Literature survey was conducted to obtain some insights into various factors relating to modelling of planar manipulators for various industrial applications. In this work several aspects regarding the kinematics, workspace, Jacobian analysis and dynamic identification of a two-linkplanarmanipulator are studied and presented. De Luca and Siciliano  presented the kinematic and dynamic issues of planarlinkmanipulator. William  described automatic Control Systems, analysis and design of serial manipulators. Kwanho  explained the adaptive control of tip point in a serial link robot. Nagrath and Gopal  explained various issues like kinematics, dynamics, control theories for different serial manipulators. Tokhi and Azad  discussed the kinematic and modelling of flexible manipulators. Finally the proposed control method is applied for the flexible manipulator to illustrate the results. Ata  presented the review on various optimal trajectory planning control techniques for serial manipulators. Islam and Liu  proposed a sliding mode control technique to serial manipulator and studied the. Kumara et al.  explained trajectorytracking control of kinematically redundant robot manipulators using neural network. Moldoveanu et al.  explained a trajectory control of a two-link robot manipulator using variable structure theory. Wang and Deng et al.  explained the design of articulated inspection arm with an embedded camera and interchangeable tools. Zhu et al.  presented the structure of a serial link robot with 8 degrees of freedom with a 3-axes wrist carrying camera. Ionescu  described an approach of measurement using a calibrated Cr252 neutron source deployed by in-vessel remote handling boom and mascot manipulator for J0ET vacuum vessel. Monochrome CCD cameras were used as image sensors. Karagulle and Malgaca  proposed the effect of flexibility on the trajectory of a planartwo-linkmanipulator is studied using integrated computer-aided design procedures. Nageshrao et al.  explained the passivity based control method. Detailed algorithm was proposed and implemented for 2- DOF manipulator. Ayala and Coelho  illustrated an algorithm to test the PID tuning by using a two degree of freedom robot manipulator.
Abstract: This paper presents dynamic analysis studies of planar parallel flexible 3-RRR manipulator with and without considering the flexibility of mobile platform. Initially, by treating all the members of the manipulator as flexible, the joint displacements, reaction forces and stresses are obtained during a specified trajectorytracking in Cartesian space. A comparative study is conducted with manipulator configuration having rigid mobile platform using coupled dynamics of limbs and kinematic constraints of mobile platform. Dynamic response of flexible manipulator is validated using ANSYS simulations for two different cases of trajectories. The results show a remarkable effect of flexibility of mobile platform on the overall dynamic response. After validation of the model, the inverse dynamic analysis data is used to create the system dynamics by employing generalized regression neural network (GRNN) model and the forward dynamic solutions of the flexible manipulator are predicted instantaneously. This study is useful for the real time implementation of motion control of flexible manipulators with complex dynamic model of manipulators.
Abstract. The paper describes the development of a software in the form of an interactive computer program that integrates a number of robotic control schemes with the active force control (AFC) strategy as the key element of the robotic system that assumes a rigid two-linkplanar configuration. The various AFC schemes are employed in conjunction with a number of conventional and intelligent techniques embedded in the main control loop to approximate the estimated inertia matrix of the robot arm. The schemes have been individually developed and rigorously experimented through simulation studies. The results of these studies clearly indicate that the AFC technique provides a practical solution to enhance the robustness of the robotic system even in the wake of uncertainties, disturbances and varied loading conditions. Thus, it is deemed useful to develop software that can integrate a number of individual AFC schemes into a single program using a graphic user interface (GUI) technique. In this manner, the user can effectively select and execute any scheme by the manipulation of a few keystrokes or buttons of the input devices. This resulted in a program that is user friendly, readily accessible, flexible and proved very convenient. On top of that, the graphical results can be observed and analysed on-line while the program is running. By using MATLAB and its GUI facility, all the AFC schemes already described in the previous works such as the AFC with crude approximation method, AFC and Iterative Learning (AFCAIL), AFC and Neural Network (AFCANN), AFC and Fuzzy Logic (AFCAFL), and AFC and Genetic Algorithm (AFCAGA) schemes were linked into a single menu-driven program where each of the scheme can be easily selected and executed by the user. A classic proportional-derivative (PD) control scheme was also included in the program for the purpose of benchmarking.
evaluation criterion is MRSE that is a type of error criteria. Despite the real robot model and increased non-linear behavior, optimal coefficients are smaller and the proposed controller gives better control operations, so it is more practical and suitable for implementation. Graphical results of tracking the first desired trajectory by controlled robot using FOPID controller optimized with GA, EDA, and PSO optimization algorithms are shown in Fig. 3, Fig. 4, and Fig. 5, respectively.
This paper evaluates a new and simple controller design method based on QFT (quantitative feedback theory) for a two-linkmanipulator whose first link is rigid and the second is flexible. A piezoelectric patch is attached to the surface of the flexible link for vibration suppression of it. This system is modeled as a nonlinear multi-input multi- output (MIMO) control systems whose inputs are two motor torques which are applied on the joints and a voltage which is applied on the piezoelectric patch. To control the manipulator’s end point position, motion of the manipulator is divided to two rigid and flexible parts. To control both parts, nonlinear equations of the motion is replaced by a family of uncertain linear time-invariant equivalent systems using Rafeeyan-Sobhani’s method(RS method) which results in three decoupled transfer functions established in the Laplace domain. Then the QFT method is used to design a diagonal matrix as the prefilter of the system an another diagonal matrix as the system controller. Results demonstrate the remarkable performance of the proposed controllers in reduction of residual vibration of elastic link and tracking a circular trajectory by the manipulator end point.
Sliding mode control has been the vast topic for research in the field of control engineering. This section discuss Extensive research work has been done on sliding mode control of the system as well as the integration of compensation technique with this control methodology. It is shown that the adaptive sliding mode control to control a 2 link robot manipulator having uncertain parameters. An adaptive algorithm is used which is based on the sliding mode control concept to ease the chattering phenomena. Lyapunov stability is applied to achieve the stability of robot manipulator system. Controller scheme proposed in that assures robustness and attain good trajectorytracking performance. Conventional design methods for controllers for a MIMO plant like a multi-joint robot require minimum knowledge of the structure and accurate mathematical model of the plant.  The dynamic model and the terminal sliding mode control for twolink robot manipulators. Lagrangian method is used to derive the closed loop dynamic equations for the robot manipulators. This technique has been used to design the controller. This technique gives the output tracking error to converge at zero in a given period of time.  A radial basis function network with SMC is designed for the link positions of twolink robot manipulator. The learning techniques has degrades its transient performance also This neural technique uses the curve fitting mode to get nonlinear mapping. A sliding mode effectively used to eliminate thenonlinearities and has given a fast response but this control created chattering. The Lyapunov and the back propagation algorithm creates switch gain and an update law respectively. Computed torque control is one of such schemes, which is based on the exact cancellation of the
Results of the effect of these gains on link 1, link 2, and their performance indices are shown in fig. 3, 4 and 5 respectively. Two cases are presented from the tuning of the gains to investigate their effect on performance index. From the performance evaluation investigated and as shown in Table 4, it is observed that the proposed PD/PID control scheme is not different from other control strategies because there is always a trade off in the performance specification requirements. By comparing Fig. 3 and Fig.4, it was observed that if a smoother tracking is desired, the tradeoff will be in energy requirement by the actuators to achieve the task. It can be seen that the performance index in case study 1 is higher than that of case study 2 because of the extra energy required in obtaining the better tracking in case study 2. The overall performance of the proposed controllers is very good at different gain values as the performance indices in the two case studies are
In these experiments, the EnRoCo controller is given a whole continuous reference trajectory that needs to be tracked by the robot’s end-effector. Fig. 6 shows one ex- periment in which the trajectory has a ﬁgure-8 shape. The EnRoCo controller is able to track the reference trajectory in task space very well. Please note that the reference trajectory is speciﬁed only in the task space and not in the time domain. This allows the EnRoCo controller to take its time to perform exploratory behavior as necessary, without penalizing the tracking performance. The goal of this experiment is also to demonstrate that EnRoCo can reuse the accumulated knowledge about the robot kinodynamics which is reﬂected by the reduced need for exploratory behavior when the robot re-visits previously explored areas of the state space. C. Adapting to changes in the robot kinematics
A. Description of a Two Degree of Freedom Manipulator Equations that characterize the robot dynamic are represented by a set of coupling differential equations, and, there are terms such as: varying inertia, centrifugal and Coriolis torques, load and gravity terms. The movement of the end-effector in a particular trajectory with constraint speed requires a complex set of torque functions to be applied to the actuators in the link of the robotic manipulator. Next, the description of the robot mathematical mod-el is presented.
control law given in  by an equivalent control law based on fuzzy-logic approach has been explored. Sub- sequently, an equivalent adaptive fuzzy controller is proposed to design a robust control law for trajectorytracking of a two-link robot manipulator with reduced control effort as well as reduced chattering in control force. Initially fuzzy controller is designed from a simple fuzzy IF-THEN rule and then an adaptive control law is adopted to update the parameters of the fuzzy controller during the adaptation procedure. Now, this adaptive fuzzy controller along with simple PD control term is used to construct the final control torque for tracking control of robot manipulators joints.
Various neural control schemes have been studied, proposed and compared. The differences in these schemes are in the role that artificial neural network (ANN) is playing in the control system and the way it is trained for achieving desired trajectorytracking performance structures (Psaltis et al., 1988; Gupta & Rao, 1994; Zalzala & Morris, 1996; Raimondi et al., 2004; Aoughellanet et al., 2005; Dinh et al., 2008). Two classes of approaches have been studied: non-model based neural control and model based neural control. Non-model based neural control consists of PD feedback controller and an ANN. The inverse dynamics is learned by measuring the input and output signals in the manipulator and then adjusting the connection weights vector by using a learning algorithm. After the learning was finished, the actual trajectory of the manipulator followed well the desired trajectory. But, when the desired trajectory was changed to one not used in the training of ANN, the error between the actual and desired trajectory became large. This means that the ANN had fitted a relationship between the input/output data but had no succeeded in learning the inverse- dynamics model (Zalzala & Morris, 1996). We want that training doesn't depend on desired trajectory. Hence, we proposed to train the ANN with q , q , q d , e , e (see Fig. 3).
Dynamic response of the double link flexible manipulators also depends upon the links length ratios. For the payloads ratios µ 1 = 0.01, µ 2 = 0.02, β = 5 and input torques τ m 1 = 0.2 N.m and τ m 2 = 0.04 N.m , effects of different links length ratios is plotted in Fig. 5, keeping length of the first link constant ( L 1 = 1.0m). The lesser the length of link 2 with respect to Link 1, the better the dynamic response i.e. more hub/joint angle and lesser residual vibration for the given set of torque. Therefore, designer should not prefer the longer second link with respect to the first link.
ABSTRACT: Most of the trajectory planning based on robot dynamics and kinematics start from the joint space, can not guarantee the robot end track corresponding relationship. To solve the above problem, the method of trajectory planning is proposed and the optimization algorithm is used to solve the optimization trajectory. Taking the SCARA robot as an example, the trajectory of the end trajectory is preset, the first trajectory is planned by combining the first order acceleration planning and the arc transition. Then, the target model is optimized for the average power and the movement time. Finally, a non-dominated sorting algorithm is introduced to optimize the trajectory to obtain the best performance trajectory. The simulation results show that the optimized trajectory has a certain amount of time-consuming increase compared with the traditional trajectory of SCARA robot, but its energy consumption is obviously reduced, and the overall optimization result is obvious.
Flexible links are lighter and lower stiffness links and can be used in robotic instead of rigid link manipulators (RLMs) to move and manipulate objects on workspaces in order to save energy and have faster speed of operations . Conventional robots’ manipulators are designed to be rigid and have high stiffness in order to reduce vibration and perform accurate operations with utilizing simple controller schemes. These robotic manipulators require big actuators size which lead to higher energy consumption and lower speed . There are several advantages of flexible link manipulators (FLMs) compared to RLMs like; FLMs need smaller size actuators which leads to lower energy consumption, less materials, faster response, and less cost -. Besides that, FLMs require less maintenance and have lower inertia . FLMs receive high attention in research due to their advantages which are important in different applications such as medical robots and lighter robots like space arm manipulators as reported by the study in, used in nuclear plant, martial activities, agriculture sectors and homecare. Additionally, FLMs are considered safer than RLMs in order to be utilized near to humans . According to the study in, manufacturing industries use flexible systems in order to keep the manufacturing industries competitive, reduce the expenses of hardware, and to enable an enterprise to produce closer to requirements.
Robots are unable to respond in emergency situations unless through situation prediction and the response is already included in the system. This scenario divides robotics into the fields of programmed and autonomous robotics. The PUMA, Stanford and others known robots are arms mechanical systems exhibit complex kinematics, static and dynamics, which makes difficult its analysis, control (Niku, 2010)and the interaction between the manipulator and environment (Hu & Xiong, 2018).
The working principles of this system are; at the beginningwill be given some input target coordinate point (x, y) which created randomly, and then SOM will conduct trainingautomatically until a certain epoch to get the best trajectory points. After the trajectory points obtained then it will be converted into angular form for link 1 and link 2by using kinematic inverse. The Fuzzy-PD control system will evaluate the given angle error, the Fuzzy-PD control system is selected due to the robust excess and it is more resistant to the noise with different object conditions when it compared to PID . Flowchart of the simulation program is created in Figure 5, the program results as in Figure 6. The initial process in this simulation program will put the target position points, then runs the SOM neural network program to generate trajectory. The trajectory result is converted into an angle with the inverse kinematic of robot manipulator. The output of the kinematic inverse is made as a setpoint for the Fuzzy-PDcontrol; its output will be processed to dynamic, so the present output is angular. This angle always is corrected by Fuzzy-PDtill the result is close to the set point. In addition the angle of the dynamic process is processed again to the kinematic forward to become the robot manipulator position.
the mobile part of the robot is reduced to the three legs and the mobile platform. Consequently, higher velocities and ac- celerations of the mobile platform can be achieved. Another benefit is that the legs are made of only thin rods, thus, reducing the risk of leg interference. Further, the geomet- rical/physical parameters of the manipulator are also opti- mized for a given constant orientation workspace. The in- verse dynamic model is obtained using the Lagrangian dy- namic formulation method (Abdellatif and Heimann, 2009). The proposed robust task-space trajectorytracking controller is based on a centralized proportional-integral-derivative (PID) control along with a nonlinear disturbance observer. The control schemes for parallel manipulator may be prin- cipally separated into two types, joint-space control estab- lished in joint-space coordinates (Davliakos and Papadopou- los, 2008; Honegger et al., 2000; Kim et al., 2000; Nguyen et al., 1992; Yang et al., 2010), and task-space control designed based on the task-space coordinates (Kim et al., 2005; Ting et al., 2004; Wu and Gu, 2005). The joint-space control ap- proach can be readily employed as an assemblage of several independent single-input single-output (SISO) control sys- tems using the data on each actuator feedback only. A classi- cal PID control in joint-space along with gravity compensa- tion has been employed in industry, but it does not always as- sure a great performance for parallel manipulators. However, the proposed robust task-space control approach improves the overall control performance by rejecting the uncertainty and nonlinear effects in motion equations. The rejections of system or model uncertainty, unknown external disturbance and nonlinear effects in the system motions have been com- pleted in the proposed control scheme with the help of an equivalent control law; a feed-forward control scheme and a nonlinear disturbance observer along with the nonlinear PID control scheme. In the proposed task-space control method, the desired motion of the end effector in task-space is used directly as the reference input of the control scheme. That is, the motion of the end effector can be obtained from the sys- tem sensors and compared with the reference input to form a feedback error in task-space. Therefore, an exact kinemat- ics model is not required in the task-space control, and thus this method is sensitive to joint-space errors or end effector pose errors due to joint clearances and other mechanical in- accuracies. The validity of the proposed control scheme is demonstrated with the help of virtual prototype experiments. The performance of the proposed control scheme including closed-loop stability, precision, sensitivity and robustness is analysed in theory and simulation.
According to the mechanical structure and operation principle of differential-drive two-wheeled robot, and aiming at the nonlinear systems with uncertainties variable structure, a trajectorytracking model based on sliding mode control (SMC) was designed by utilizing state vector to establish the model of system and controller. The simulating results show that robot can track line, circle and S shape trajectories well, which gave reasonable dynamic responses, adjustment performance, as well as perfect disturbance rejection. The system can eliminate errors according to the deviation from sliding surface by switching the structure of controller and is robust to external disturbance.
Another method of bioprocess control based on neural network model has been developed in , where the process is controlled via a neural predictive controller in that case the controller doesn’t refer to a mathemat- ical model for the process but consider the black box identification. In our case we are based on the mathe- matical model for the synthesis of the controller, the obtained results are satisfactory regarding the result obtained in . Another work in the same spirit devel- oped by A. Nikfetrat , where the study considers a predictive controller applied to a biological feed-batch process without taking into account the constraints on the input variables and shows an important error in tracking reference trajectories, where the present work gave better results.
Abstract — Flexible manipulator systems exhibit many advantages over their traditional (rigid) counterparts. However, they have not been favored in production industries due to its obvious disadvantages in controlling the manipulator. This paper presents theoretical investigation into the dynamic modeling and characterization of a constrained two-link flexible manipulator, by using finite element method. The final derived model of the system is simulated to investigate the behavior of the system. A Genetic Algorithm (GA) based fuzzy logic control strategy is also developed to reduce the end-point vibration of a flexible manipulator without sacrificing its speed of response. An uncoupled fuzzy logic controller approach is employed with individual controllers at the shoulder and the elbow link utilizing hub-angle error and hub-velocity feedback. GA has been used to extract and optimize the rule base of the fuzzy logic controller. The fitness function of GA optimization process is formed by taking weighted sum of multiple objectives to trade off between system overshoot and rise time. Moreover, scaling factors of the fuzzy controller are tuned with GA to improve the performance of the controller. A significant amount of vibration reduction has been achieved with satisfactory level of overshoot, rise time and settling time and steady state error.