Visual Motor Control of a 7 DOF Robot Manipulator Using Function Decomposition and Sub-Clustering in Configuration Space

A fuzzy self-organizing map (SOM) network is proposed in this paper for visual motor control of a 7 degrees of freedom (DOF) robot manipulator. The inverse kinematic map from the image plane to joint angle space of a redundant manipulator is highly nonlinear and ill-posed in the sense that a typical end-effector position is associated with several joint angle vectors. In the proposed approach, the robot workspace in image plane is discretized into a number of fuzzy regions whose center locations and fuzzy membership values are determined using a Fuzzy C-Mean (FCM) clustering algorithm. SOM network then learns the inverse kinematics by on-line by associating a local linear map for each cluster. A novel learning algorithm has been proposed to make the robot manipulator to reach a target position. Any arbitrary level of accuracy can be achieved with a number of fine movements of the manipulator tip. These fine movements depend on the error between the target position and the current manipulator position. In particular, the fuzzy model is found to be better as compared to Kohonen self-organizing map (KSOM) based learning scheme proposed for visual motor control. Like existing KSOM learning schemes, the proposed scheme leads to a unique inverse kinematic solution even for a redundant manipulator. The proposed algorithms have been successfully implemented in real-time on a 7 DOF PowerCube robot manipulator, and results are found to concur with the theoretical findings.

SUMMARYIn most dynamic adaptive control simulation of robotic manipulators, the Langrange–Euler (L–E) dynamic equations are first piecewise linearized about the desired reference and then discretized and rewritten in a state space form. This makes things very complicated and it is easy to make errors. What is more is that with a different reference this work must be done again. A new simulation scheme – Backward Recursive Self-Tuning Adaptive (BRSTA) – as it will be called, is suggested in this paper for adaptive controller design of robot manipulators. A two degree of freedom robot manipulator is used to verify the scheme in the condition of highly nonlinear and highly coupled system. A one degree of freedom robot manipulator is used for comparing both the forward and backward methods. The main advantages of this scheme include that it can be used for evaluating the self-tuning adaptive control laws and provide the initial process parameters for real-time control. And it is concluded here that the Newton–Euler (N–E) dynamic equations are equally well qualified as the Langrange–Euler (L-E) equations for the simulation of self-tuning adaptive control of robot manipulators.

This paper presents a decentralized control scheme, based on a recurrent neural identifier with a block control structure, and its application to robotics manipulators. A local joint controller is proposed for each joint, using only local angular position and velocity measurements. These very simple local joint controllers allow trajectory tracking, with reduced computations. The applicability of the proposed scheme is illustrated, via simulations, first by the applications to a two degree of freedom robotic manipulator and then to a seven degree of freedom one.

A robust controller is proposed for the accurate trajectory control of a general n degree of freedom robotic manipulator, using feedback of task space coordinates, in the presence of large perturbations of the manipulator dynamic parameters. The controller is shown to consist of two separate devices: 1) a robust compensator which makes the system insensitive to parameter perturbation and causes asymptotic regulation to occur for a certain class of reference input/disturbance signals, and 2) a stabilizing compensator which stabilizes the closed-loop system. Asymptotic stability of the closed-loop system is demonstrated, using a Lyapunov approach, for large perturbations of the plant parameters. A numerical simulation of a two degree of freedom manipulator, with a large unknown payload mass is used to demonstrate the effectiveness of the controller.

The authors analyse the contour error dynamics in contouring control of dual‐arm robotic manipulators with holonomic constraints. With the modified dynamics of robot, the dynamics of dual‐arm robot with holonomic constraints is symetrically transformed into dynamics error problem by considering the equivalent error method. It becomes the control problem of stabilisation such that it is suitable for robust control approach to improve control performance in terms of contouring control, i.e. contour accuracy with high speed. The proposed method can deal with both analytic and non‐analytic functions of desired path in task space. The experimental results reveal that the proposed method yields excellent performance in comparison to conventional distributed control. As a result, the proposed method can lead to the development of a modified distributed control for high degree of freedom robot manipulators.

Robotic control is an interesting subject due to its extensive industrial applications. This paper proposes a new continuous control design for tracking problem of a three degree-of-freedom (DOF) robot manipulator in presence of uncertainties and bounded external disturbances. The proposed method is based on the combination of the recently developed robust integral of the sign of the error (RISE) feedback and neural network (NN) feed forward terms. In this control strategy, a feed forward NN is utilized to compensate uncertainties of the nonlinear system. Furthermore, the RISE feedback control term is used to eliminate the NN approximation error and bounded external disturbances. Typical NN-based controllers generally provide the convergence only with uniformly ultimately bounded (UUB) error due to the NN reconstruction error. However, the proposed method guarantees asymptotic tracking by eliminating this error. Using Lyapunov stability analysis, a semi-global asymptotic tracking of the robot joints is achieved. Besides, a comparative study on the system performance is conducted between the proposed control strategy and an NN-based controller. Simulation results demonstrate that the proposed controller is robust to deal with uncertainties, and verify the effectiveness of the proposed control scheme.

A new evolutionary-based algorithm is proposed to solve the robot manipulator optimal path generation problem. The following scenario is considered: given a learnt joint path describing a robot manipulator simple task in the Cartesian space, an optimal path is calculated when a different initial joint configuration is considered. The optimization problem is formulated as the minimization of both the end-effector pose error and the total joint displacement so as to ensure convergence towards the learnt path and a smooth joint motion. To solve the optimization problem an algorithm based on an evolutionary method called Differential Evolution (DE) is used. DE is a stochastic direct search optimization method based on the evolution of a candidate solution population in an iterative process of mutation, recombination, and selection. Since the algorithm does not require the use of the Jacobian matrix during the kinematic inversion, singularities problems are overcome. Results on the optimal path generation of a six degrees of freedom robot manipulator are also presented.

In the impedance control scheme in robotic manipulation applications, the interaction force can be indirectly controlled by acting on the manipulator reference position trajectory. However, the reference position depends on the environment parameters, like location and stiffness, which in practice are not exactly known. To deal with those uncertainties, this paper presents a fuzzy adaptive approach which determines the appropriate reference (target) positions to an impedance controller in order to obtain the desired force/position trajectory. Moreover, only an estimate of the environment location is necessary, and so the fuzzy adaptive controller corrects this estimated position based on the force error. The fuzzy adaptive controller is a kind of self organizing controller, which consists of a direct fuzzy controller and an adaptation mechanism, (the fuzzy inverse model) which adjusts the membership functions of the consequent parts of the direct fuzzy controller. To validate the proposed control scheme, simulation results with a two degree of freedom robot manipulator are presented where it is shown a good force/tracking performance with uncertainties on the environment location and on the stiffness value.

In the paper fuzzy logic controller for rehabilitation robot manipulator is presented. The control object is two degree of freedom robot manipulator. In this case there are two main problems. The first is, that the object is for rehabilitation process so the quality of control system is very important problem. The next problem is with the highly nonlinear dynamics of a robot manipulator. Suggest fuzzy logic control system for that reasons. The model-based Takagi-Sugeno fuzzy control strategy is applied. Described model have two inputs (error and derivation) and one output. The first part of research, was the simulation tests. For this part simulation model was prepare. The dynamic equations was used to build a model in Matlab. During this research the main problem was suitable control quality. It is very important because control quality is connected with rehabilitation process. The control algorithms enable to movement realization and obtain set position given by the physiotherapist. The tests results show that the fuzzy logic control have good control quality.

In this study, trajectory tracking control of six–degrees of freedom robotic manipulator has been performed using the proposed fractional-order adaptive integral sliding mode control scheme. The proposed method is first composed by fractional-order and adaptive integral sliding mode control to achieve the finite-time convergence, chattering-free control inputs, better tracking performance and robustness for the robotic manipulator. Furthermore, an adaptive method has been utilized to evaluate and compensate the uncertain and unknown dynamics of the system without relying on the prior knowledge of the upper bounds. To illustrate the efficiency of the proposed fractional-order adaptive integral sliding mode control method, the real-time experimental studies have been performed for the six–degrees of freedom industrial robot manipulator. The experimental outcomes strongly verified that the proposed controller gives quite well trajectory tracking response and faster convergence compared with the classical integral sliding mode control under the external payload.

Three degrees of freedom (3-DOF) robotic manipulator is a kind of cost-effective industrial robot which is widely used in production lines. A method to analyze the structural design and kinematic equations for a 3-DOF robotic manipulator is presented in this paper. Firstly, a new type of 3-DOF robotic manipulator was introduced. Its kinematic equations and inverse solution were established based on the analysis of the structural configuration. Then, we design and assemble the 3D mechanical parts of the robotic manipulator in the virtual environment of Solid Edge ST4. And the 3D robotic manipulator is imported into ADAMS virtual prototype environment for simulation analysis and obtaining the motion curve. The simulation results and the kinematic equations of the robotic manipulator were compared, which shows that the kinematic equations are valid and structural configuration is reasonable.

This paper presents a general methodology and accompanying formulation for planning kinematically smooth path trajectories for serial robot manipulators. Starting from an initial point on the path, it is required to traverse a path trajectory without halting the motion (typically due to switch from one inverse solution to another). The problem focuses on determining a starting configuration at the initial point on the path. The problem is formulated in terms of a constraint function and characterized by a system of differential-algebraic equations (DAEs) of index 2. These DAEs are solved numerically by Runge-Kutta (RK) methods while a best starting configuration is chosen using a cost-function driven optimization method. The formulation is demonstrated through a planar 3 degree of freedom robot manipulator.

This paper presents a stability analysis of nonlinear bang-bang impact control for a one degree of freedom robotic manipulator based on an analysis in L/sub 2/ space. The physical implications of sufficient stability conditions are explained in terms of sampling time, accuracy of inertia estimation, control gains, and rate of change in the Coriolis, centrifugal, and disturbance forces. The stability conditions are not stringent and are verified by simulations.

In this paper, an estimation of the dynamics of a 2 degrees of freedom robot manipulator with uncertainties, is derived, using an extended state observer. Decentralizing approach in multivariable systems, is an methodolgy used in an increasing number of practical systems to simplify the controller design. On the other hand, these systems usually contain uncertainties, and also parts of the system's dynamics are unknown. Due to the robust characteristics of extended state observers, these observers would be able to estimate these unknown dynamics, which has been discussed in the literature thoroughly. In this paper, a special class of extended state observers, namely the time varying extended state observer, will be discussed to estimate the dynamics and the disturbances related to the couplings in a manipulator with 2 degrees of freedom. The proposed observer significantly reduces the estimation error's peaking phenomenon, using time variant gains. Thus, it has a better performance compared to similar observers in the literature. This specific class, has time varying parameters, which makes its design simpler and presents a better performance, compared to other linear or nonlinear observers available. As shown in the simulations, the estimation error pick phenomena reduces drastically.

In this study a five Degrees of Freedom (DOF) serial robot manipulator was designed and implemented. The inverse kinematics problem, which has not exact analytical solution (only one inverse kinematic solution for a predefined end effector position in three dimensional space), of the robot mechanism was solved by using the combination of the analytical method and a simple search method. In order to use the proposed method in real-time applications, the method is designed so that it can be used to solve the inverse kinematics problem for the next point of the end-effector while the mechanism is working. Moreover, so that to control the implemented mechanism, a user interface program was written by using Visual Basic programming language. Finally, the proposed inverse kinematic solution method was tested on two different trajectories, an arc shaped trajectory that composed of 58 points and a linear trajectory divided into 29 points. The obtained results revealed that the proposed method can be used successfully in solving the inverse kinematic problem of the designed mechanism.