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The coordinate frame attachments and unit vector ( ) (k i u r ) representations for the three-link robot manipulator.
Source publication
Formulating the suitable mathematical models and deriving the efficient algorithms are very crucial for simplifying the complexity of the kinematics problems in robotics. Forward and inverse kinematics of industrial robot manipulators is generally performed using Denevit and Hartenberg method. In this paper, the algebra based on the exponential rot...
Contexts in source publication
Context 1
... forward kinematics of a serial robot manipulator can be obtained using the algebra based on the exponential rotational matrices directly without deriving the DH table as follows: Consider a three link robot manipulator whose joints are revolute as illustrated in Fig. 1. A coordinate frame is attached to each link of the robot manipulator. The kinematics parameters are assigned according to this attached coordinate frame. The z axes of the coordinate frames are assigned for pointing along the rotation axis of the each joint. The axes of the kth coordinate frame are denoted by the unit ...
Context 2
... denote the link length, the link offset, the orientation matrix of kth coordinate frame with respect to the base coordinate frame and corresponding column vector, respectively. It can be noted that it is not necessary to have both the link length and the link offset related to the same joint. The position vector of the robot manipulator given by Fig. 1 is obtained as 1 2 2 3 2 3 1 2 2 1 2 3 1 3 2 1 3 1 2 2 1 2 3 1 3 2 ...
Citations
... The first row of Equation (34) is the unity that indicates both joints are in the zero states or no rotation, and the robot is in the initial attitude or home position. From Equations (36) and (37) we proof that the desired orientation can be aligned by joint (4) or joint (5) independently or aligned to the desired attitude by a value of both last joints' rotations, as shown in the last row. Therefore, it is concluded that for the general 6R robot arm only needs to establish the position and attitude equation with the first five joint variables. ...
... Substitute the desired orientation obtained from the step above to calculate the IK solution of the wrist's last two joints variables of the robot arm from Equations (36) or (37). ...
... The joints angle response for EF positioning are Known; and the desired orientation is obtain from Algorithm 1 or given as desired poses. Then the solution of the wrist joint variables can be obtained from Equations (36) or (37) and then take them into Equation (17) to find (θ 6 ) if the robot EF attached with tools as introduced in Remark in Section 3.3. The wrist IK solution and time cost are shown in the last 4th columns of Table 5. ...
This paper introduces a new method for kinematic modeling of the robot arm by deriving a new elegant mathematical formula based on the axis vector with the tangent of the rotation angle. For this purpose, an innovative analytical quaternion is introduced through integration between Axis-Invariants and unit quaternion features named Ju-Gibbs quaternion, which expresses the body rotation with non-redundant parameters compared with the quaternions in literature. Two theorems based on the new form of the quaternion are developed and proved for the kinematic modeling of the robot arm. The first is attitude alignment, which is essential in multiaxial rotation systems. The second theorem for the wrist inverse kinematic (IK) solution is utilized to obtain the joint variables for the last joints of the end effector. In order to verify the effectiveness and accuracy of the proposed method, a numerical example and simulation of different structural configurations of robot and human arms are intensively studied. The novel quaternion provides a new tool for kinematic analysis and reduces the computational complexity of the kinematic solutions of the Robot-Arms wrist. Furthermore, the method laid a new foundation for the IKs of multi-axis systems based on Axis-Invariant and tangent quaternion.
... To achieve high performance control of the robot motion process, it is necessary to establish an accurate relationship between the robot end position and the joint coordinates, so that the arbitrary spatial posture of the end-effector can be represented in the joint coordinate space (Ayiz and Kucuk, 2009). In this paper, the FAUNC-2000iC six-degree-offreedom robot is used for the polishing study of aero-engine blade. ...
Purpose
Considering the response lag and viscous slip oscillation of the system caused by cylinder piston friction during automatic polishing of aero-engine blades by a robotic pneumatic end-effector, the purpose of this study is to propose a constant force control method with adaptive friction compensation.
Design/methodology/approach
First, the mathematical model of the pneumatic end-effector is established based on the continuous LuGre model, and the static parameters of the LuGre model are identified to verify the necessity of friction compensation. Second, aiming at the problems of difficult identification of dynamic parameters and unmeasurable internal states in the LuGre model, the parameter adaptive law and friction state observer are designed to estimate these parameters online. Finally, an adaptive friction compensation backstepping controller is designed to improve the response speed and polishing force control accuracy of the system.
Findings
Simulation and experimental results show that, compared with proportion integration differentiation, extended state observer-based active disturbance rejection controller and integral sliding mode controller, the proposed method can quickly and effectively suppress the polishing force fluctuation caused by nonlinear friction and significantly improve the blade quality.
Originality/value
The pneumatic force control method combining backstepping control with the friction adaptive compensation based on LuGre friction model is studied, which effectively suppresses the fluctuation of normal polishing force.
... The first row of Equation (34) is the unity that indicates both joints are in the zero states or no rotation, and the robot is in the initial attitude or home position. From Equations (36) and (37) we proof that the desired orientation can be aligned by joint (4) or joint (5) independently or aligned to the desired attitude by a value of both last joints' rotations, as shown in the last row. Therefore, it is concluded that for the general 6R robot arm only needs to establish the position and attitude equation with the first five joint variables. ...
... Substitute the desired orientation obtained from the step above to calculate the IK solution of the wrist's last two joints variables of the robot arm from Equations (36) or (37). ...
... The joints angle response for EF positioning are Known; and the desired orientation is obtain from Algorithm 1 or given as desired poses. Then the solution of the wrist joint variables can be obtained from Equations (36) or (37) and then take them into Equation (17) to find (θ 6 ) if the robot EF attached with tools as introduced in Remark in Section 3.3. The wrist IK solution and time cost are shown in the last 4th columns of Table 5. ...
This paper introduces a new method for kinematic modeling of the robot arm by deriving a new elegant mathematical formula based on the axis vector with the tangent of the rotation angle. For this purpose, an innovative analytical quaternion is introduced through integration between Axis-Invariants and unit quaternion features named Ju-Gibbs quaternion, which expresses the body rotation with non-redundant parameters compared with the quaternions in literature. Two theorems based on the new form of the quaternion are developed and proved for the kinematic modeling of the robot arm. The first is attitude alignment, which is essential in multiaxial rotation systems. The second theorem for the wrist inverse kinematic (IK) solution is utilized to obtain the joint variables for the last joints of the end effector. In order to verify the effectiveness and accuracy of the proposed method, a numerical example and simulation of different structural configurations of robot and human arms are intensively studied. The novel quaternion provides a new tool for kinematic analysis and reduces the computational complexity of the kinematic solutions of the Robot-Arms wrist. Furthermore, the method laid a new foundation for the IKs of multi-axis systems based on Axis-Invariant and tangent quaternion.
... The representation concept of the homogeneous matrix was first applied by Denavit-Hartenberg (D-H), the most common method for its compendious description of the kinematics relationship of joints movement and linkage positions, requires fewer parameters to represent the kinematics modeling [13]. Another special type of matrices appears for kinematic modeling of robots, such as dual orthogonal matrix, dual special unitary matrix, dual Pauli spin matrices and exponential rotational matrices [14,15]. Those matrices cannot represent rotation and displacement in a compact form in some cases. ...
... Subtracting Eq. (15) ,from (14) to obtain ...
This paper presents an analytical solution of the inverse kinematics (IK) for a 6R robotic arm to improve positioning and orientation accuracy based on the axis-invariant (AI) method. For this purpose, a new method based on dual quaternion and AI theory has been proposed to analyze and eliminate accumulated errors in the forward kinematic and IK of the robot arm. The compactness between accuracy and reduction of the computational cost has been used by combining dual quaternion and AI features in modeling. The method was validated with the selected Denavit–Hartenberg parameters and the measured parameters. The simulation results showed that the method is efficient and accurate. Thus, the relative accuracy has improved, and the error is less than 0.0003 and 0.00014 for position and orientation, respectively. The joint angle error obtained by the IK solution has not exceeded 0.01∘. Besides, this method can obtain the robot arm parameters even without knowing the robot’s structure data in advance.
... Firstly, the kinematic model of the manipulator needs to be established. In terms of kinematic model, literature (Ayiz and Kucuk, 2009) uses exponential rotation matrix to directly describe the physical mechanism of the manipulator, but the multiple transformations of matrix produce a large amount of calculation.In this paper the coordinate system of the 6-DOF manipulator is established according to the Danavit and Hartenberg model (Danavit and Hartenberg, 1964), which is shown in Figure 1. ...
A multi-objective full-parameter optimization particle swarm optimization (MOFOPSO) algorithm is proposed in this paper to overcome the drawbacks of poor accuracy, low efficiency, and instability of the existing algorithms in the inverse kinematics(IK) solution of the manipulator. In designing the multi-objective function, the proposed algorithm considers the factors such as position, posture, and joint. To improve PSO, the proposed algorithm comprehensively analyzes all factors affecting the global and local searching abilities. Based on this, the initial population is designed following the localized uniform distribution method. Meanwhile, the inertia weight, asynchronous learning factor, and time factor are respectively designed by introducing the iteration factor. Finally, this paper tests the performance of MOFOPSO with three typical functions to obtain a better inverse kinematics solution of the 6-DOF manipulator. Also, six other algorithms are taken for performance comparison. The experimental results indicate that the proposed method not only ensures the stability of the manipulator but also achieves high accuracy and efficiency in solving the inverse kinematics of the 6-DOF manipulator.
... 14 Ayiz and Kucuk used POE theory to solve kinematics problems of industrial robots. 15 POE theory allows global description of rigid body motion and greatly simplifies the analysis of mechanism. At present, the most common methods for solving inverse kinematics of robots are algebraic method, geometric method, and numerical method. ...
... Given that the previous point is P iÀ1 , the appropriate inverse solution is Q iÀ1 . According to "Nonlinear error evaluation based on multijoint industrial robot for 3D printing" section, n intervals are inserted between Q iÀ1 and Q i , and the forward kinematics of the nþ1 angle value after interpolation is solved to obtain P i, j, k , where jE[0, n]. e i, j, k can be calculated by equation (15), and the nonlinear error e i, k ¼ maxfe i, j, k , 0 < j < n, 1 < k < mg between P iÀ1 and P i is found therefrom. Finally, by comparing the nonlinear error e i value of m groups of solutions, the inverse solution corresponding to the minimum e i value is an appropriate solution of P i . ...
Multijoint industrial robots can be used for 3D printing to manufacture the complex freeform surfaces. The postprocessing is the basis of the precise printing. Due to the nonlinear motion of the rotational joint, nonlinear error is inevitable in multijoint industrial robots. In this article, the postprocessing and the path optimization based on the nonlinear errors are proposed to improve the accuracy of the multijoint industrial robots-based 3D printing. Firstly, the kinematics of the multijoint industrial robot for 3D printing is analyzed briefly based on product of exponential (POE) theory by considering the structure parameters. All possible groups of joint angles for one tool pose in the joint range are obtained in the inverse kinematics. Secondly, the nonlinear error evaluation based on the interpolation is derived according to the kinematics. The nonlinear error of one numerical control (NC) code or one tool pose is obtained. The principle of minimum nonlinear error of joint angle is proposed to select the appropriate solution of joint angle for the postprocessing. Thirdly, a path smoothing method by inserting new tool poses adaptively is proposed to reduce the nonlinear error of the whole printing path. The smooth level in the smoothing is proposed to avoid the endless insertion near the singular area. Finally, simulation and experiments are carried out to testify the effectiveness of the proposed postprocessing and path optimization method.
... An et al. gave a generalized solution of a kinematics problem based on POE in order to analyze the kinematics problems of serial robots [8]. Ayiz et al. used POE theory to solve kinematics problems of industrial robots [9]. POE theory allows global description of rigid body motion and greatly simplifies the analysis of mechanisms. ...
... Due to the limitation of the mechanical structure of the robot modeled in this paper and the existing 3D-printing methods, only three joints were considered. Thus, the forward kinematics equations of the printing nozzle relative to the workpiece were expressed as P x = cos α[a 3 cos(β + γ) + a 2 cos β + a 1 + a 4 ] − U x P y = sin α[a 3 cos(β + γ) + a 2 cos β + a 1 + a 4 ] − U y P z = a 3 sin(β + γ) + a 2 sin β + d 1 − a 5 − U z (9) Appl. Sci. ...
The workspace of a robot provides the necessary constraint information for path planning and reliable control of the robot. In this paper, a workspace visualization method for a multijoint industrial robot is proposed to obtain a detailed workspace by introducing the 3D-printing layering concept. Firstly, all possible joint-angle groups of one pose in the joints’ ranges are calculated in detail according to the POE (product of exponential) theory-based forward-kinematics expressions of the multijoint industrial robot. Secondly, a multisolution selection method based on the key degree of the joint is proposed to select the appropriate joint-angle groups. The key degrees of all joints and their key order are obtained according to the sensitivity expressions of all joint angles, calculated from the Jacobian matrix of the robot. One principle based on the smallest differences of the nominal angle is established to select the possible solutions for one joint from the possible solutions for the joint with the smaller key order. The possible solutions for the joint with the highest key order are the appropriate joint-angle group. Thirdly, a workspace visualization method based on the layering concept of 3D printing is presented to obtain a detailed workspace for a multijoint industrial robot. The boundary formula of each layer is derived by forward kinematics, which is expressed as a circle or a ring. The maximum and minimum values of the radius are obtained according to the travel range of the joint angles. The height limitations of all layers are obtained with forward kinematics. A workspace boundary-extraction method is presented to obtain the array of path points of the boundary at each layer. The proposed postprocessing method is used to generate the joint-angle code of each layer for direct 3D printing. Finally, the effectiveness of the multisolution selection method and the workspace visualization method were verified by simulation and experiment.
... In the modular robot control system, kinematics and dynamics model is crucial and important. Kinematics description methods are common D-H parameters method, the improved method of D-H parameters, exponential product formula method (POE), and so forth [9,10]. Modular robot dynamics modeling methods are the Newton-Euler method [11], Lagrange method [12], Kane method [13,14], the principle of virtual work method [15], spinor even method [16], and so forth. ...
... The generalized angular velocitỹis expressed as Formula (9). The generalized angular velocity of partial derivative is expressed as Formula (10). The generalized velocity is expressed as Formula (11). ...
We propose an improved Kane dynamic model theory for the 7-DOF modular robot in this paper, and the model precision is improved by the improved function T′it . We designed three types of progressive modular joints for reconfigurable modular robot that can be used in industrial robot, space robot, and special robot. The Kane dynamic model and the solid dynamic model are established, respectively, for the 7-DOF modular robot. After that, the experimental results are obtained from the simulation experiment of typical task in the established dynamic models. By the analysis model of error, the equation of the improved torque T′it is derived and proposed. And the improved Kane dynamic model is established for the modular robot that used T′it . Based on the experimental data, the undetermined coefficient matrix is five-order linear that was proved in 7-DOF modular robot. And the explicit formulation is solved of the Kane dynamic model and can be used in control system.
