Showing papers on "Kinematics equations published in 2009"

Closed-Form Inverse Kinematics for Continuum Manipulators

Abstract: This paper presents a novel, analytical approach to solving inverse kinematics for multi-section continuum robots, defined as robots composed of a continuously bendable backbone. The problem is decomposed into several simpler subproblems. First, this paper presents a solution to the inverse kinematics problem for a single-section trunk. Assuming endpoints for all sections of a multi-section trunk are known, this paper then details applying single-section inverse kinematics to each section of the multi-section trunk by compensating for the resulting changes in orientation. Finally, an approach which computes per-section endpoints given only a final-section endpoint provides a complete solution to the multi-section inverse kinematics problem. The results of implementing these algorithms in simulation and on a prototype continuum robot are presented and possible applications discussed.

Sliding Mode Control for Trajectory Tracking of Mobile Robot in the RFID Sensor Space

Abstract: This paper presents a sliding mode control method for wheeled mobile robots. Because of the nonlinear and nonholonomic properties, it is difficult to establish an appropriate model of the mobile robot system for trajectory tracking. A robust control law which is called sliding mode control is proposed for asymptotically stabilizing the mobile robot to a desired trajectory. The posture of the mobile robot (including the position and heading direction) is presented and the kinematics equations are established in the two-dimensional coordinates. According to the kinematics equations, the controller is designed to find an acceptable control law so that the tracking error will approximate 0 as the time approaches infinity with an initial error. The RFID sensor space is used to estimate the real posture of the mobile robot. Simulation and experiment demonstrate the efficacy of the proposed system for robust tracking of mobile robots.

A Path Following Control of an Unmanned Autonomous Forklift

Abstract: In this paper, the development of an unmanned autonomous forklift is discussed. A system configuration using vision, laser ranger finder, sonar, etc. for autonomous navigation is presented. The kinematics of a spin-turn mechanism is analyzed first, and then the obtained kinematics equations are transformed to the equations represented by path variables. These equations are nonlinear state equations to be used for control purposes. A time varying feedback control law via the chained form of Murray and Sastry [12] is derived. The effectiveness of the proposed control law is examined through simulations and experiments.

Design and forward kinematics of the compliant micro-manipulator with lever mechanisms

Abstract: This paper presents the forward kinematics of a five-bar compliant micro-manipulator. To overcome the limited displacement of such a flexure-based mechanism driven by piezoelectric actuators, lever mechanisms are utilized to enlarge the working range. The mechanical design of the micro-manipulator is firstly described. Mathematical formulations for the five-bar mechanism are described and the solutions are developed to decide the end-effector position in Cartesian space. The amplification factor of the lever mechanism is also derived based on the analytical solution of the four-bar linkages. The velocity of the end-effector is obtained by differentiating the forward position kinematic equation, and the local mobility index of the five-bar compliant mechanism is determined and analysed. Based on linearization of trigonometric functions and constant Jacobian matrix, numerical simulations are carried out to investigate the performance of the five-bar compliant manipulator and to determine the optimal geometric parameters for the configuration. The comparisons between the exact solution and simplified methodologies are conducted. Experiments are carried out to validate the established model and the performance of the developed micro-manipulator.

Optimization of a novel mechanism for a minimally invasive surgery robot.

Abstract: Background Minimally invasive surgery (MIS) has many advantages compared with open surgery, but there are still many drawbacks in performing MIS. Using robotic technologies, many problems caused by human restrictions, such as fatigue and low precision, can be solved. In this paper, a novel mechanism for a MIS robot is proposed. Methods Kinematics analysis was carried out and singularity and isotropy configurations were also investigated, based on kinematics equations. In order to evaluate the performance of the robot, a combined measure gave attention to the mean value and standard deviation of the reciprocal of the condition number. Optimization was achieved by maximizing the combined measure subjected to a set of constraints in the task workspace. The effectiveness of the measure was demonstrated by comparing the performance and volume of the optimized mechanism with those of the mechanism optimized by the Global Condition Index (GCI). Results The robot met the volume constraints with the dimensional parameter a ≤ 115 mm. The combined measure φ was maximized when a is 100 mm. The robots optimized by the GCI and the combined measure showed similar performance in terms of condition number, but the latter had advantages on volume compared with the former. Conclusions A novel mechanism that satisfied the incision point constraint of MIS was proposed. A systematic methodology for optimizing the mechanism was developed and the combined measure was effective to evaluate the performance. A prototype was set up based on the outcomes mentioned in the paper. Copyright © 2009 John Wiley & Sons, Ltd.

Kinematics of an offset 3-UPU translational parallel manipulator by the homotopy continuation method

Abstract: For most parallel manipulators, the inverse kinematics is straightforward, while the direct kinematics is challenging. The latter requires the solution of a system of nonlinear equations. In this paper we use the homotopy continuation method to solve the forward and inverse kinematic problems of an offset 3-UPU translational parallel manipulator. The homotopy continuation method is a novel method which alleviates drawbacks of the traditional numerical techniques, namely; the acquirement of good initial guess values, the problem of convergence and computing time. The direct kinematics problem of the manipulator leads to 16 real solutions.

Analysis of a 6-DOF redundantly actuated 4-legged parallel mechanism

Abstract: In this paper, we propose a new 4-legged 6-DOF redundantly actuated UPS parallel mechanism. Kinematics, singularity and dynamics analyses of the proposed mechanism are addressed. Inverse kinematics has a closed-form solution, whereas the forward kinematics has a semi-closed form solution. Also, the Jacobian matrix has been determined using the concept of reciprocal screws. Using the principle of virtual work and minimum norm method, a general formulation for the inverse dynamics of redundantly actuated parallel manipulator is presented.

Kinematics and Statics of Cooperative Multi-Robot Aerial Manipulation With Cables

Abstract: This paper addresses the forward and inverse kinematics of payloads carried by aerial robots. We address the cases with one, two, and three aerial robots and derive the kinematics and conditions for stable static equilibrium. For the case with one or two robots, we can establish the maximum number of equilibrium positions. The three-robot case is seen to be much harder primarily because of the non-negative tension constraints. We restrict the set of possible solutions to the forward and inverse problems by considering the equations of static equilibrium and kinematic constraints. Analytic and numeric methods to determine equilibrium configurations and stability are presented.Copyright © 2009 by ASME

Explicit dynamics equations of the constrained robotic systems

Abstract: Recursive matrix relations concerning the kinematics and the dynamics of a constrained robotic system, schematized by several kinematical chains, are established in this paper. Introducing frames and bases, we first analyze the geometrical properties of the mechanism and derive a general set of relations. Kinematics of the vector system of velocities and accelerations for each element of robot are then obtained. Expressed for every independent loop of the robot, useful conditions of connectivity regarding the relative velocities and accelerations are determined for direct or inverse kinematics problem. Based on the general principle of virtual powers, final matrix relations written in a recursive compact form express just the explicit dynamics equations of a constrained robotic system. Establishing active forces or actuator torques in an inverse dynamic problem, these equations are useful in fact for real-time control of a robot.

Dynamics of the spherical 3-\mathit{U\underline{P}S/}S parallel mechanism with prismatic actuators

Abstract: Recursive relations in kinematics and dynamics of the symmetric spherical 3- $\mathit{U\underline{P}S}/S$ parallel mechanism having three prismatic actuators are established in this paper. Controlled by three forces, the parallel manipulator is a 3-DOF mechanical system with three parallel legs connecting to the moving platform. Knowing the position and the rotation motion of the platform, we develop first the inverse kinematics problem and determine the position, velocity, and acceleration of each manipulator’s link. Further, the inverse dynamic problem is solved using an approach based on the principle of virtual work, but it has been verified using the results in the framework of the Lagrange equations with their multipliers. Finally, compact matrix relations and graphs of simulation for the input forces and powers are obtained.

Forward kinematics of the 6-6 general parallel manipulator using Real Coded Genetic Algorithms

Abstract: This article examines an optimization method to solve the forward kinematics problem (FKP) applied to parallel manipulators. Based on Genetic Algorithms (GA), a non-linear equation system solving problem is converted into an optimization one. The majority of truly parallel manipulators can be modeled by the 6-6 which is an hexapod constituted by a fixed base and a mobile platform attached to six kinematics chains with linear (prismatic) actuators located between two ball joints. Parallel manipulator kinematics are formulated using the explicit Inverse Kinematics Model (IKM). The position based equation system is implemented. In order to implement GA, the objective function is formulated specifically for the FKP using one squared error performance criteria applied on the leg lengths augmented by three platform joint distances. The proposed approach implements an elitist selection process where a new mutation operator for Real-Coded GA is analyzed. These experiments are the first to converge towards several exact solutions on a general Gough platform manipulator with fast convergence.

Kinematics and design of two variants of a reconfigurable parallel robot

Abstract: In order to reach the desired results solutions must be different for each individual industrial application. For solving certain tasks special mechanisms should be developed for each application. Reconfigurable robots can be defined as a specific category of robots in which their components (individual joints and links) can be assembled in different configurations and geometries. In this paper several aspects of the kinematics and design for two variants of reconfigurable parallel robots are presented and some kinematics simulation results for these reconfigurable parallel robots are illustrated as well.

A new method to solve robot inverse kinematics using assur virtual chains

Abstract: This paper describes a numerical algorithm to solve the inverse kinematics of parallel robots based on numerical integration. Inverse kinematics algorithms based on numerical integration involve the drift phenomena of the solution; as a consequence, errors are generated when the end-effector location differs from that desired. The proposed algorithm associates a novel method to describe the differential kinematics with a simple numerical integration method. The methodology is presented in this paper and its exponential stability is proved. A numerical example and a real application are presented to outline its advantages.

Dynamics equations of a mobile robot provided with caster wheel

Abstract: Kinematics and dynamics of a mobile robot, consisting of a platform, two conventional wheels and a crank that controls the motion of a free rolling caster wheel, are analyzed in the paper. Based on several matrix relations of connectivity, the characteristic velocities and accelerations of this non-holonomic mechanical system are derived. Using the principle of virtual work, expressions and graphs for the torques and the powers of the two driving wheels are established. It has been verified the results in the framework of the second-order Lagrange equations with their multipliers. The study of the dynamics problems of the wheeled mobile robots is done mainly to solve successfully the control of the motion of such systems.

Application of genetic algorithms to robot kinematics calibration

Abstract: Position and orientation accuracy of an end-effector is affected by the precision of kinematics parameters of the robot manipulator. Thus, good precision requires good knowledge of robot physical parameter values. However, this condition can be difficult to meet in practice. Hence, calibration techniques can be devised in order to improve the robot accuracy through estimation of these particular parameters. In this article, the genetic algorithm is used to calibrate the robot kinematics accuracy. A kinematics model is formulated and conducted as an optimisation problem for ABB Irb 6000 robot manipulator. The objective is to analyse and evaluate the performance of the GA in optimising such robot kinematics accuracy. In this algorithm, small changes in the kinematics parameters values represent the parent and offspring population and the end-effector error represents the fitness functions. A numerical example has been used to demonstrate the convergence and effectiveness of the given model.

Analysis of Human Arm Joints and Extension of the Study to Robot Manipulator

Abstract: The paper presents the analysis of human arm joints is carried out and the study is extended to the robot manipulator. This study will first focus on the kinematics of human upper arm which include the movement of each joint in shoulder, wrist, elbow and fingers. Those analyses are then extended to the design of a human robot manipulator. A simulator is built for Direct Kinematics and Inverse Kinematics of human upper arm. In the simulation of Direct Kinematics, the human joint angles can be inserted, while the position and orientation of each finger tips (end-effector) are shown. The simulation of human arm forward kinematics is performed through MATLAB Graphical User Interface and VRML. tained from kinematics analysis, the human manipulator joints can be designed to follow prescribed position trajectories. This paper focuses on the kinematics analysis of human upper arm and extends it to the human manipulator. Kinematics is the study of motion without regard to the forces that create it. The representation of the robot's end-effector position and orientation through the geometries of robots (joint and link parameters) are called Direct Kinematics. Using Direct Kinematics, the mathematical model is developed to compute the position and orientation of each fingertip (end- effector's) based on the given human joint position. Each human joint is considered as revolute joint. The homogenous transformation of the fingertip related to the base frame (arm upper limb) is formulated using Denavit-Hartenberg (D-H) method. (3) Inverse Kinematics analysis is a formulation to compute a set of joint variables from the given end-effector or tool piece pose. In the present study, an articulated finger consists of a set of rigid segments connected with joints. Each finger joint angles will be computed by the given fingertip position and orientation. Varying the angles of the joints yields an indefinite number of configurations. Geometric approach will be used to solve this problem.

Robot formation modelling and control based on the relative kinematics equations

Abstract: This paper deals with the problem of modeling, initialization, and control of mobile robots formation. We suggest to use a new family of methods that consists of a combination between classical guidance laws and kinematics rules. These methods allow modeling and controlling a dynamic robotic formation using sets of differential equations that give the relative motion between the robots. These differential equations give the range rate and the visibility angle between leaders and followers. Graph theory is used to store the relationship leader-follower and plan the formation by using three different matrices. The configuration of the formation is based on these matrices. Initialization of formation is also considered, where different approaches are suggested. Because of the nature of the kinematics laws, it is easy to model, initialize, and keep any formation shape. Simulation is provided to illustrate the method.

Capturability of a Geometric Guidance Law in Relative Velocity Space

Abstract: In this paper, capturability of a recently proposed geometric guidance law is analyzed in the plane defined by the relative velocity vector. The kinematic equations for planar engagements are derived in the relative velocity space. The analysis is done completely in the time domain. The capturability analysis of the guidance law is carried out for the entire relative velocity space as compared with the existing work where classical geometric curve theory is used to obtain and analyze the guidance law. The entire relative velocity space is partitioned into subsets corresponding to different missile and target engagement geometries. Sufficient conditions for capture are then obtained by analyzing the differential equations governing the motion of the trajectories in the relative velocity space. A comparison of the capture conditions obtained in this paper and previous work is presented. It is seen that analysis in the relative velocity space relaxes the condition on the navigation gain in the guidance law. From the analysis of both nonmaneuvering and maneuvering targets, it is also seen that a combination of these sufficient conditions can be used to obtain a more general capturability analysis of the guidance law. Numerical simulation results are given to validate the analytical results.

Modeling and sliding mode control of a snake-like robot with holonomic constraints

Abstract: In this paper modeling and robust sliding mode control of a snake-like robot in tracking of serpenoidal motion is addressed. By considering holonomic constraints, the kinematic and dynamic equations of a hyper redundant robot are obtained using Kane's method. The Coulomb friction between robot's wheels and the ground is modeled in two perpendicular directions (i.e. tangential and normal directions) with unknown coefficients of friction in each direction. A sliding manifold is defined by using position and velocity tracking errors of the relative motion between consecutive joints. Continuous approximation of switching control laws is used to eliminate chattering phenomena. The simulation results demonstrate that the snake-like robot realizes the trajectory tracking with desired robustness to the parameter uncertainties.

Forward Kinematics Analysis of the General 6-6 Platform Parallel Mechanism Based on Algebraic Elimination

Abstract: A new algebraic elimination method for the forward kinematics analysis of the general 6-6 platform parallel mechanism is presented.Six in nine constraint quadratic equations are transformed into linear equations by introducing substitution variables and six in nine variables are eliminated by using Cramer algorithm.The reduced Groebner basis under degree lexicographic ordering for the substitution equations and the remainder closed-form equations are obtained.A univariate equation of higher degree is derived from the determinant of the Sylvester's matrix,constructed by the 4th degree subset of the Groebner basis,the size of which is 15×15. Based on computer symbolic manipulating,it can be concluded that the degree of the univariate polynomial equation is at most 20 and the number of closed-form solutions is at most 40.It is proved theoretically that there are many completely different resultants which can derive all closed-form solutions in terms of different term orderings through changing the degree lexicographic order.The direct kinematics of the general 6-6 Stewart platform can be solved directly by the 15 derived equations.And the mathematical mechanized solution of the problem can be realized.The result is verified by a numerical example,whose solutions agree with the original equations without extraneous roots.

Artificial Neural Network with Steepest Descent Backpropagation Training Algorithm for Modeling Inverse Kinematics of Manipulator

Abstract: � Abstract—Inverse kinematics analysis plays an important role in developing a robot manipulator. But it is not too easy to derive the inverse kinematic equation of a robot manipulator especially robot manipulator which has numerous degree of freedom. This paper describes an application of Artificial Neural Network for modeling the inverse kinematics equation of a robot manipulator. In this case, the robot has three degree of freedoms and the robot was implemented for drilling a printed circuit board. The artificial neural network architecture used for modeling is a multilayer perceptron networks with steepest descent backpropagation training algorithm. The designed artificial neural network has 2 inputs, 2 outputs and varies in number of hidden layer. Experiments were done in variation of number of hidden layer and learning rate. Experimental results show that the best architecture of artificial neural network used for modeling inverse kinematics of is multilayer perceptron with 1 hidden layer and 38 neurons per hidden layer. This network resulted a RMSE value of 0.01474.

Inverse Kinematics and Motion Simulation of a 2-DOF Parallel Manipulator with 3-PUP Legs

Abstract: This paper presents a position analysis of a novel parallel manipulator with three \({\underline P}UP\) legs. By investigating the loop-closure equation for the manipulator, the paper presents a closed-form solution of the inverse kinematics problem. The platform of the parallel mechanism under investigation has two independent degrees of freedom, namely, a translation and a rotation about a skew axis. The paper also shows that the platform is subjected to one parasitic motion, which is an additional translation. The paper validates the obtained closed-form equations with a numerical example. Finally, the results of this example are compared with the results of a kinematics simulation using a commercially available software package.

Adaptive Jacobian Force/Position Tracking Control of Robotic Manipulators in Compliant Contact with an Uncertain Surface

Abstract: Most research so far on force/position tracking control of robots has assumed that the kinematics and dynamics are exactly known. In this work, we deal with force/position tracking under uncertainties arising from robot kinematics, dynamics, surface stiffness and position with an emphasis on uncertain kinematics. A robot with uncertain kinematics and dynamics in contact with a compliant surface is considered. A new adaptive Jacobian controller has been designed to cope with the uncertain robot kinematics, dynamics, environmental stiffness and position. It is shown that the controller can achieve force and position tracking via Lyapunov stability analysis. Simulation results demonstrate the performance of the controller.

Closed-form forward kinematics solutions of a 4-DOF parallel robot

Abstract: It is well known that the forward kinematics of parallel robots is a very difficult problem. Closed-form forward kinematics solutions have been reported only to a few special classes of parallel robots. This paper presents closed-form forward kinematics solutions of a 4-DOF parallel robot H4. A 16th order polynomial in a single variable is derived to solve the forward kinematics of the H4. The 16 roots of the polynomial lead to at most 16 different forward kinematics solutions. A numerical verification is also presented.

Algorithm for the Inverse Kinematics Calculation of 6-DOF Robots Based on Screw Theory and Paden-Kahan Sub-problems

Abstract: Denavit-Hartenberg(D-H) notation method and screw theory method are usually used to set up the kinematics model of a robot when its inverse kinematics calculation is to be carried out.D-H method is relatively mature and wildly used in kinematics analysis of robots.Screw method is relatively less in practical application,but with this method,the coordinate of each link of the robot is set up with reference to the base of the robot,so the coordinate has definite geometric meaning.For the kinematics model set up by screw method,the inverse kinematics calculation is usually realized by using Paden-Kahan sub-problem method.Pure Paden-Kahan sub-problems method can only be used for the inverse kinematics calculation of robot with low-DOF.The kinematics model of the robot with 6-DOF and with the last three joint axes intersecting to one point is set up by using screw method,and a new algorithm is proposed for the inverse kinematics calculation of this kind of robot,by using the combined method of algebraic elimination method and Paden-Kahan sub-problem method,and the result of explicit solution is given.The correctness of the algorithm is verified by KUKA KR-150 robot,whose kinematics mode is set up by using the proposed algorithm.