Showing papers on "Kinematics equations published in 2016"

Comparison of four different heuristic optimization algorithms for the inverse kinematics solution of a real 4-DOF serial robot manipulator

Abstract: In this study, a 4-degree-of-freedom (DOF) serial robot manipulator was designed and developed for the pick-and-place operation of a flexible manufacturing system. The solution of the inverse kinematics equation, one of the most important parts of the control process of the manipulator, was obtained by using four different optimization algorithms: the genetic algorithm (GA), the particle swarm optimization (PSO) algorithm, the quantum particle swarm optimization (QPSO) algorithm and the gravitational search algorithm (GSA). These algorithms were tested with two different scenarios for the motion of the manipulator's end-effector. One hundred randomly selected workspace points were defined for the first scenario, while a spline trajectory, also composed of one hundred workspace points, was used for the second. The optimization algorithms were used for solving of the inverse kinematics of the manipulator in order to successfully move the end-effector to these workspace points. The four algorithms were compared according to the execution time, the end-effector position error and the required number of generations. The results showed that the QPSO could be effectively used for the inverse kinematics solution of the developed manipulator.

The forward kinematics of the 6-6 parallel manipulator using an evolutionary algorithm based on generalized generation gap with parent-centric crossover

Abstract: In this paper, a fast and efficient evolutional algorithm, called the G3-PCX has been implemented to solve the forward kinematics problem (FKP) of the general parallel manipulators being modeled by the 6-6 hexapod, constituted by a fixed and mobile platforms being non planar and non-symmetrical. The two platforms are connected by six linear actuators, each of which is located between one ball joint and one universal joint. Forward kinematics are formulated using Inverse Kinematics applying one position based equation system which is converted into an objective function by expressing the sum of squared error on kinematics chain lengths and mobile platform distances. In less than one second, the 16 unique real solutions are computed with improved accuracy when compared to previous methods.

Kinematics analysis and simulation of a robotic arm using MATLAB

Abstract: In order to enhance the study of the kinematics of any robot arm, parameter design is directed according to certain necessities for the robot, and its forward and inverse kinematics are discussed. The DH convention Method is used to form the kinematical equation of the resultant structure. In addition, the Robotics equations are modeled in MATLAB to create a 3D visual simulation of the robot arm to show the result of the trajectory planning algorithms. The simulation has detected the movement of each joint of the robot arm, and tested the parameters, thus accomplishing the predetermined goal which is drawing a sine wave on a writing board.

Pose Determination of a Robot Manipulator Based on Monocular Vision

Abstract: This paper presents an approach to determine the pose of a robot manipulator by using a single fixed camera. Conventionally, the pose determination is usually achieved by using the encoders to sense the joint angles, and then the pose of the end effector is obtained by using the direct kinematics of the manipulator. However, when the encoders or the manipulators are malfunctioning, the pose may not be accurately determined. This paper presents an approach based on machine vision, where a single camera is fixed away from the base of the manipulator. Besides, based on the kinematics of the manipulator and a calibrated camera, the pose of the manipulator can be determined. Furthermore, a graphical user interface is developed, which is convenient for users to operate the entire system. Two examples are demonstrated, and the estimated results are compared with those from the encoders. The proposed approach does not compete with the encoders. Instead, the approach can be treated as a backup method, which can provide a reference solution.

Accuracy analysis of omnidirectional mobile manipulator with mecanum wheels

Abstract: This article is based on the omnidirectional mobile manipulator with mecanum wheels built at Shanghai University. The article aims to find and analyze the parameters of kinematic equation of the omnidirectional system which affects its motion accuracy. The method of solving the parameter errors involves three phases. The first step is equation operation to achieve the equation of relative errors. The second step is to obtain the displacement errors of the system via experiment and combine the error results with kinematic equation deduction to solve the geometric parameter errors in two methods. The third step is to verify its validity via comparing experiments. We can then revise its kinematics equation afterwards.

A Novel Reconfigurable 7R Linkage with Multifurcation

Abstract: This paper investigates constraint singularity induced multifurcation of a novel 7R (R for revolute joint) linkage. Kinematic structure of the 7R linkage is described first for the purpose of geometric analysis. According to geometric properties of the kinematic structure, D-H parameters and kinematics equations in dual quaternion are derived subsequently. The study further explores analytical form of mechanism constraint-screw systems corresponding to distinct motion branches reconfigured from the 7R linkage based on reciprocity in screw theory. The constraint analysis reveals inherent properties of motion branch changes induced by constraints variation and geometric restriction of joints in these motion branches. This leads to identification of multifurcation of the reconfigurable 7R linkage, meaning motion-branch transitions between the non-overconstrained 7R linkage and overconstrained 6R and 4R mechanisms.

Kinematics, dynamics, and control system of a new 5-degree-of-freedom hybrid robot manipulator:

Abstract: Hybrid robotic application is a continuously developing field, as hybrid robot manipulators have demonstrated clearly to possess benefits of both serial structures and parallel mechanisms. In this article, the physical prototype and the specially designed control system for a new 5-degree-of-freedom hybrid robot manipulator are developed. The mechanical structure, kinematics, dynamics, and control system of this robot manipulator are presented. A newly appropriate set of closed-form solutions, which can avoid multiple solutions, is proposed to address the inverse kinematics problem of this robot manipulator. Additionally, simulations of the kinematics and dynamics of this robot manipulator and the tests for the repeatability and accuracy of both the position and path are first simulated with two numerical examples and then conducted on the physical prototype.

Robot Kinematics and Dynamics Modeling

Abstract: The robotic kinematics is essential for describing an end-effector’s position, orientation as well as motion of all the joints, while dynamics modeling is crucial for analyzing and synthesizing the dynamic behavior of robot. In this chapter, the kinematics and dynamics modeling procedures of the Baxter robot are investigated thoroughly. The robotic kinematics is briefly reviewed by highlighting its basic role in analyzing the motion of robot. By extracting the parameters from an URDF file, the kinematics model of the Baxter robot is built. Two experiments are performed to verify that the kinematics model matches the real robot. Next, the dynamics of robot is briefly introduced by highlighting its role in establishing the relation between the joint actuator torques and the resulting motion. The method for derivation of the Lagrange–Euler dynamics of the Baxter manipulator is presented, followed by experimental verification using data collected from the physical robot. The results show that the derived dynamics model is a good match to the real dynamics, with small errors in three different end-effector trajectories.

Instantaneous Kinematics Analysis via Screw-Theory of a Novel 3-CRC Parallel Mechanism

Abstract: This paper presents the mobility and kinematics analysis of a novel parallel mechanism that is composed by one base, one platform and three identical limbs with CRC joints. The paper obtains closed...

Minimum base attitude disturbance track planning method for redundant space manipulator

Abstract: The invention relates to a minimum base attitude disturbance track planning method for a redundant space manipulator, and belongs to the technical field of aerospace. The method comprises the steps of (1), designing a three-dimensional model of the redundant space manipulator; (2), establishing a kinematic model of the redundant space manipulator; (3) establishing a kinematic equation of the redundant space manipulator by employing a generalized Jacobian matrix; (4), parameterizing joints by employing a 5-order sine polynomial function; (5), establishing a cost function equation under a minimum constraint condition of base attitude disturbance; (6), providing an improved hybrid particle swarm optimization; and (7), carrying out optimization solution to the cost function by employing the hybrid particle swarm optimization, thereby obtaining planning tracks under the constraint condition. According to the method, the track planning problem of the redundant space manipulator under the minimum constraint condition of the base attitude disturbance is solved, and the planning tracks solved by the improved hybrid particle swarm optimization is high in precision and good in effect and is steady.

Design, kinematics and dynamics modeling of a lower-limb walking assistant robot

Abstract: This paper focuses on a lower limb walking assistant robot. This robot has been designed and modeled for two tasks of facilitating healthy people, and assisting patients for walking. First, basic concepts of the motion mechanism are presented. Next, its kinematics and dynamics equations have been developed. Kinematics analysis has been done using Denavit-Hartenberg scheme to obtain position, velocity and acceleration of center of mass (COM) of all links. Dynamics equations have been developed using recursive Lagrange method and finally inverse dynamics problem has been solved. Obtained simulation results will be discussed which validate the proposed model.

Position Kinematics of a 3-RRS Parallel Manipulator

Abstract: The 3-RRS parallel manipulator presented in this study comprises of parallel revolute joint axes in each leg. The manipulator is composed of a base and a moving platform which are in the shape of equilateral triangles. Moving platform has two rotational and one translational degrees-of-freedom. This study formulates the forward and inverse kinematics of the parallel manipulator. A 16\(^{th}\) order polynomial in terms of one of the passive joint variables is obtained for the forward kinematic analysis. Numerical results and the corresponding pose of the manipulator for inverse and forward kinematics are presented.

Mechanism and Actuation

Abstract: This chapter focuses on the principles that guide the design and construction of robotic systems. The kinematics equations and Jacobian of the robot characterize its range of motion and mechanical advantage, and guide the selection of its size and joint arrangement. The tasks a robot is to perform and the associated precision of its movement determine detailed features such as mechanical structure, transmission, and actuator selection. Here we discuss in detail both the mathematical tools and practical considerations that guide the design of mechanisms and actuation for a robot system.

A Three Finger Tendon Driven Robotic Hand Design and Its Kinematics Model

Abstract: Anatomy of human hand is very complex in nature. The structure of human hand consists of number of joints, bones, muscles and tendons, which creates a wide range of movements. It is very difficult to design a robotic hand and incorporate all the features of a normal human hand. In this paper, the model of a three finger robotic hand has been proposed. To replace the muscles and tendons of real human hand, it is proposed to use tendon wire and place the actuator at the palm. The advantage of using tendon and placing actuator at remote location is that it actually reduces the size of the hand. Pulling the tendon wire produces flexor motion in the hand finger. Currently torsional spring is considered at the joint for the extension motion of the finger. The purpose of design of such a hand is to grasp different kinds of object shapes. The paper further presents a kinematics model of the three finger hand and a mapping function to map the joint space coordinates to tendon space coordinates. Finally the hand model is simulated to validate the kinematics equations.

Kinematic modeling and control of the Hexapod parallel robot

Abstract: The so-called Hexapod robot is a parallel manipulator produced by Quanser Inc. This mechanism is constituted of two triangular rigid bodies, one fixed (the base), and one mobile (the platform) joined together by six kinematic chains (the legs) conforming a structure of the type known as 6-3-PUS. This paper first reports a procedure for computing the forward and inverse kinematics models of the Hexapod robot. After that, we show how to implement an operational space tracking controller which employs a two-loop structure: a resolved motion rate controller (RMRC) in the outer loop and a joint-velocity PI controller in the inner loop. Experimental results of the real-time implementation are included.

Optimum design of a 4-PSS-PU redundant parallel manipulator based on kinematics and dynamics:

Abstract: This paper presents an optimum design of a 4-PSS-PU redundant parallel manipulator by taking the workspace, conditioning performance, and acceleration into account. On the basis of rank of the Jacobian matrix, a method to directly find out the workspace is presented, rather than the search method. Based on the dynamic model, a maximum acceleration index is defined. The corresponding atlases of these performance indices are represented graphically in the established design space. Based on these atlases, the optimum design is performed and the optimum region is determined. It is expected to realize the high acceleration of parallel manipulators by using the optimum method.

Fault tolerance kinematics and trajectory planning of a 6-DOF space manipulator under a single joint failure

Abstract: A space manipulator plays an important role in spacecraft capturing, repairing, maintenance, and so on. However, the harsh space environment will cause its joints fail to work. For a non-redundant manipulator, single joint locked failure will cause it lose one degree of freedom, hence reducing its movement ability. In this paper, the key problems related with the fault-tolerant, including kinematics, workspace and trajectory planning, of a non-redundant space manipulator under single joint failure are handled. Firstly, the analytical inverse kinematics equations are derived for the 5-DOF (degree of freedom) manipulator formed by locking the failure joint of the original 6-DOF manipulator. Then, we define the missions can be completed by the 5-DOF manipulator. According to the constraints of the on-orbital mission, a fault tolerance parameter is defined and a planning method is proposed to generate the reasonable trajectory, based on which, the 5-DOF manipulator can complete the desired tasks. Finally, typical cases are simulated and the simulation results verify the proposed method.

Inverse kinematics and design of a novel 6-DoF handheld robot arm

Abstract: We present a novel 6-DoF cable driven manipulator for handheld robotic tasks. Based on a coupled tendon approach, the arm is optimized to maximize movement speed and configuration space while reducing the total mass of the arm. We propose a space carving approach to design optimal link geometry maximizing structural strength and joint limits while minimizing link mass. The design improves on similar non-handheld tendon-driven manipulators and reduces the required number of actuators to one per DoF. As the manipulator has one redundant joint, we present a 5-DoF inverse kinematics solution for the end effector pose. The inverse kinematics is solved by splitting the 6-DoF problem into two coupled 3-DoF problems and merging their results. A method for gracefully degrading the output of the inverse kinematics is described for cases where the desired end effector pose is outside the configuration space. This is useful for settings where the user is in the control loop and can help the robot to get closer to the desired location. The design of the handheld robot is offered as open source. While our results and tools are aimed at handheld robotics, the design and approach is useful to non-handheld applications.

Moving trajectory planning method for space moving multi-arm robot

Abstract: Provided is a moving trajectory planning method for a space moving multi-arm robot. The moving trajectory planning method includes that firstly, according to the specific position transfer task of the space moving multi-arm robot, the position to be reached by the two ends of a first robot arm and the position to be reached by the two ends of a second robot arm are determined; the moving trajectories of the two ends of the first robot arm and the moving trajectories of the two ends of the second robot arm are calculated based on a quintic polynomial planning method; the moving trajectories of the joints of the first robot arm and the moving trajectories of the joints of the second robot arm are calculated according to the kinematic equation of the robot arms to determine the moving trajectory of the space moving multi-arm robot; and a collision detection algorithm is designed to detect the collision safety between the robot arms and a robot platform, between the robot arms and a target spacecraft, and between the robot arms during the movement of the robot.

A Direct and Non-Singular UKF Approach Using Euler Angle Kinematics for Integrated Navigation Systems

Abstract: This paper presents a direct and non-singular approach based on an unscented Kalman filter (UKF) for the integration of strapdown inertial navigation systems (SINSs) with the aid of velocity. The state vector includes velocity and Euler angles, and the system model contains Euler angle kinematics equations. The measured velocity in the body frame is used as the filter measurement. The quaternion nonlinear equality constraint is eliminated, and the cross-noise problem is overcome. The filter model is simple and easy to apply without linearization. Data fusion is performed by an UKF, which directly estimates and outputs the navigation information. There is no need to process navigation computation and error correction separately because the navigation computation is completed synchronously during the filter time updating. In addition, the singularities are avoided with the help of the dual-Euler method. The performance of the proposed approach is verified by road test data from a land vehicle equipped with an odometer aided SINS, and a singularity turntable test is conducted using three-axis turntable test data. The results show that the proposed approach can achieve higher navigation accuracy than the commonly-used indirect approach, and the singularities can be efficiently removed as the result of dual-Euler method.

Forward kinematics of a human-arm system and inverse kinematics using vector calculus

Abstract: Simple procedure in designing and studying forward and inverse kinematics of a 5-DOF humanoid robotic arm. Firstly, the idea of imitating human's joint behavior using servo-pairs is introduced. Then, using Denavit-Hartenberg parameters, the forward kinematics of the arm is calculated. After that, one solution for the inverse kinematics problem is proposed, in an iterative way such that further models can be solved also.

Kinematic analysis and simulation of 6-DOF industrial robot capable of picking up die-casting products

Abstract: This paper describes a 6-DOF industrial robot capable of picking up die-casting products. The link coordinate system of the 6-DOF robot is established based on the D-H parameter method and the forward and inverse kinematics are discussed. ADAMS is utilized to establish a virtual prototyping and the kinematic simulation is carried out. The results show that the validity of the kinematic equations is verified.

Inverse kinematics solution for 6R serial manipulator based on RBF neural network

Abstract: Calculation of 6R serial manipulator's inverse kinematics is a highly complex nonlinear mapping problem. As the process of 6R serial manipulator's inverse kinematics calculating concerned, these traditional algorithms, like inverse transformation, geometry, pieper solution, etc., are very complex, and they often involve in the problem of multiple solutions and singularity. So, the calculation efficiency is very low. Artificial Neural Network (ANN) has a great advantage in solving these problems of nonlinear mapping, like parallel processing, self-adaptive, and fast, efficient handling of the multivariable system, etc. So, ANN has been widely used to solve the complex kinematics problems of the redundant robotic manipulators. This paper adopts a RBF-based neural network to solve the inverse kinematics problem of 6R serial manipulator. From the final simulation, we can find that, by using this new calculating algorithm, it can give an accurate inverse kinematics solution fast and with a high efficiency. Apart from these, when using in practice, it also reflects a perfect performance.

A Multi-objective Differential Evolution Algorithm for Robot Inverse Kinematics

Abstract: This paper presents the robot inverse kinematics solution for four Degrees of Freedom (DOF) through Differential Evolution (DE) algorithm. DE can handle real numbers (float, double) which leads more powerful than Genetic Algorithm (GA). We propose a multi-objective fitness function that makes an attempt to minimize the positional error and maximum angular displacement of the robot joints. Maximum angular displacement based fitness function adopt the constraints on different unrealistic rotational movement of the manipulator. We employ an equitable treatment of both fitness functions while maximizing these two over generations that iteratively selects the optimal weights of these two fitness functions automatically. Trigonometric mutation and binomial crossover improve the performance of the conventional DE technique. We compared the results of proposed multi-objective DE with GA and Algebraic Method (AM). Proposed multi-objective DE algorithm obtains less positional error than conventional DE, GA and AM while meeting the rotational constraints of the manipulator’s joints. Keywords— Inverse Kinematic, Differential Evolution, Multi-objective optimization, Genetic Algorithm, Robot manipulator with four degrees of freedom.

Kinematics and Jacobian analysis of a 6UPS Stewart-Gough platform

Abstract: In this paper a complete kinematics analysis of a 6UPS Stewart-Gough platform is performed. A new methodology to deal with the forward kinematics problem based on a multibody formulation and a numerical method is presented, resulting in a highly efficient formulation approach. The idea of a multibody formulation is basically to built for each joint that links the body of the robot, a set of equations that define the constraints on their movement so that the joint variables are included in these equations. Once the constraint function is defined, we may use a numerical method to find the kinematic solution. In order to avoid the problem reported with the orientation (Euler's Angles) of the moving platform, a generalized coordinates vector using quaternions is applied. Then, the Jacobian analysis using reciprocal screw systems is described and the workspace is determined. Finally, a design of a simulator using MATLAB as programming tool is presented.

Wind estimation using the position information from a hovering quadrotor

Abstract: In this paper, an approach to estimating the wind at a fixed place is proposed by using the observed position information of a hovering quadrotor. The aerodynamic characteristics of the propeller are firstly analyzed to establish the quadrotor model in a windy environment. Then, a PID method is adopted to maintain the stable hovering flight. Next, according to the hovering state equations, the wind estimating algorithm can be obtained by decomposing three-dimensional kinematics equations into two parts, one is the motion caused by wind, and another is the motion to keep itself hovering at a fixed point. Finally, the effectiveness of the proposed method is proved with the MATLAB/Simulink simulation.

Control of system dynamics and constraints stabilization

Abstract: Problems of program control for dynamic systems with elements of various physical natures are considered. The equations of classical mechanics is used for describing a dynamical process of controlled systems. The method of constructing differential equations of the known particular integrals is used to stabilize the constraints imposed on the dynamical system, which is described with the Lagrange or Hamilton equations. Stability conditions for solutions of dynamics equations with respect to the constraint equations are obtained. An algorithm for constructing equations of constraint perturbations that guarantees stabilization of constraints in the course of numerical solution by the Runge-Kutta method is proposed. The proposed methods are used for solving problems of control of production, logistics and technical systems: a discrete adaptive optical system, an electromechanical system consisting of a power supply unit and a direct current motor, which controls the crank mechanism, a unit controlling wheel system's movement along a given trajectory with avoidance of moving bodies; enterprise consisting of two plants; rectilinear motion of a cart with inverted pendulum. The content of the work distributed in the following titles: Introduction; Statement of the problem; Construction of dynamics equations; Stability and stabilization; Applications.