In this paper, dynamic modeling of FLEXIBLE links MANIPULATORs is discussed. The modeling approach is based on the Lagrange equations and finite element discretization method. In order to obtain the closed form of dynamic equations for FLEXIBLE links MANIPULATORs, symbolic calculation in MATLAB's symbolic mathematics toolbox is utilized, then the non-linear dynamic equations of a single-link MANIPULATOR have been obtained and compared with the results presented in other references. In this study, the nonlinear effects of centrifugal, Coriolis and gravity are Also considered which is rarely studied in other contributions. Then the equations of motion are solved by the Runge-Kutta method for different levels of excitation torque. The simulation results show that at low levels of excitation torque, the linear and non-linear models have the same results, while with the increase of the excitation level, the difference between the linear and non-linear models is considerable and the size of the elastic components in the non-linear model becomes smaller.

In this paper, we consider robust regulation of a class of nonlinear systems, via H¥, controller using slow-fast decomposition. First, using normal form equations, we eliminate the nonlinear part of the system matrix of equations of system and transform it to a linear diagonal form. Separating new equations to slow and fast subsystems, due to the two-time scale property of system, and with the assumption of norm-boundedness of the fast dynamics, we have treated them as disturbance and design H¥, controller for nominal system with a lower order than the original one that stabilizes the overall closed loop system. The proposed method is applied to a single link, FLEXIBLE joint robot MANIPULATOR.

In this paper, optimal trajectory planning of FLEXIBLE joint MANIPULATOR in point-to-point motion is presented in which besides the determining the maximum load carrying capacity, the vibration amplitude is also reduced. The solution method is on the base of the indirect solution of optimal control problem. For this purpose, an appropriate objective function is defined, dynamic equations are derived in state space form, Hamiltonian function is developed and necessary optimality conditions are obtained by using the Pontryagin maximum principle. In order to reduce the vibration of the end effector during the path, an appropriate state variables are defined and the control law is improved to omit the suddenly variation in applied torque. Then, in order to illustrate the power and efficiency of the proposed method, a number of simulation tests are performed for a two-link MANIPULATOR. To this end, after deriving the equation in details, two simulations are performed. In the first case, determining the maximum load without considering the vibration is solved, in the second simulation, optimal trajectory with maximum load and minimum vibration is obtained. Finally discussions on the obtained results are presented.

Recently, robotic MANIPULATORs are the key industry requirement. These have find the importance to enhance the productivity as well as accuracy. Furthermore, industries are also moving towards the use of FLEXIBLE Link MANIPULATOR (FLM) owing to their unique characteristics i. e. light weight, high speed operations, and the larger workspace. The FLM system has flexibility of link that causes vibrations and oscillations which affect adversary to the performance of robotic arm. The performance of FLM system is measured w. r. t. minimum error and oscillations in trajectory tracking. In this research paper, an attempt has been made to overcome the complications of FLM system. A full state feedback Linear Quadratic Regulator (LQR), is designed for FLM. It is observed that the designed controller can enhance the accuracy of the robotic arm, while reducing oscillations and vibrations. In addition, to enhance the performance of controller and to reduce the hassle in terms of selecting the parameter of Q matrix in LQR, modified particle swarm optimization (m-PSO) is used. The effectiveness of designed controller is simulated in MATLAB. Further, the validation of designed controller is tested on hardware FLM device. The results obtained from the simulation and hardware are compared.

In this paper, to solve the output tracking problem of a single-link FLEXIBLE joint MANIPULATOR, Polytopic Linear Models (PLMs) of the dynamics are made to take advantage of this method. Although linear control methods are very useful due to their powerful theories and simplicity, they can only be used in a neighborhood of the equilibrium point. One way to solve this problem is a PLMs-based method that linearizes the dynamics around several operating points. Therefore, in this paper, after calculating the PLMs of the MANIPULATOR, a state feedback control is applied to the derived linear dynamics that are augmented with the dynamics of the output tracking error. An extended method is used to decompose the scheduling space to construct PLMs, which is the segregation method improved with an extra aggregation. In order to avoid creating a large number of local models, an axis-oblique decomposition strategy is used instead of an axis-orthogonal decomposition. In addition, the scheduling functions of the PLMs are determined such that overlaps between the regions are avoided. By this selection, the output tracking problem becomes as a Linear Matrix Inequality (LMI) problem instead of a bilinear matrix inequality problem, which is more difficult to solve and may not lead to an optimal global solution.

In this paper is proposed a new approach to controlling a FLEXIBLE-joint robot MANIPULATOR based on a predictive controller and voltage control strategy in the presence of external disturbances. In this approach is used a 2DSFJ[1] Robot for modeling, design, analysis, and simulation.  The controller design is done once with feedback from all system states (main controller) and again only with feedback of the motor position (reduced controller), which in this case, some hardware equipment will be eliminated. The designed controller will have the advantages of predictive control method and voltage control strategy at the same time. So, in addition to simplicity, the control law has an independent joint structure. Also this approach resolves the limitations of the torque control strategy, such as the high computational volume, ignoring of the actuators electrical dynamics, and implementation problems. The prominent features of the proposed approach as follow: online optimization of the voltage control signal, design of predictive controller based on voltage strategy and controller order reduction. Other advantages of this approach include: simplicity in design and proof of stability, flexibility in tuning the sampling time and predictive control horizon, consideration of system input and output limitations in the voltage control law, good disturbance rejection, and improved performance of closed-loop system. In order to analyze the performance of the proposed approach, stability analysis of control system for both main and reduced controllers was performed by Lyapunov-based method, and computer simulation in problem of regulation and tracking of the reference signal along with increasing and decreasing its frequency for evaluating the response speed, and adding external disturbance by using the main and reduced controller will be done. Also, the advantages and limitations of the presented approach in terms of hardware and controller performance are analyzed by comparing the results of the simulations with other papers, and thus the stability of the closed-loop system and its proper performance is guaranteed.   [1] 2-DOF Serial FLEXIBLE-Joint Robot

This paper presents an indirect method for computing optimal trajectory, subject to robot dynamics, flexibilities and actuator constraints. One key-issue that arises from mechanism flexibility is finding the Dynamic Load Carrying Capacity (DLCC). The motion planning problem is first formulated as an optimization problem, and then solved using Pontryagin's minimum principle. The basic problem is converted to the Two-Point Boundary Value Problem (TPBVP), which includes joint flexibility. Some examples are employed to compare three models, dynamic, FLEXIBLE joint, and rigid. The results illustrate the effectiveness of this indirect method.