Planar Parallel Robot Research Articles

Closeness to singularity based on kinematics and dynamics and singularity avoidance of a planar parallel robot with kinematic redundancy

Planar parallel robots are appealing due to their structural simplicity, high stiffness, and large payload capacity. One major problem is that workspace and singularity of non-redundant parallel robots are unchangeable. Hence, when the desired path crossed with singularity or exceeded the workspace’s boundary, the robot is incapable of finishing the task. Another one is closeness to singularity. If one can know the distance between the end manipulator and singularity or workspace’s boundary, the robot will avoid lose control or breakdown. Compared with the traditional planar parallel robot, the planar parallel robot with kinematic redundancy possesses the advantages of avoiding singularity, expanding workspace by adjusting kinematic redundancy parameter. Therefore, the objective of this article is to present an offline action-strategy of a planar robot with kinematic redundancy to measure the closeness to singularity and avoid singularity. It includes two main parts: First, before the robot moves along the desired paths, the closeness to singularity was measured based on the performance of the kinematics and dynamics so that one can know where to pause the robot. Second, an algorithm is designed to previously find the proper kinematic redundancy parameters for changing singularity and workspace. Hence, the robot can smoothly move far from the singularity to finish all paths. The results indicate that the robot can adjust its configuration to well realize the goal by the offline action-strategy.

Determination of the available wrench set of a 3-RPRR kinematically-redundant planar parallel manipulator

Parallel robots that incorporate kinematic redundancy in their designs are frequently considered for use in different applications due to their ability to avoid direct kinematic singularities within their workspace. Knowledge of a robot’s wrench generation capabilities constitutes essential information when designing its geometry and planning its optimal use to accomplish various tasks. In the presence of kinematic redundancies, the determination of a robot’s wrench generation capabilities at a given pose of its mobile platform depends not only on the limits of its actuators but also on the configurations of its legs. In this work, an algorithm allowing for the closed-form computation of the available wrench set of the 3-RPRR planar parallel robot is presented. This results in generating the boundary of the available wrench set as a set of faces in the wrench space. Based on this representation, algorithms allowing for the computation of various application-based performance indices are also described. Example numerical results are included to demonstrate how the tools that are presented could be used in the context of robot design.

A Simulation Study of a Planar Cable-Driven Parallel Robot to Transport Supplies for Patients with Contagious Diseases in Health Care Centers

Currently, a large number of investigations are being carried out in the area of robotics focused on proposing solutions in the field of health, and many of them have directed their efforts on issues related to the health emergency due to COVID-19. Considering that one of the ways to reduce the risk of contagion is by avoiding contact and closeness between people when exchanging supplies such as food, medicine, clothing, etc., this work proposes the use of a planar cable-driven parallel robot for the transport of supplies in hospitals whose room distribution has planar architecture. The robot acts in accordance with a procedure proposed for each task to be carried out, which includes the process of disinfection (based on Ultraviolet-C light) of the supplies transported inside the robot’s end effector. The study presents a design proposal for the geometry of the planar cable-driven parallel robots and its end effector, as well as the software simulations that allow evaluating the robot’s movement trajectories and the responses of the position control system based on Fuzzy-PID controllers.

Development of a planar cable parallel robot for practical application in the educational process

Cable-driven parallel robot (CDPR) has the great potential for various applications in industry and in everyday life. They consist of an end effector and a base, which connected by several cables. CDPRs have a large workspace compared to the workspace of classic parallel robots. CDPR have a simpler structure have good dynamic properties, high carrying capacity, mobility and low cost. The only drawback is that the CDPR cables can only work for retraction and cannot push. This article presents the design of a prototype of a planar CDPR with four cables for practical use in the educational process. This prototype of a planar CDPR is necessary for a better understanding of the design features, structure, kinematics, statics and dynamics of the CDPR by students. The planar CDPR performs two translational motions, due to the controlled 4 cables, and one rotational motion of the end effector. The research of the kinematics and statics of the planar cable-driven parallel robot is carried out. Simulation of the motion of a planar cable-driven parallel robot in the Python programming language has been carried out. A design was developed and a prototype of the planar cable-driven parallel robot was manufactured. Experimental researches of a prototype of the planar cable-driven parallel robot have been carried out. The results of experimental researches have shown that the CDPR works well enough. During the tests of the prototype of the planar cable-driven parallel robot, it was found that the distortions of the trajectory of the end effector depend on the tension of the cables. It is necessary to monitor the tension level using strain gauges. Based on the analysis of the results obtained, the effectiveness of the use of the prototype of a planar CDPR in the educational process of the robotics course has been confirmed

Research on a 3-DOF Planar Cable-Driven Parallel Robot Based on Fuzzy Adaptive PD Computed Torque Control

Cable-driven parallel robots (CDPR) with spatial configuration are widely used while ones with plannar configuration are rarely applied. Therefore, this paper studies the modeling and control characteristics of a three degree-of-freedom cable-driven planar parallel robot with great application prospects. Aiming at the shortcomings of the existing control methods towards CDPR, a new method based on fuzzy adaptive PD computing torque control is proposed which contains a reasonable optimal distribution of cable forces. To validate the method, the tracking control simulation research and analysis are carried out for the trajectory of high-order interpolation planning, the results of which show that the control method has favorable dynamic tracking accuracy and mechanical properties. Moreover, compared with the fixed-gain computed torque control, the proposed control method can overcome the influence of model inaccuracy more effectively.

Design and optimization of three-degree-of-freedom planar adaptive cable-driven parallel robots using the cable wrapping phenomenon

Cable-driven parallel robots (CDPRs) are gaining increasing attention due to their low weight, cost, and power consumption characteristics. Adaptive CDPRs are special cable-driven systems in which the locations of the pulley blocks can be modified. In this paper, we propose a new type of adaptive CDPR that can passively modify the attachment points on the end-effector (moving platform) without augmented kinematic redundancy, but this depends on the cable wrapping over these adaptive attachment points. We demonstrate the proposed approach on some practical cases of planar adaptive CDPRs to expand the workspace and dexterity of the robot especially for the large rotation capability. The proposed robot can be passively reconfigured to several configurations. The kinematics modeling and static equilibrium of the adaptive CDPRs are established. Scale optimization of the adaptive attachment point is performed. The results show that this design can effectively increase the workspace, especially the rotation workspace, without increasing the actuation redundancy and kinematic redundancy.

Task-Based Design Approach: Development of a Planar Cable-Driven Parallel Robot for Upper Limb Rehabilitation

This paper deals with the optimal design of a planar cable-driven parallel robot (CDPR), with three degrees of freedom, intended for assisting the patient’s affected upper limb along a prescribed movement. A Qualisys motion capture system was used to record the prescribed task performed by a healthy subject. For each pose taken by the center of mass of the end-effector, the cable tensions, the elastic stiffness and the dexterity were optimized while satisfying a set of constraints. First, a multiobjective formulation of the optimization problem was adopted. Since selecting a single solution among the multiple ones given by the Pareto front presents an issue, a mono-objective formulation was chosen, where the objective function was defined as a weighted sum of the chosen criteria. The appropriate values of the weighted coefficients were studied with the aim of identifying their influence on the optimization process and, thus, a judicious choice was made. A prototype of the optimal design of the CDPR was developed and validated experimentally on the prescribed workspace using the position control approach for the motors. The tests showed promising reliability of the proposed design for the task.

Self-excited vibration of a 3-PRR planar parallel robot

Self-excited vibration of parallel robots can seriously affect the motion performance and damage the mechanical structure. In order to study the self-excited vibration characteristics of a 3-PRR (where P and R represent the prismatic and revolute joints respectively and the underlined letter represents the actuated joint) planar parallel robot, dynamic model is firstly established and the singularity is analyzed theoretically. Then the dynamic characteristics at internal and boundary singularities are both explored experimentally. The motion form and generating mechanism of the self-excited vibration are researched. The influencing factors on vibration frequency are obtained and the self-excited vibration during trajectory tracking motion is analyzed. Finally, a singularity escaping strategy is proposed and tested. Theoretical analysis and experimental results show that the performance of parallel robot deteriorates dramatically at singularities. Nevertheless, the parallel robot can pass through the internal singularity successfully with optimized load and motion speed so that the workspace can be expanded. The 3-PRR planar parallel robot exhibits self-excited vibration at internal singularities, which is mainly caused by the singularity, self-regulation of motors and the closed-chain coupling effect. The vibration frequency is mainly determined by singular configuration and the structural parameters. The parallel robot can maintain self-excited vibration state while carrying out trajectory tracking under a singular attitude angle. Moreover, the proposed singularity escaping strategy is verified to be feasible so that the self-excited vibration can be eliminated effectively.

A Non-Linear Continuous-Time Generalized Predictive Control for a Planar Cable-Driven Parallel Robot

This paper addresses a novel nonlinear algorithm for the trajectory tracking of a planar cable-driven parallel robot. In particular, we outline a nonlinear continuous-time generalized predictive control (NCGPC). The proposed controller design is based on the finite horizon continuous-time minimization of a quadratic predicted cost function. The tracking error in the receding horizon is approximated using a Taylor-series expansion. The main advantage of the proposed NCGPC is based on using an analytic solution, which can be truncated to a desired degree of order of the Taylor-series. This allows us to achieve a prediction horizon of NCGPC tracking performance. The description of the proposed NCGPC method is followed by a comparison between NCGPC and a conventional computed torque control (CTC) method. Robustness tests are performed by considering payload and parameter uncertainties for both controllers. Simulation results of NCGPC compared to the commonly used CTC prove the effectiveness and advantages of the proposed approach.

Analysis and multi-objective optimal design of a planar differentially driven cable parallel robot

AbstractIn this work, a planar cable parallel robot (CPR) driven by four cable-and-pulley differentials is proposed and analyzed. A new cable-and-pulley differential is designed by adding an extra pulley to eliminate the modeling inaccuracies due to the pulley radius and obviate the need of solving the complex model which considers the pulley kinematics. The design parameters of the proposed CPR are determined through multi-objective optimal design for the largest total orientation wrench closure workspace (TOWCW) and the highest global stiffness magnitude index. The proposed differentially driven CPR is evaluated by comparing various performance indices with a fully actuated CPR.

Deep regression of convolutional neural network applied to resolved acceleration control for a robot manipulator

This paper presents a modified resolved acceleration control scheme based on deep regression of the convolutional neural network. The resolved acceleration control scheme can achieve precise motion control of robot manipulators by regulating the accelerations of the end-effector, and the conventional scheme needs the position and orientation of the end-effector, which are obtained through the direct kinematics of the robot manipulator. This scheme increases the computational loads and might obtain inaccurate position and orientation due to mechanical errors. To overcome the drawbacks, a camera is used to capture the images of the robot manipulator, and then a deep regression of convolutional neural network is imposed into the resolved acceleration control to obtain the position and orientation of the end-effector. The proposed approach aims to enhance the positioning accuracy, to reduce the computational loads, and to facilitate the deep regression in real-time control. In this study, the proposed approach is applied to a 3-DOF planar parallel robot manipulator, and the results are compared with those by the conventional resolved acceleration control and a visual servo-based control. The results show that those objectives are achieved. Furthermore, the robustness of the proposed approach is tested through only the partial image of the end-effector available, and the proposed approach still works functionally and effectively.

Proposal of a Decoupled Structure of Fuzzy-PID Controllers Applied to the Position Control in a Planar CDPR

The design of robot systems controlled by cables can be relatively difficult when it is approached from the mathematical model of the mechanism, considering that its approach involves non-linearities associated with different components, such as cables and pulleys. In this work, a simple and practical decoupled control structure proposal that requires practically no mathematical analysis was developed for the position control of a planar cable-driven parallel robot (CDPR). This structure was implemented using non-linear fuzzy PID and classic PID controllers, allowing performance comparisons to be established. For the development of this research, first the structure of the control system was proposed, based on an analysis of the cables involved in the movement of the end-effector (EE) of the robot when they act independently for each axis. Then a tuning of rules was carried out for fuzzy PID controllers, and Ziegler–Nichols tuning was applied to classic PID controllers. Finally, simulations were performed in MATLAB with the Simulink and Simscape tools. The results obtained allowed us to observe the effectiveness of the proposed structure, with noticeably better performance obtained from the fuzzy PID controllers.

Social spider optimization algorithm for tuning parameters in PD-like Interval Type-2 Fuzzy Logic Controller applied to a parallel robot

This paper presents control design based on an Interval Type-2 Fuzzy Logic (IT2FL) for the trajectory tracking of 3-RRR (3-Revolute-Revolute-Revolute) planar parallel robot. The design of Type-1 Fuzzy Logic Controller (T1FLC) is also considered for the purpose of comparison with the IT2FLC in terms of robustness and trajectory tracking characteristics. The scaling factors in the output and input of T1FL and IT2FL controllers play a vital role in improving the performance of the closed-loop system. However, using trial-and-error procedure for tuning these design parameters is exhaustive and hence an optimization technique is applied to achieve their optimal values and to reach an improved performance. In this study, Social Spider Optimization (SSO) algorithm is proposed as a useful tool to tune the parameters of proportional-derivative (PD) versions of both IT2FLC and T1FLC. Two scenarios, based on two square desired trajectories (with and without disturbance), have been tested to evaluate the tracking performance and robustness characteristics of proposed controllers. The effectiveness of controllers have been verified via numerical simulations based on MATLAB/SIMULINK programming software, which showed the superior of IT2FLC in terms of robustness and tracking errors.

A Dynamically Balanced Kinematically Redundant Planar Parallel Robot

AbstractA dynamically balanced robotic manipulator does not exert forces or moments onto the base on which it is fixed; this can be important for the performance of parallel robots as they are able to move at very high speeds, albeit usually have a reduced workspace. In recent years, kinematically redundant architectures have been proposed to mitigate the workspace limitations of parallel manipulators and increase their rotational capabilities; however, dynamically balanced versions of these architectures have not yet been presented. In this paper, a dynamically balanced kinematically redundant planar parallel architecture is introduced. The manipulator is composed of parallelogram linkages that reduce the number of counter rotary elements required to moment balance the mechanism. The balancing conditions are derived, and the balancing parameters are optimized using Lagrange multipliers, such that the total mass and inertia of the system is minimized. The elimination of the shaking forces and moments is then verified via a simulation in the multi-body dynamic simulation software msc adams.

Concurrent Design of a 2 Dof Five-Bar Parallel Robot a Hybrid Design of Rigid and Flexible Links

In this article, the concurrent optimal design of a planar five-bar parallel robot for a high-speed pick and place task is considered. A trade-off between trajectory tracking, energy consumption and deformation of the flexible links is sought. Due to the high-speed operation, the minimization of the vibratory effect is considered since the design stage. Thus, the design is stated as a non-linear multi-objective dynamic optimization problem that is solved through the Differential Evolution (DE) algorithm, as well as, feasibility rules for constraints handling. Mechanical structural variables that modify the inertial parameters of the rigid and flexible links, as well as, control variables related to gains of a PID controller are considered as independent variables. This problem is subject to maximum torque that each motor could provide; inherent constraints for link manufacture; dimensional synthesis; Grashof’s criterion and initial and boundary conditions. Results show that it is possible, despite the vibrational phenomenon, to reduce the energy consumption without loss of precision through an appropriate mass balance of the actuated links.

Planar cable-driven parallel robot with fin-like chains for water jet impact acoustic wall inspection

Planar cable-driven parallel robot with fin-like chains for water jet impact acoustic wall inspection

Tendon Actuated Continuous Structures in Planar Parallel Robots: A Kinematic Analysis

Abstract The use of continuous and flexible structures instead of rigid links and discrete joints is a growing field of robotics research. Recent work focuses on the inclusion of continuous segments in parallel robots to benefit from their structural advantages, such as a high dexterity and compliance. While some applications and designs of these novel parallel continuum robots have been presented, the field remains largely unexplored. Furthermore, an exact quantification of the kinematic advantages and disadvantages when using continuous structures in parallel robots is yet to be performed. In this paper, planar parallel robot designs using tendon actuated continuum robots instead of rigid links and discrete joints are proposed. Using the well-known 3-RRR manipulator as a reference design, two parallel continuum robots are derived. Inverse and differential kinematics of these designs are modeled using constant curvature assumptions, which can be adapted for other actuation mechanisms than tendons. Their kinematic performances are compared to the conventional parallel robot counterpart. On the basis of this comparison, the advantages and disadvantages of using continuous structures in parallel robots are quantified and analyzed. Results show that parallel continuum robots can be kinematic equivalent and exhibit similar kinematic performances in comparison to conventional parallel robots depending on the chosen design.

Wrench Feasibility and Workspace Expansion of Planar Cable-Driven Parallel Robots by a Novel Passive Counterbalancing Mechanism

This article focuses on the essential limitations of planar point-mass cable-driven parallel robots (CDPRs) in covering all poses of their footprint, which results in concave-shape static workspaces (SW) and also providing a zero force level on the borders of such a SW. Accordingly, a novel passive counterbalancing mechanism is proposed which not only expands SW to fully cover the footprint but also enables CDPR's platform to balance a desired minimum force magnitude in any arbitrary direction all over the SW. Maximizing such force magnitude is defined as an optimization problem which is used to find the optimal values of the proposed mechanism's design parameters. By comparing the SW of different CDPRs with and without the proposed mechanism, effectiveness of the proposed approach is demonstrated. In some examples, it is shown that the effects of the proposed method on the SW size increment is more than doubling the size and number of actuators. Finally, two experimental setups are presented and tested, where effectiveness of the proposed approach in covering the CDPRs’ footprint and also providing the desired minimum force level over the SW are demonstrated.

Control of a 3-RRR Planar Parallel Robot Using Fractional Order PID Controller

3-RRR planar parallel robots are utilized for solving precise material-handling problems in industrial automation applications. Thus, robust and stable control is required to deliver high accuracy in comparison to the state of the art. The operation of the mechanism is achieved based on three revolute (3-RRR) joints which are geometrically designed using an open-loop spatial robotic platform. The inverse kinematic model of the system is derived and analyzed by using the geometric structure with three revolute joints. The main variables in our design are the platform base positions, the geometry of the joint angles, and links of the 3-RRR planar parallel robot. These variables are calculated based on Cayley-Menger determinants and bilateration to determine the final position of the platform when moving and placing objects. Additionally, a proposed fractional order proportional integral derivative (FOPID) is optimized using the bat optimization algorithm to control the path tracking of the center of the 3-RRR planar parallel robot. The design is compared with the state of the art and simulated using the Matlab environment to validate the effectiveness of the proposed controller. Furthermore, real-time implementation has been tested to prove that the design performance is practical.

Trajectory-tracking control of a planar parallel robot using generalized predictive control with constraints

This paper presents the generalized predictive control with constraints, implemented to a planar parallel robot in order to calculate and track the desired trajectory of the end-effector of this robot. The manipulator is driven by three brushless direct current motors, and each one has an encoder to measure the velocity and rotation angles of the motors. Three constraints were considered to interact with the control law: control signal, terminal response and the over impulse constraints. The performance of the control law is evaluated in the simulation environment using Matlab/Simulink with the physic model developed through simscape multibody. The angular position and velocity errors for each of the three motors were calculated. Likewise, the output torques for each one were estimated. The results proved that the control law proposed with the constraints imposed for each motors has a good efficiency with a stable response time of the robot in performing the trajectory tracking, contributing to the scientific community a strategy of predictive optimization of control actions with multiple constraints applied on parallel robots.