The motivation for this thesis is to obtain the **inverse** kinematic solutions of **redundant** **manipulator** such as 5-DOF **Redundant** **manipulator** and 7-DOF **Redundant** **manipulator**. As the **inverse** kinematic equation of these types of manipulators contain non-linear equations, time varying equations and transcendental functions. Due to the complexity in solving this type of equation by geometric, iterative or algebraic method is very difficult and time consuming. It is very important to solve the **inverse** **kinematics** **solution** for this type of **redundant** **manipulator** to know the exact operational space and to avoid the obstacles. So various researcher had applied various methods for solving the kinematic equation. L. Sciavicco et al. [7] used **inverse** jacobian, pseudo **inverse** jacobian or jacobian transpose and solve the IK problem of 7-DOF **redundant** **manipulator** iteratively. But the main drawback of this method are, these are slow and suffer from singularity issue. Shimizu et al. [8] proposed an IK **solution** for the PA 10-7C 7-DOF **manipulator** and considered arm angle as redundancy parameter. In his study, a detailed analysis of the variation of the joint angle with the arm angle parameter is considered, which is then utilizes for redundancy resolution. However link offset were not considered in his work. Some authors also applied ANN, due to its adapting and learning nature. Although ANN are very efficient in adopting and learning but they have the negative attribute of ‘black box’. To overcome this drawback, various author adopted neuro fuzzy method like **ANFIS** (Adaptive Neuro-fuzzy Inference system). This can be justify as **ANFIS** combines the advantage of ANN and fuzzy logic technique without having any of their disadvantage [9]. The neuro fuzzy system are must widely studied hybrid system now a days, as due to the advantages of two very important modelling technique i.e. NN [10] and Fuzzy logic [11]. So the goal of this thesis is to predict the **inverse** **kinematics** **solution** for the **redundant** **manipulator** **using** **ANFIS**. As a result suitable posture and the trajectories for the **manipulator** can be planned for execution of different work in various fields.

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In this study, the **inverse** **kinematics** **solution** **using** **ANFIS** for a 5-DOF and 7-DOF **Redundant** **manipulator** is presented. The difference in joint angle deduced and predicted with **ANFIS** model for a 5-DOF and 7-DOF **Redundant** **manipulator** clearly depicts that the proposed method results with an acceptable error. The modelling efficiency of this technique was obtained by taking three end-effector coordinates as input parameters and five and seven joint positions for a 5-DOF and 7-DOF **Redundant** **manipulator** respectivly as output parameters in training and testing data of NF models. Also, the **ANFIS** model used with a smaller number of iteration steps with the hybrid learning algorithm. Hence, the trained **ANFIS** model can be utilized to solve complex, nonlinear and discontinuous **kinematics** equation complex robot **manipulator**; thereby, making **ANFIS** an alternative approach to deal with **inverse** **kinematics**. The analytical **inverse** **kinematics** model derived always provide correct joint angles for moving the arm end-effector to any given reachable positions and orientations.

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and 7-DOF **Redundant** **manipulator** clearly depicts that the proposed method results with an acceptable error. The modelling efficiency of this technique was obtained by taking three end-effector coordinates as input parameters and five and seven joint positions for a 5-DOF and 7-DOF **Redundant** **manipulator** respectivly as output parameters in training and testing data of NF models. Also, the **ANFIS** model used with a smaller number of iteration steps with the hybrid learning algorithm. Hence, the trained **ANFIS** model can be utilized to solve complex, nonlinear and discontinuous **kinematics** equation complex robot **manipulator**; thereby, making **ANFIS** an alternative approach to deal with **inverse** **kinematics**. The analytical **inverse** **kinematics** model derived always provide correct joint angles for moving the arm end- effector to any given reachable positions and orientations. As the **ANFIS** approach provides a general frame work for combination of NN and fuzzy logic. The efficiency of **ANFIS** for predicting the IK of **Redundant** **manipulator** can be concluded by observing the 3-D surface viewer, residual and normal probability graphs. The normal probability plots of the model are also plotted. The normal probability plot of residuals of training and testing data obtained from **ANFIS** shows that the data

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Humans and animals control their extremities without recourse to solving a set of equations. There ought to be a methodology that more closely mimics the mechanisms whereby we move our arms without consciously determining (i.e., calculating) the necessary joint angles, and velocities that enable that motion. An acceptable **solution** must recognize the existence and location of singularities and find a valid **solution** such that the continuity of the mapping between world and joint space is preserved. Possible solutions to this problem include both numerical procedures and neural network based methods. The success of numerical **solution** procedures depends to a great extent on the formulation of a mathematical expression that accurately describes the functional relationship between the input parameters (specified end-point position of the **manipulator** in world coordinates, in our case) and the output **solution** parameters (the joint angles in our case). There are similarities between traditional numerical **solution** procedures and neural net methods. These include the existence of an iterative adaptation procedure and a performance measure. However, we wish to limit ourselves to neural net procedures in which the **solution** is not determined based on a mathematical expression defining the input/output relationship, but is captured in

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the training process can not even converge to an expected error goal in some cases. In [5], an MLPN with various structures of the input layer were proposed to solve the **inverse** **kinematics** problem of a 6 DOF **manipulator**. Three di ﬀ erent forms representing the orientation of the end-e ﬀ ector with respect to the base were defined: a 33 rotation matrix, a set of 3 Euler angles and one angle and a 13 unit vector. Another **solution** combining an MLPN and a lookup table to solve an **inverse** **kinematics** problem of a **redundant** **manipulator** was proposed in [6]. Although the use of MLPN in the **inverse** **kinematics** prob- lem has a greater extent, there have some significant disadvantages. For example, there is no reasonable mechanism to select a suitable network configuration relating to the system characteristics represented by training sets. In addition, training MLPN **using** the back-error propagation algorithm is complex and slow. For a complex MLPN structure required for a complex configuration **manipulator**, or a large set of training data, the training process is slow to converge to a specific goal. Therefore, trends towards **using** RBFN which are conceptually simpler and possess the ability to model any nonlinear function conveniently have become more popular.

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Therefore, we will have 8 possible candidate points for M 2 : Finding these points does not mean that the robot arm’s second joint can be placed in each of them. The robotic arm has physical limits, as it is mention at the very begging and it can move with angle of θ 1min - θ 1max and θ 2min - θ 2max . For that reason, additional validation and selection needs to be done. Only those angles falling into intervals between θ 1min - θ 1max , θ 2min - θ 2max will be taken into consideration and will be used to determine a single possible **solution**. Fig 2: Spatial position of the robot arm links 3. **ANFIS** CONTROLLER FOR SOLVING THE **INVERSE** **KINEMATICS** PROBLEM Adaptive Neuro Fuzzy Interface System, or shortly **ANFIS**, generally represents combination of fuzzy logic and neural network. Fuzzy systems have the ability to represent comprehensive linguistic knowledge (given for example by a human expert and preform reasoning by means of rules). However, fuzzy systems do not provide a mechanism to automatically acquire or tune those rules. On the other hand, neural networks are adaptive systems that can be trained and tuned from a set of samples. Therefore, this combination of the positive characteristics of the neural networks with the fuzzy logic could be a viable option for **solution** of non-linear problems, such as **inverse** **kinematics** of a robot manipulators. In our specific case of a planar two degrees of freedom robot arm the **ANFIS** controller is composed of two **ANFIS** networks aimed at computing the joint angles θ 1 and θ 2 taking as input the coordinates of the end effector. The proposed controller architecture is presented in Figure 3. Fig 3: **ANFIS** Controller architecture for 2DOF planar **manipulator** **inverse** **kinematics** problem calculation The first phase of development of an **ANFIS** controller foresees the network training. For this reason, training data are required so that later on **ANFIS** output can be computed. In order to generate the training dataset, the forward **kinematics** equations are used: (19)

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[H. Sadjadian and H.D. Taghirad; 2008] developed Neural Networks Approaches for Computing the Forward **Kinematics** of a **Redundant** Parallel **Manipulator**. In this paper, different approaches to solve the forward **kinematics** of a three DOF actuator **redundant** hydraulic parallel **manipulator** are presented. It is concluded that **ANFIS** presents the best performance compared to MLP, RBF and PNN networks in this particular application. [Gallaf ; 2008 ]developed Neural Networks for Multi-Finger Robot Hand Control. This paper investigates the employment of Artificial Neural Networks (ANN) for a multi-finger robot hand manipulation in which the object motion is defined in task-space with respect to six Cartesian based coordinates. The paper demonstrates the proposed algorithm for a four fingered robot hand, where **inverse** hand Jacobian plays an important role in robot hand dynamic control.

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degrees-of-freedom (DOFs) over several decades, such as the pseudo-**inverse** (PI) method, the extended Jacobian matrix (EJM) method, and geometric methods for special structures, apart from the weighted least-norm (WLN) and the gradient projection method (GPM) [5] and [6]. Note that the WLN method and the GPM method are the most frequently used ones, but both methods are seriously flawed. In WLN, the major limitation is that it can only be used to constrain joint position limits effectively and dampen joint motion to exceed the limit without backing away from it. Meanwhile, the scalar factor in GPM for the performance criterion is often selected empirically, which may incur the poor performance of subtasks. Furthermore, a novel **solution** [7] and [8] to the kinematic analysis of a single-loop reconfigurable 7R (R: revolute joints) mechanism is given based on the algorithm of IK about a general serial 6R **manipulator** but neglects the advantages of redundancy in the 7R **manipulator**.

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Abstract- Automatic control to any of robot manipulators, some kind of issues are being observed. A numerical method for **solution** generation to the **inverse** **kinematics** problem of **redundant** robotic manipulators is presented to obtain the smoothest algorithm as possible, leading to a robust iterative method. After the primary objective of the reachability of end-effectors to the target point is achieved, the aim is set to resolve the **redundant** degrees of freedom of **redundant** **manipulator**. This method is numerically stable since it converges to the correct answer with virtually any initial approximation, and it is not sensitive to the singular configurations of the **manipulator**. In addition, this technique is computationally effective and able to apply for serial manipulators with any DOF applications. A planar 3R-DOF serial link **redundant** **manipulator** is considered as exemplar problem for solving. Also, the continuum approach for resolving more complex structure with variable DoF is illustrated here and their brief applicability to support surgeries and adaptive use of artificial linkage moments is also calculated.

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Many algorithmic solutions have been proposed for solving IK of serial-link manipu- lators with high DoF. Generally, these algorithms can be categorized as analytical or numerical approaches. Analytical approach is a closed-form **solution** of IK obtained from pure algebra and algebraic geometry. Both methods have been applied to solve IK problems in serial-link **redundant** robots. In an extensive study, Chirkijian [18] presented a novel framework for modeling IK of hyper **redundant** robots which are analogous to snake in morphology with planar rotational axis. Also, Sheng et al. proposed a geometric method for solving joint angles in a hyper-**redundant** **manipulator** [19]. Theoretic analysis and simulation results show that the method can precisely obtain accurate joint angles required by the manipulator’s end effector to reach a given target in the joint space with fewer computations. However, this approach is limited to planar robots. The geometric method can be extended by spatial decomposition of the robot’s workspace into multiple independent planes. Thence, IK of a robot’s links can be solved by exploring the individ- ual links in their respective planes. In an attempt for 3D path planning, Yahya et al. [20] presented a unique-angle geometric method for positioning the end-effector of planar **redundant** manipulators in the workspace. The method was adapted for 3D **manipulator** with a twisted joint at the first joint, while a unique value was determined for other joints. The **solution** makes the **manipulator** to always exhibit open polygonal shapes which can- not be suitable for operations in confined environments.

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System modelling based on conventional mathematical tools (e.g., differential equations) is not well suited for dealing with ill-defined and uncertain systems. By contrast, a fuzzy inference system employing fuzzy if then rules can model the qualitative aspects of human knowledge and reasoning processes without employing precise quantitative analysis. This fuzzy modelling or fuzzy identification, first explored systematically has found numerous practical applications control **prediction** and inference .However, there are some basic aspects of this approach which are in need of better understanding. More specifically:

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Abstract. Kinematic control of a special hyper-**redundant** **manipulator** with lockable joints is studied. In this **manipulator**, the extra cables are replaced by a locking system to reduce the weight of the structure and the number of actuators. This **manipulator** has discrete and continuous variables due to its locking system. Therefore, a hybrid approach has been adopted in control. At rst the forward **kinematics** and velocity **kinematics** of this **manipulator** are derived, and then a novel closed-loop control algorithm is presented. This algorithm consists of decision making, an inner loop controller, and kinematic calculation blocks. The decision making block is the logical part of the control scheme in which suitable switches will be chosen. The control block uses the end-eector position feedback to generate appropriate commands. The performance of the proposed hybrid control scheme in position tracking is assessed for several trajectories.

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Stock market **prediction** is the process of trying to predict the future value of a company stock or other financial instrument. The successful **prediction** of a stocks future price could yield significant profit. The stock price are highly unpredictable as they change every other second. Others disagree and those with this viewpoint possess myriad methods and technologies which purportedly allow them to gain future price information.This project is merely about the stock market. Nowadays there is increase in the number of daily dealing with the stock market. The stock price of any stock is fluctuating everysecond so it becomes very difficult for the stock dealer to predict about the price of any stock. **Prediction** of the stock prices will help such dealer to predict the stock price efficiently and make a proper decision about stock dealing. There are many models developed for predicting the stock price based on various different methods and technology. Also there are many hybrid models developed for better and more accurate **prediction** of the stock prices. Artificial Neural Networks (ANNs) are proposed as one of the most promising methods for predictions. The ANNs are inspired by the activity of human brain cells and can learn the data patterns and generalize their behavior to predict the future data. There are various existing model such as Back Propagation Neural Network (BPNN), Fuzzy Neural Network, Adaptive Neuro Fuzzy Inference System(**ANFIS**), Markov model etc. The two models i.e. BPNN and **ANFIS** will be trained which will help in predicting the future stock price. In order to study the behavior of the stock of the particular company, the graph of historical data is plotted. Thus this will help in predicting the future stock price efficiently and overcome the difficulties faced by the stockholders for predicting the accurate stock price.

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These two categories are split because in some cases only the control of the attitude change is enough to reach the target position and to avoid loss of communication with ground stations and disorientation of solar panels. The third is the free-floating case, where the attitude control of the base is inactive and thus, the base is completely free to translate and rotate in reaction to the **manipulator** motion. In general the forward **kinematics** problem for a space **manipulator** becomes a dynamic problem with the property that the robot’s end-effector position at the end of a maneuver is not only a function of the final joint angles, but also depending on the time history of the joint angles and the inertial properties of the system. People prefer it to use in different field, such as industry, some dangerous jobs including radioactive effects. They can be managed easily and provides many advantages. In a kinematic analysis the position, velocity and acceleration of all the links are calculated without considering the forces that cause this motion. The relationship between motion, and the associated forces and torques is studied in robot dynamics. Robot **kinematics** deals with aspects of redundancy, collision avoidance and singularity avoidance. While dealing with the **kinematics** used in the robots we deal each parts of the robot by assigning a frame of reference to it and hence a robot with many parts may have many individual frames assigned to each movable parts. Each frame is named systematically with numbers. In the kinematic analysis of **manipulator** position, there are two separate problems to solve: direct **kinematics**, and **inverse** **kinematics**. Direct **kinematics** involves solving the forward transformation equation to find the location of the hand in terms of the angles and displacements between the links. **Inverse** **kinematics** involves solving the **inverse** transformation equation to find the relationships between the links of the **manipulator** from the location of the hand in space. Further chapters will discuss step by step implementation of a **manipulator**.

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Serial manipulators usually have some merits such as large workspace, dexterity for maneuvering in small spaces, ability for accessing to points at large distances and design simplicity. However, lack of rigidity because of cantilever structure, small payload capacity, operating inaccuracy and poor dynamical performance at high-speed operations are some drawbacks of serial manipulators. To overcome these drawbacks, an alternate type of **manipulator**, comprising **kinematics** loops, known as parallel **manipulator** has been proposed. The main advantages of parallel manipulators, as compared with their counterparts, are greater rigidity causing higher natural frequencies, homogeneous distribution of inertia, higher accuracy and higher load-carrying capacity [1]. The most important types of parallel manipulators are those with moving and fixed platforms connected by means of parallel legs [1-4]. Figure 1

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In order to adjust the poses of the segment mirrors and give the correct surface shape to a large aperture telescope, an active adjusting platform for segment mirror with a novel 3CPS parallel **manipulator** as core module is proposed. The platform has 6 degree-of-freedoms (DOFs) including three translational freedoms and three rotational freedoms. Its **kinematics** are analysed systematically. By means of the Rodrigues parameters method, the formulae for solving the **inverse**/forward displacement, the **inverse**/forward velocity, and the **inverse**/ forward acceleration **kinematics** are derived. A numerical simulation of the **kinematics** model is then carried out combining the topological structure characteristics of the **manipulator**. The correctness of the **kinematics** model is verified by an experiment in which the pose of moving platform is measured **using** a photogrammetric method.

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τ (13) Where τ is a given micro variable matrix, M can be obtained according to the initial transformation of the rigid body. ε can be obtained by this equation，and γ can be obtained by equation (8), then the rigid body transformation matrix of the platform will be g γ . g γ will be respected as a new rigid body transformation matrix g and substituted into equation (13), a new ε can be obtained. Circulating above-mentioned process, through the iteration of g γ and track the movement trajectory of the rod, once all the length of the rods are close to the expectation length, iteration is completed, the result of direct **kinematics** **solution** will be obtained.

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Today robots are used in every walk of human life. All over the world, robots are on the move. As the robots grow tougher, nimbler, and smarter, today’s robots are doing more and more things human cannot or do not want to do. In order to co-operate with a human, a robot should have a humanlike behavior when moving. Then, the robot can act in a world made for humans and does not perform movements which cannot be anticipated by the human partner. To achieve this, it is necessary to give the robot human like configuration and human like **kinematics**.

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This paper investigates the use of a neural network to produce the **solution** to the **inverse** **kinematics** problem for a three-link robotic **manipulator**. The neural network is trained **using** the data provided by the forward **kinematics** to learn the **inverse** forward mapping of the configuration space. This means the end effecter’s position and orientation are given as inputs and the neural network identifies which joint configuration corresponds to the given localization of the end effecter.