Planar Manipulator Research Articles

Planar Cable-Driven Manipulators for Inspection of Large Surfaces

Cable-Driven Parallel Manipulators (CDPM) are a type of parallel robots in which the rigid links connecting the base with the terminal link, also called end-effector, are replaced by cables. This kind of system has been introduced during the last two decades, since then many issues have been addressed, but there are still open problems. Thanks to the nature of the cables, lightweight if compared to the overall structure, and the very large workplace, their possible applications are increasing. Recently, Robotics and Automation have been applied to the inspection of structures and infrastructure; therefore, they are starting to be used to substitute personnel in dangerous or unsafe operations. Related to the inspection, autonomous or tele-operated systems can be used for securing the access to the buildings or infrastructure. In this paper, we propose the application of CDPMs for the inspection of large surfaces, constituted by buildings facades, top roofs, and parts of infrastructures. The development of suitable model of the system, also called Digital Twin, allows the managing of the operation in safe conditions. As new application, we propose the use of a planar CDPM for being applied to the inspection and monitoring. The 3D model acts as a Digital Twin of the real prototype that has been developed and used for experimental testing. Since the purpose is to drive the end-effector to point of interest carrying suitable sensors, tests for trajectory planning and experimental tests are proposed. The inspection of structures and infrastructures has become a very important issue for the security of critical infrastructures, not only at European level but worldwide.

Adaptive Admittance Control for Safety-Critical Physical Human Robot Collaboration

Physical human-robot collaboration requires strict safety guarantees, due to the fact that robots and humans work in a shared workspace. This paper presents a novel control framework to handle safety-critical position-based constraints for human-robot physical interaction. The proposed methodology is based on admittance control, exponential control barrier functions (ECBFs), and quadratic program (QP) to achieve compliance during the force interaction between human and robot, while simultaneously guaranteeing safety constraints. In particular, the formulation of admittance control is formulated as a second-order nonlinear control system, and the interaction forces between humans and robots are regarded as the control input. A virtual force feedback for admittance control is provided in real-time by using the ECBFs-QP framework as a compensator of the external human forces. A safe trajectory is therefore derived from the proposed adaptive admittance control scheme for a low-level controller to track. The main innovation of the proposed approach is the ability to enable the robot to naturally comply with human forces without violating any safety constraints, even when external human forces incidentally force the robot to do so. The effectiveness of our approach is demonstrated in simulation studies on a two-link planar robot manipulator.

A self-adjusting and modular supervisory control algorithm for planar dexterous manipulation

Many applications require precise handling and manipulation of delicate objects. In some cases, the object must be transported to a new location following a strict travel path including time-related constraints. This paper presents a self-adjusting modular control algorithm for dexterous manipulation of planar objects using multiple manipulators with precise path and timing deliveries. The popular caging approach is simple, and usually effective when manipulating objects with multiple devices but can fail following complex paths with orientation adjustments under time-critical tracking requirements. The proposed approach exploits the dynamics of the object in real-time using tracking control and allocates the force that needs to be applied by each manipulator based on their current position around the object to maximize their capability to push in the direction of the contact angle. The new algorithm is self-adjusting and modular; It can adjust its force allocation according to configuration changes during operation, and manipulators execute the same algorithm regardless of their number. The advantages of the new approach are successfully demonstrated both with simulations and testbed experiments, including orientation tracking, which is not typically featured with the caging approach. Conditions to check when the new algorithm is most effective are also analyzed. The closed-loop stability and performance of the new algorithm are also studied and necessary conditions are identified.

Experimental tolerance design of robot manipulators accounting for positioning accuracy reliability

AbstractA new tolerance design method based on experimental design and positioning accuracy reliability is presented to deal with uncertainties of robot manipulators resulting from manufacturing and assembly processes. Initially, the performance function of positioning accuracy is established according to the kinematic model and response surface technique. An analytical algorithm for positioning accuracy reliability calculation is developed based on eigen‐decomposition and saddlepoint approximation methodologies. Inner orthogonal arrays of kinematic parameter tolerances along with the outer uniform arrays of joint variables are then constructed to analyze significant tolerances that affect the positioning accuracy reliability within the entire workspace. Finally, the applicability and performance of the proposed method are verified by case studies of a two‐link planar manipulator and a six‐degree‐of‐freedom robot manipulator. The results confirmed that the proposed method can efficiently and accurately analyze the positioning accuracy reliability, and the method recognizes the impact of kinematic parameters on the motion performance which is able to guide the tolerance range selection of robot manipulators.

АНАЛИЗ СОБСТВЕННЫХ ЧАСТОТ И ФОРМ КОЛЕБАНИЙ ПЛОСКОГО МАНИПУЛЯТОРА ПАРАЛЛЕЛЬНОЙ СТРУКТУРЫ

The study objective is to analyze the own frequencies and small-amplitude oscillations of a plane manipulator having parallel structure and to determine the influence of elastic and inertial properties of intermediate links and the drive on own frequencies and forms. The paper is devoted to solving the problem of ensuring vibration stability of manipulators. Analytical methods of the theory of oscillations and computational experiments in the software package "Universal Mechanism" are used. The novelty of the work is in defining the dependence of the own frequencies and oscillation forms of a plane parallel manipulator on the ratio of elastic and inertial properties of the links and the drive. As a result of the research, analytical and several computer models of a plane manipulator with three degrees of freedom are developed, own frequencies and oscillation forms for the developed models are determined. Conclusions: the replacement of absolutely rigid intermediate links with elastic rods led to the appearance of own frequencies and own modes corresponding to them , on which the output link oscillates in the vertical plane perpendicular to the plane of the manipulator links movement; the oscillations of the output link in the vertical and horizontal planes on their own forms are separated; the values of own frequencies at which the output link oscillates in the vertical plane do not depend on the coefficient of rigidity of the drive, but are determined by the elastic and inertial properties of the rods; the values of own frequencies at which the output link oscillates in the horizontal plane depend on the ratio of the drive and rods compliance; the influence of the elastic link masses on the values of their own frequencies is determined by the type of their own forms and the ratio of inertial parameters of the output link and rods.

A Novel Semi-Supervised Graph-Guided Approach for Intelligent Health State Diagnosis of a 3-PRR Planar Parallel Manipulator

As one of the most important operation and maintenance approaches, health state diagnosis technology plays a crucial role in ensuring the safety and reliability of mechanical equipment. The planar parallel manipulator, as a typical actuator, is widely employed in the field of precision manufacturing due to its advantages of high stiffness, large load support capability, and high precision. However, compared with common key functional components (such as bearings and gearboxes), planar parallel manipulators have more complicated operating mechanisms and failure behaviors. To satisfy the health state diagnosis demands of planar parallel manipulators in the scenario of insufficient label information, a novel intelligent health state diagnosis approach, termed semi-supervised graph-guided network with perception attention (SGN-PA), is developed for a 3-PRR (P and R represent prismatic and revolute pairs, respectively) planar parallel manipulator. Specifically, an improved multiorder graph perception module is constructed to extract multiscale feature information, and achieve feature fusion by combining perceptual attention mechanism, which enables the proposed SGN-PA model to have adaptation adjustment capabilities. Following that, local and nonlocal feature constraint strategies are employed with pseudo-label technology to reduce intraclass differences and maximize interclass differences, and then to fit the demands of health state diagnosis tasks. Eventually, based on the simulation and experimental scenarios of a 3-PRR planar parallel manipulator, the effectiveness and feasibility of the proposed SGN-PA model is extensively confirmed, and the diagnosis results show that it can significantly relax the constraints of label information while maintaining superior performances.

Position-posture Control Strategy for Planar Underactuated Manipulators with Second-order Nonholonomic Constraint

Position-posture Control Strategy for Planar Underactuated Manipulators with Second-order Nonholonomic Constraint

Nonlinear dynamic analysis of a multi-link manipulator with flexible links-joints mounted on a mobile platform

The present work theoretically demonstrates the dynamic analysis of a planar multi-link manipulator considering flexible links and joints mounted on a moving base. A nonlinear model of a multi-manipulator (N-links) has been developed accounting for an equivalent bi-directional mobile base. The nonlinear Euler-Bernoulli beam and spring-inertia/mass system have been introduced to demonstrate the flexibilities of links and joints, respectively. Modal analysis followed by trajectory analysis has been performed to investigate the behaviors of manipulator taking into account of accurate boundary conditions. Further, vibration characteristics, steady-state responses, and their stability at resonant situations due to joint motions and inertial coupling have been studied. Results of exploiting geometric and inertial coupling due to flexible arms on stability analysis of steady-state responses have been investigated and have been subsequently verified with the findings by directly solving the governing equations. Steady-state response characteristics to explore the dynamics of the multi-link manipulators under resonant states have been studied with the varying actuator mass, the flexibility of links, lifted payload, and joint parameters. The results thus obtained, deliver a useful insight into the position analysis and long-term behavior of multi-link flexible manipulators under harmonic hub-joint motions that shall further enable its proper vibration attenuation and control.

A Design of a 2-DoF Planar Parallel Manipulator with an Electro-Pneumatic Servo-Drive

This paper presents the design of a planar parallel manipulator with a pneumatic drive. Such manipulators are used in production lines for sorting, selecting, packing, and palletizing workpieces. This paper presents simulation studies of the designed manipulator in Matlab/Simulink software and using the SimMechanics library. A simple kinematics problem and an inverse kinematics problem were solved in order to carry out simulation studies of the designed manipulator. Simulation studies were also carried out on the dynamics of the manipulator using a mathematical model describing the physical phenomena occurring during the operation of the manipulator’s electro-pneumatic servo-drives. The main objective of the simulation study was to determine the manipulator working space and the possibility of positional control of the manipulator end-effector using a fuzzy logic controller.

Solving zero‐sum multi‐objective games with a‐priori secondary criteria

AbstractSolving non‐cooperative zero‐sum multi‐objective Games (zsMOGs), under undecided objective preferences results, for each of the players, in a Set of Rationalizable Strategies (SRS) to choose from. First, this paper deals with finding for each of the players a preferred subset of such rationalizable strategies based on a‐priori incorporation of partial preferences of the decision‐makers using secondary criteria. The obtained subset is termed the Set of Preferred Strategies (SPS). Here, a novel archive‐based co‐evolutionary algorithm is suggested to search for the SPS for each of the players. An academic example is suggested to demonstrate and validate the algorithm. It concerns a zsMOG that involves two adversarial planar manipulators. Based on a theorem that is proven here, a theoretic reference SRS is found for each of the players. This reference SRS is applied to find a reference SPS, which is used for validating the algorithm. Next, a comparison study is performed between the proposed archive‐based co‐evolutionary algorithm and an elite‐based version of this algorithm. The results clearly show that the archive‐based algorithm is superior to the elite‐based version, yielding results that correspond well to the theoretic sets.

Modeling and Verification for a Three-Degree-of-Freedom Flexure-Based Planar Parallel Micro Manipulator

Abstract Micro positioning systems are popular devices to achieve ultrahigh precision motion. In this paper, a three-degree-of-freedom (3-DOF) flexure-based planar parallel micro manipulator is presented. The existing literature focusing on the modeling of micro manipulator is difficult to fully reflect the real internal physical characteristic in the relationship between the input voltage and output pose. A new comprehensive nonlinear model for a three-DOF flexure-based planar parallel micro manipulator considering the errors of compliant joint in multiple non-functional directions, inherent force, moment, and nonlinear properties of the piezoelectric actuator is proposed. The ideal kinematic model and stiffness model are derived for comparison to verify the comprehensive nonlinear model. The simulation results show that the accuracy of the comprehensive nonlinear model is higher than that of other two models. Finally, the experimental results demonstrate that the average accuracy of the proposed modeling method in the translational direction is 26.35% better than that of the ideal kinematic model. The average accuracy in the rotational direction is 27.49% better than that of the ideal kinematic model. The proposed comprehensive nonlinear model can improve the modeling accuracy. It can be applied to other types of flexure-based micro manipulator.

Silicon-based soft parallel robots 4D printing and multiphysics analysis

Four-dimensional printing has set the stage for a new generation of soft robotics. The applications of rigid planar parallel robotic manipulators are also significant because of their various desirable characteristics, such as lower inertia, higher payload, and high accuracy. However, rigid planar parallel robots are heavy and require different actuators and components. This study introduces a novel technique to produce a light three degrees of freedom soft parallel manipulator at a low cost, which can be stimulated easily. This technique allows researchers to customize the actuator’s design based on the requirement. The robot is made by 3D printing based on fused deposition modelling and a direct ink writing process. The design, development, and additive manufacturing of a soft parallel robot electrothermally driven by a linear silicon-based actuator and polylactic acid parts are presented. Silicon-based soft actuators replace the rigid conventional linear actuators in this study to drive the planar parallel manipulator. The actuation of actuators is conducted using simple heating compared to the conventional rigid actuator. Various heating approaches and configurations are compared and analysed to find the most suitable one for the effective linear stroke of the soft actuator. The finite element model is used to analyse the performance of the electrothermally silicon-ethanol soft actuators in ABAQUS. The kinematics of the planar parallel robotic manipulator are simulated in MATLAB to achieve its workspace. The final soft parallel robot mechanism and the active and passive links are fabricated and tested experimentally.

Multiscale Graph-Guided Convolutional Network With Node Attention for Intelligent Health State Diagnosis of a 3-PRR Planar Parallel Manipulator

The data-driven intelligent health state diagnosis strategy has been successfully applied in modern industrial equipments. However, many of existing research works suffer from two major deficiencies: First, the sample independence assumption is widely adopted, so the influences of the relationship between samples on the overall performances are not explored. Second, most of the abovementioned application objects are typical key functional components (such as bearings, gearboxes, etc.), and research works on the intelligent health state diagnosis of planar parallel manipulator are rarely reported. To address these issues, a novel intelligent health state diagnosis method, termed multiscale graph-guided convolutional network with node attention (MSGCN-NA), is proposed for a 3-PRR (P and R represent prismatic and revolute pairs, respectively) planar parallel manipulator. Specifically, the developed MSGCN-NA model mainly contains the following two parts: first, the one is an unsupervised convolutional autoencoder, which is employed for the extraction of deep representation features, and then combined with Pearson metric to establish the adjacency matrix. Second, The other part is the constructed multiscale graph convolutional network, in which the node attention mechanism is adopted to achieve cross-scale fusion of different neighborhood information. The effectiveness of the proposed MSGCN-NA method is fully verified based on the simulation and experimental scenarios, the results show that MSGCN-NA can achieve superior diagnosis performances.

Analysis and validation of a planar parallel continuum manipulator with variable Cartesian stiffness

Manipulators with variable stiffness provide more flexibility between safety and performance when executing delicate tasks. In this paper, a novel planar parallel continuum manipulator (PPCM) with variable Cartesian stiffness is presented. The proposed manipulator consists of three flexible parallel limbs, with each limb made up with one PR drive and one slender flexible link, while the moving platform connects the links together. Except for the PR drive, there is no other rigid joint in this manipulator. An efficient kinetostatics analysis method is used based on previous research, and the stiffness model is built to compute the Cartesian stiffness. The advantage of the proposed PPCM is its intrinsic stiffness variation capability, which is achieved by the coupled large deflections of the flexible links and redundant actuation. An iterative algorithm is developed to calculate the actuator input under prescribed pose and required stiffness. A prototype of the manipulator is fabricated and its characteristics are validated by experiments. The measured results show that the studied PPCM has high position accuracy and its stiffness can be changed under different postures.

Optimal Design of a Five-Bar Planar Manipulator and Its Controller by Using Different Algorithms for Minimum Shaking Forces and Moments for the Largest Trajectory in a Usable Workspace

In this paper, a structural design and controller optimization process for a five-bar planar manipulator are studied using three different population-based optimization techniques: particle swarm optimization, genetic algorithm, and differential evolution. First, the desired kinematic properties of the manipulator, such as the position, velocity, and acceleration of the endpoint, are determined using inverse kinematics. Then, an optimization problem is created to minimize the shaking force and moments, and the desired kinematic quantities are implemented as constraints. All the link properties of the manipulator are defined as design variables, and the optimization results are obtained. The results show that it is possible to significantly reduce the shaking force and moment significantly thanks to the optimal design parameters. Finally, the controller is optimized to find the best PID gains considering the forward kinematics of the manipulator. It is observed that the shaking force and shaking moment can be reduced by 99% and 54%, respectively, which has a very positive effect on the accuracy of the trajectory tracking. Moreover, the performances of the optimization methods are compared by using the same number of iterations in the calculations, and thus, it can be seen that the GA method achieves the best results compared to the others. Therefore, the results of this study are of utmost importance for a manufacturer, who wants to design a five-bar planar manipulator and its controller.

Spring efficiency assessment and efficient use of spring methods of statically balanced planar serial manipulators with revolute joints only

Abstract. This paper proposes a spring efficiency assessment of a statically spring-balanced planar serial manipulator. The admissible spring configurations for the static balancing of planar serial manipulators without auxiliary links have been determined in the past. Gravity is balanced by the spring configuration systematically; however, the spring configuration also contains counter-effects between springs. Conceptually, with fewer counter-effects between springs, there is less burden on the spring system, which means that the springs are used more efficiently, and accordingly, the system would be safer, and its service life would be longer. In this study, the spring energy is represented in a quadratic form. The coefficients in a quadratic form represent the change in elastic energy with the relative position between links, which is named “elastic pseudo-stiffness”. Compared to the quadratic form of gravity energy, those elastic pseudo-stiffnesses for static balancing are regarded as positive contributions of a spring, while those that contain counter-effects are seen as negative ones. Spring efficiency is defined as the ratio of the elastic pseudo-stiffnesses, which has positive contributions for balancing to total elastic pseudo-stiffnesses. To use springs efficiently, the counter-effects, which are functions of spring parameters, need to be decreased, including spring stiffness and the attachment location of springs on links. A method to use spring efficiently by adjusting spring parameters is developed. Furthermore, it is found that, for a spring attached between adjacent links, the spring efficiency is 100 %, and the spring efficiency decreases while the number of joints over which the spring spans increases. In a spring manipulator system, the efficiency is negatively correlated to the payload. As an example, an efficiency assessment on a 3 degrees of freedom (DOF) manipulator is shown at the end.

Shape Reconstruction of Soft Manipulators Using Vision and IMU Feedback

In recent times, soft manipulators have gardened immense interest given their dexterous abilities. A critical aspect for their feedback control involves the reconstruction of the manipulator shape. The research, for the first time, presents shape reconstruction of a soft manipulator through sensor fusion of information available from Inertial Measurement Units (IMUs) and visual tracking. The manipulator is modeled using multi-segment continuous curvature Pythagorean Hodograph (PH) curves. PH curves are a class of continuous curvature curves with an analytical expression for the hodograph (slope). The shape reconstruction is formulated as an optimization problem that minimizes bending energy of the curve with a length constraint and the information from IMUs and/or visual markers. The paper experimentally investigates the robustness of shape reconstruction for scenarios when position of all visual markers, or slope at all the knots (placement of sensors) are known. Occlusion of manipulator segments is frequent, hence, this scenario is simulated by fusing information of available slopes (IMUs) at all knots and position (vision) at some knots. The experiments are performed on a planar tensegrity manipulator with IMUs feedback and visual tracking. The robustness study indicates reliability of these models for real world applications. Additionally, the proposed sensor fusion algorithm provides promising results where, for most cases, the shape estimates benefit from additional position information. Finally, the low dimensionality of the optimization problem argues for extension of the approach for real-time applications.

Planar Pattern Manipulation Surfaces Using Dual-Polarized Pin-Loaded Patch Resonating Elements

This article proposes a novel design concept to realize planar pattern manipulation surfaces (PPMSs) using dual-polarized pin-loaded patch resonating elements. First, the resonant frequency and reflection coefficient of the pin-loaded patch element are investigated through its equivalent circuit model. By changing the positions of shorting pins, the reflection phase of such a patch element can be appropriately adjusted while maintaining the reflection magnitude unchanged. Additionally, varying the positions of shorting pins possesses a significant property of polarization independence. Then, the dual-polarized pin-loaded patch element is employed to design the proposed PPMS. In this way, the incident wave is manipulated for different reflection angles with the dual-polarization response by adjusting the position distributions of shorting pins in two orthogonal polarization directions. To prove our presented design concept, two prototypes with reflection angles of ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta ^{r} = 45^{\circ }$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\phi ^{r} = 0^{\circ }$ </tex-math></inline-formula> ) and ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta ^{r} = 45^{\circ }$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\phi ^{r} = 45^{\circ }$ </tex-math></inline-formula> ) are finally implemented, fabricated, and measured. Measurements and calculations agree well with each other, which indicates that the reflection angle is experimentally obtained as predicted in theory. Thus, the proposed PPMS can be apparently viewed as a promising candidate to efficiently customize the radio environment in future wireless networks.

Lateral Disturbance Compensation of a Gondola-Embedded Façade Cleaning Robot via Compliant Planar Arm Structure

Façade cleaning is a dangerous task for human workers. If a façade cleaning robot is equipped with a gondola, it can perform façade cleaning with a simple planar manipulator via the vertical movement of the gondola. To clean a façade using a gondola-embedded robot successfully, the disturbance in the lateral direction of the gondola movement should be measured and compensated. In this study, we propose a compliant parallel structure-based position sensing device to measure the lateral directional disturbances. The compliant structure keeps contacts on the edge of the glass frame during the operation of the gondola and obtains disturbance information from forward kinematics of the joint mechanism. The prototype was produced, and experiments were performed on a test bench designed with a similar façade geometry as that of the target building. The disturbance compensation feature of the proposed mechanism was verified by experimental analysis.

Safe-by-design control for Euler–Lagrange systems

Safety-critical control is characterized as ensuring constraint satisfaction for a given dynamical system. Recent developments in zeroing control barrier functions (ZCBFs) have provided a framework for ensuring safety of a superlevel set of a single constraint function. Euler–Lagrange systems represent many real-world systems including robots and vehicles, which must abide by safety-regulations, especially for use in human-occupied environments. These safety regulations include state constraints (position and velocity) and input constraints that must be respected at all times. ZCBFs are valuable for satisfying system constraints for general nonlinear systems, however their construction to satisfy state and input constraints is not straightforward. Furthermore, the existing barrier function methods do not address the multiple state constraints that are required for safety of Euler–Lagrange systems. In this paper, we propose a methodology to construct multiple, non-conflicting control barrier functions for Euler–Lagrange systems subject to input constraints to satisfy safety regulations, while concurrently taking into account robustness margins and sampling-time effects. The proposed approach consists of a sampled-data controller and an algorithm for barrier function construction to enforce safety (i.e. satisfy position and velocity constraints). The proposed method is validated in simulation on a 2-DOF planar manipulator.