped with Serial Elastic Actuators

AbstractRedundantly actuated parallel kinematic manipulators (RA‐PKM) are ideal candidates in robotic applications combining dynamic performance with high accuracy. Actuation redundancy further allows for modulation of the end‐effector (EE) stiffness. A recent trend in robotics is the use of inherently compliant and elastic components, eventually leading to soft continuum robots, which shall provide tailored solutions for human‐robot collaboration and assistance applications. One way to introduce compliance is to use serial elastic actuators (SEA). This yields two kinematically decoupled dynamic systems, the RA‐PKM mechanism and the actuation system, that are force‐coupled by (passive) elastic elements. The DOF of the actuation system exceeds the DOF of the RA‐PKM according to the degree of actuation redundancy. Due to the kinematic decoupling the RA‐PKM is underactuated. To address this issue, a flatness‐based feedback‐linearizing position control approach along with a stiffness modulation approach is proposed.

The implementation of an optical computer mouse as a low-cost displacement sensor

The accurate measurement of distance, position or displacement is a requirement in many robotics projects. This paper presents the investigation of a HP M-UAE96 optical mouse as a low-cost displacement sensor. Various resolutions were obtained on a Windows operating system in conjunction with MATLAB®. The Arduino IDE was used with a linear actuator module to accurately produce predetermined linear movements. The most suitable resolution was found to be 0.2 mm/pixel and was implemented on a parallel kinematic manipulator in a case study. Surface contact and length of measurement were significant factors that influenced measurement accuracy.

Methods of workspace generation for parallel kinematic manipulators

This paper presents the geometric, discretization and Monte Carlo method to generate the workspace for Parallel Kinematic Manipulators (PKMs). The geometric method does not require the solution to the inverse kinematics as opposed to the Monte Carlo and discretization methods. Each method possesses advantages and drawbacks concerning accuracy, time and ease of implementation. A case study concerning constant orientation workspace of a planar 3RRR PKM showed that the most efficient and accurate method was the geometric method but it also possessed the most limitations. The discretization and Monte Carlo methods produced the workspace with an accuracy of 92.49% and 95.67% respectively.

A Spatial Parallel Kinematic Manipulator with Nested Kinematic Chains and High Rotational Range

A Spatial Parallel Kinematic Manipulator with Nested Kinematic Chains and High Rotational Range

Novel Reconfigurable Walking Machine Tool Enables Symmetric and Nonsymmetric Walking Configurations

Current research on walking robots strives to achieve a higher efficiency, a better load capacity, and an increased adaptability. Parallel kinematic manipulators (PKMs) are characterized by high payload and accuracy, but conventional PKMs with fixed configurations are limited to constrained workspaces in known structured environments. In this article, we propose a parallel reconfigurable walking machine tool that overcomes these limits by adapting its configuration and gaits to different scenarios. A lightweight and compact positioning system with shape memory alloy actuation is presented to achieve reconfiguration capabilities. Furthermore, kinematic, stability, and force analyses are reported to determine the optimal walking gaits in three different scenarios (with inclined slopes at different angles) and four robot configurations. Finally, a set of experiments with the physical prototype validates the proposed models. The results show that symmetric configurations present a better performance at lower ground inclinations (0.5% error), whereas asymmetric configurations can climb on slope conditions that would prevent the use of conventional PKMs (18% or 10°).

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.

Object-oriented modeling, simulation and control of a 6-DoF parallel kinematic manipulator for remote handling in DONES facility

This paper describes the modeling and simulation activities performed, within the EUROfusion framework, to support the engineering design and the development of the control system of the DONES Parallel Kinematic Manipulator (PKM), a 6-DoF parallel robot part of the Remote Handling System of the DONES facility. The main tasks of the PKM are the planned annual replacement of the Target Assembly and the High Flux Test Module, two of the crucial and most activated components of DONES. The PKM model, developed using the Modelica object-oriented language, is able to simulate the dynamics of the entire robots, including the main non-linear effects due to backlashes and static friction. The simulator is employed to support the preliminary design of the control system, based on an independent-joint approach with dual-loop cascade-PID logic. Simulations are then conducted to assess robot performances in terms of resolution, accuracy, repeatability and generated forces.

A constraint embedding approach for dynamics modeling of parallel kinematic manipulators with hybrid limbs

Parallel kinematic manipulators (PKM) are characterized by closed kinematic loops, due to the parallel arrangement of limbs but also due to the existence of kinematic loops within the limbs. Moreover, many PKM are built with limbs constructed by serially combining kinematic loops. Such limbs are called hybrid, which form a particular class of complex limbs. Design and model-based control requires accurate dynamic PKM models desirably without model simplifications. Dynamics modeling then necessitates kinematic relations of all members of the PKM, in contrast to the standard kinematics modeling of PKM, where only the forward and inverse kinematics solution for the manipulator (relating input and output motions) are computed. This becomes more involved for PKM with hybrid limbs. In this paper a modular modeling approach is employed, where limbs are treated separately, and the individual dynamic equations of motions (EOM) are subsequently assembled to the overall model. Key to the kinematic modeling is the constraint resolution for the individual loops within the limbs. This local constraint resolution is a special case of the general constraint embedding technique. The proposed method finally allows for a systematic modeling of general PKM. The method is demonstrated for the IRSBot-2, where each limb comprises two independent loops.

Analysis of 3-DOF Cutting Stability of Titanium Alloy Helical Milling Based on PKM and Machining Quality Optimization

Aiming at the requirements of titanium alloy holes in aircraft industry, the 3-DOF cutting stability and surface quality optimization of parallel kinematic manipulator (PKM) are studied. The variation of natural frequencies with the end-effector position of the PKM is analyzed. The cutting force model of titanium alloy helical milling based PKM is developed, and the cutting force coefficients are identified. The prediction model for 3-DOF the stability of helical milling based on the PKM is established through a Semi-Discrete method, and the stability lobes are obtained. The correctness of the stability lobes is verified by subjecting the cutting force signal to time-frequency transformation and roughness detection. The step-cutter is used for machining process improvement to enhance the stability domain. The method proposed in this paper can provide a reference for further optimization of the prediction and optimization of the milling process of difficult-to-process materials based on PKM in the future.

An efficient combined local and global search strategy for optimization of parallel kinematic mechanisms with joint limits and collision constraints

The optimization of parallel kinematic manipulators (PKM) involve several constraints that are difficult to formalize, thus making optimal synthesis problem highly challenging. The presence of passive joint limits as well as the singularities and self-collisions lead to a complicated relation between the input and output parameters. In this article, a novel optimization methodology is proposed by combining a local search, Nelder–Mead algorithm, with global search methodologies such as low discrepancy distribution for faster and more efficient exploration of the optimization space. The effect of the dimension of the optimization problem and the different constraints are discussed to highlight the complexities of closed-loop kinematic chain optimization. The work also presents the approaches used to consider constraints for passive joint boundaries as well as singularities to avoid internal collisions in such mechanisms. The proposed algorithm can also optimize the length of the prismatic actuators and the constraints can be added in modular fashion, allowing to understand the impact of given criteria on the final result. The application of the presented approach is used to optimize two PKMs of different degrees of freedom.

Kinematic sensitivity analysis of manipulators using a novel dimensionless index

Geometric errors directly affect the position of the end-effector of a Parallel Kinematic Manipulator (PKM), thus reducing its positioning accuracy. However, the tasks that are performed by PKMs, such as high-precision machining using a kinematic model with nominal values, are affected by machine errors that are not taken into account. Therefore, it is important to make an accurate determination of a machine’s error factors to obtain an accurate error model. Identifying the most crucial geometric errors and determining a method to control them is key in improving the accuracy of PKMs. To achieve this objective, a new method of sensitivity analysis, allowing the crucial geometric errors for parallel and serial manipulators to be identified, is proposed. A new dimensionless sensitivity index, based on the definition of a Local Sensitivity Index (LSI), is used to perform this analysis. The geometric error modeling is performed by deriving the position vector of the end-effector of the PKM. To test the efficiency of the proposed method, the main sources of PAR2 PKM errors are identified. The results show that 33.3% of the error components (main errors) from all error sources can be improved, to achieve a 51.8% improvement in the accuracy of the position error. These results indicate that the error sensitivity analysis method is quite effective, and can significantly contribute to improving the accuracy of a PKM.

A New Augmented RISE Feedback Controller for Pick-and-Throw Applications with PKMs

Most of the current industrial applications (like food packaging, waste sorting, machining, etc.) use parallel kinematic manipulators (PKMs) owing to their high speed and accuracy. However, parallel robots are exposed to highly nonlinear dynamics, time-varying parameters and uncertainties, especially in those applications. Considering all these issues, the synthesis of advanced and robust control schemes for PKMs is considered a challenging task. A new control scheme based on the Robust Integral of the Sign of the Error (RISE) control scheme is proposed in this work. A revision of the standard RISE control law is proposed by considering, in the control loop, a compensation term computed from the dynamic model of the robot, the measured and the desired trajectories, and the tracking error. In addition, we propose to extend the resulting controller with a nonlinear feedback function to compensate for the errors resulting from using the desired trajectories instead of the measured ones in the dynamic compensation term. The proposed control contribution can compensate for PKM parameter uncertainties and high nonlinearities as well as improve the robustness of the standard RISE controller. Numerical simulations have been conducted on a parallel robot, called T3KR, in a pick-and-throw task under different operating conditions to confirm the effectiveness of the proposed control scheme.

A New Time-Varying Adaptive Feedforward Sliding Mode Control of PKMs

This paper deals with the development of a new time-varying adaptive feedforward sliding mode control (SMC). The proposed controller is designed based on the original SMC by adding a feedforward term, which can be adaptive, in order to estimate the dynamic parameters. The main contribution of this study is a time-varying adaptation gain, which is proposed to efficiently identify these parameters. The objective is then to outperform the original SMC scheme. The proposed controller has been designed and applied to parallel kinematic manipulators (PKMs). It is validated through numerical simulation for different operating conditions on the VELOCE PKM. The obtained simulation results show the efficiency of the proposed controller in terms of tracking performances and robustness, with improvements up to 55% with respect to another adaptive controller (Adaptive Feedforward PD: AFFPD).

Acceleration analysis of 6-RR-RP-RR parallel manipulator with offset hinges by means of a hybrid method

In this work, the kinematics of a symmetrical hexapod parallel manipulator is investigated by means of Denavit-Hartenberg method and differential transformation method. When compared with a general Gough-Stewart platform, the limbs of the parallel manipulator are connected to the mobile and fixed platforms through offset hinges, rather than traditional spherical and universal hinges. Because the offset variable of the hinge axis are introduced by the offset hinge, the kinematics of the parallel manipulator studied becomes more complicated. The forward and inverse displacement analysis are approached by means of the Denavit-Hartenberg method. Then, the velocity and acceleration are analyzed using differential transformation method. The concise expression is obtained and can be easily translated into computer program. The derivation of acceleration analysis of the 6-RR-RP-RR parallel manipulator using the hybrid approach is novel in this research field. Finally, a numerical example is given and the numerical results are verified via co-simulation.

Shared Control for a Handheld Orthopedic Surgical Robot

A handheld robot with embedded parallel kinematic manipulator (PKM) is of compact size and is able to provide a similar workflow and exhibit great usability in robot-assisted surgery. The handheld robot is particularly advantageous for tremor suppression and motion stabilization, but also suffers from the issues of the actuators reaching the limit of their range of motion and the reflected force artifact from the actuators. These two pitfalls could make the handheld robot produce intermittent pause or jerky force during human operation. In this paper, a shared control with a handle-based navigation human-machine interface (HMI) has been proposed. A guiding pose region was designed to meet both the indices of dexterity maximization and kinetic energy minimization of the PKM. The control of the handheld robot is shared by the human for holding the handle entering the guiding pose region and by the PKM for positioning the tool and eliminating human tremor. The experimental results presented that the handheld robot under shared control with handle-based HMI could achieve an improvement both in tool tracking accuracy and force artifact reduction without intermittent pause than the counterpart which is under cooperative control with the traditional tool-based HMI.

T-Flex: A fully flexure-based large range of motion precision hexapod

Six degree of freedom manipulation provides full control over position and orientation, essential for many applications. However, six degree of freedom parallel kinematic manipulators (e.g. hexapods) either have a limited range of motion combined with a good repeatability when comprising flexure joints, or they have limited repeatability with a large workspace when using traditional rolling- or sliding-element bearings. In this paper, the design and optimization of a fully flexure-based large range of motion precision hexapod robot is presented. The flexure joints have been specifically developed for the purpose of large range of motion and high support stiffness for this manipulator. The obtained system allows for ±100 mm of translational and more than ±10° of rotational range of motion in each direction combined with a footprint of 0.6 m2 and a height of 0.4 m. Furthermore, a dedicated flexure-based design for the actuated joints combines high actuation forces with the absence of play and friction, allowing for accelerations exceeding 10 g. Experiments on a prototype validate the sub-micron repeatability, which is merely limited by the selected electronics.

On Robust Mechanical Design of a PAR2 Delta-Like Parallel Kinematic Manipulator

Abstract Sensitivity analysis of manipulators aims at studying the influence of variations in its own geometric parameters on its performance. This information is useful for evaluating the position error of the end-effector as well as for the synthesis of tolerances. Indeed, the synthesis of tolerances is a very important issue in the design and manufacturing of robot manipulators. In this paper, a sequential procedure for modeling, dimensioning, and tolerance synthesis of the Parallel Kinematic Manipulator (PKM) PAR2 is proposed. For optimal dimensional design, an approach based on the optimization of the workspace is proposed, taking into account several constraints, followed by a numerical matrix analysis-based deterministic method for sensitivity analysis whose performance is studied in terms of accuracy. To calculate the optimal dimensional tolerances, a new tolerance synthesis method is used. The effect of geometric tolerance on accuracy is analyzed.