Robot Inverse Kinematics Research Articles

Approximating a Robot Inverse Kinematics Solution Using Fuzzy Logic Tuned by Genetic Algorithms

A new scheme based on recursive fuzzy logic is presented in this paper for solving the point-to-point inverse kinematics problem of serial robots. To improve the convergence problem in the whole workspace, the membership functions of the fuzzy logic are searched for, tuned, and optimised using a simple genetic algorithm. A dominant joint, which brings the end-effect closer to the desired target, has to be selected before the implementation of the fuzzy logic in order to reduce the number of fuzzy logic iterations. The inverse kinematics solution of robots is usually obtained by direct inversion of the kimenatics equations, but this technique often leads to a singular Jacobian matrix during the calculations. The work presented in this paper provides a direct approach to the calculation of the kinematics inverse problem which bypasses the kinematic singularities. Computer simulations of the proposed scheme confirm the findings of the theoretical developments.

Control of a six‐axis pneumatic robot

AbstractThe article presents a control system for a six‐degree of freedom (DOF) anthropomorphic robot powered entirely by pneumatic actuators. The control uses digital valves driven by pulse width modulation (PWM) to regulate air flow to the actuators. The robot is equipped with position sensors, which are used to provide feedback signals for local fuzzy controllers actuating the individual servoaxes. Trajectory tracking is guided by a module, which computes the robot's inverse kinematics, generating the references for the servoaxes. Experimental results illustrated in the article indicate that the controller is effective both in controlling single axes, and in tracking a trajectory. © 2002 Wiley Periodicals, Inc.

Introduction to robotics analysis, systems, applications

Most chapter begins with an Introduction and conclude with a Summary, References and Problems. 1. Fundamentals. What is a Robot? Classification of Robots. What is Robotics? History of Robotics. Advantages and Disadvantages of Robots. Robot Components. Robot Degrees of Freedom. Robot Joints. Robot Coordinates. Robot Reference Frames. Programming Modes. Robot Characteristics. Robot Workspace. Robot Languages. Robot Applications. Other Robots and Applications. Social Issues. 2. Robot Kinematics: Position Analysis. Robots as Mechanisms. Matrix Representation. Homogeneous Transformation Matrices. Representation of Transformations. Inverse of Transformation Matrices. Forward and Inverse Kinematics of Robots. Denavit-Hartenberg Representation of Forward Kinematic Equations of Robots. The Inverse Kinematic Solution of Robots. Inverse Kinematic Programming of Robots. Degeneracy and Dexterity. The Fundamental Problem with the Denavit-Hartenberg Representation. Design Project 1: A Three-Degree-of-Freedom Robot. 3. Differential Motions and Velocities. Differential Relationships. Jacobian. Differential Motions of a Frame. Interpretation of the Differential Change. Differential Changes Between Frames. Differential Motions of a Robot and Its Hand Frame. Calculation of the Jacobian. How to Relate the Jacobian and the Differential Operator. Inverse Jacobian. Design Project. 4. Dynamic Analysis and Forces. Lagrangian Mechanics: A Short Overview. Effective Moments of Inertia. Dynamic Equations for Multiple-Degree-of-Freedom Robots. Static Force Analysis of Robots. Transformation of Forces and Moments Between Coordinate Frames. Design Project. 5. Trajectory Planning. Path vs. Trajectory. Joint-Space vs. Cartesian-Space Descriptions. Basics of Trajectory Planning. Joint-Space Trajectory Planning. Cartesian-Space Trajectories. Continuous Trajectory Recording. Design Project. 6. Actuators. Characteristics of Actuating Systems. Comparison of Actuating Systems. Hydraulic Devices. Pneumatic Devices. Electric Motors. Microprocessor Control of Electric Motors. Magnetostrictive Actuators. Shape-Memory Type Metals. Speed Reduction. Design Project 1. Design Project 2. 7. Sensors. Sensor Characteristics. Position Sensors. Velocity Sensors. Acceleration Sensors. Force and Pressure Sensors. Torque Sensors. Microswitches. Light and Infrared Sensors. Touch and Tactile Sensors. Proximity Sensors. Range-finders. Sniff Sensors. Vision Systems. Voice Recognition Devices. Voice Synthesizers. Remote Center Compliance (RCC) Device. Design Project. 8. Image Processing and Analysis with Vision Systems. Image Processing versus Image Analysis. Two- and Three-Dimensional Image Types. What is an Image. Acquisition of Images. Digital Images. Frequency Domain vs. Spatial Domain. Fourier Transform of a Signal and its Frequency Content. Frequency Content of an Image Noise, Edges. Spatial Domain Operations: Convolution Mask. Sampling and Quantization. Sampling Theorem. Image-Processing Techniques. Histogram of Images. Thresholding. Connectivity. Noise Reduction. Edge Detection. Hough Transform. Segmentation. Segmentation by Region Growing and Region Splitting. Binary Morphology Operations. Gray Morphology Operations. Image Analysis. Object Recognition by Features. Depth Measurement with Vision Systems. Specialized Lighting. Image Data Compression. Real-Time Image Processing. Heuristics. Applications of Vision Systems. Design project. 9. Fuzzy Logic Control. Fuzzy Control: What is Needed. Crisp Values vs. Fuzzy Values. Fuzzy Sets: Degrees of Membership and Truth. Fuzzification. Fuzzy Inference Rule Base. Defuzzification. Simulation of Fuzzy Logic Controller. Applications of Fuzzy Logic in Robotics. Design Project. Appendix. Matrix Algebra and Notation: A Review. Calculation of an Angle From its Sine, Cosine, or Tangent. Problems. Index.

Robotic Tele-Ultrasound System (TER): Slave Robot Control

This paper focuses on robotic tele-ultrasound (TER) slave system. A demonstrator for obstetrical tele-ultrasound applications based on the use of a tele-operated robot controlled by a distant medical expert is developed. Based on the analysis of a typical ultrasound examination and the requirements of medical doctors, the tele-ultrasound system architecture is defined, in particular that of the tele-operated robot. The master-slave configuration allows to control the ultrasound probe with 6 degrees of freedom (DOF). Slave robot inverse kinematics, control approaches and numerical results are presented.

Visual Servoing of Robotic Manipulator in a Virtual Learned Articular Space

A position control approach for Robotic Manipulator based on visual feedback is presented. This feedback, originated from a pair stereo fixed camera, is converted into a Virtual Articular Space, so-called because it is an approximation of real articular space of robot. A multilayered neural network trained to build the correspondence from the visual information of the robot hand and the articular position of the arm generates this approximation. By using this mapping we avoid the complexity of the analytic approach which requires the both robot inverse kinematics and the inverse camera-space mappings, including calibration. This approach is tested experimentally in real time on a 5 degrees-offreedom laboratory manipulator, including the required cameras and image processing boards.

Visual Servoing of Fixed Camera Robotic Systems via Neural Networks

Integration of vision systems to robotic cells enlarges the potential application of manufacturing systems. Related to this integration is the calibration of cameras which needs the knowledge of the robot and cameras geometries. In this paper we exploit the approximation capabilities of neural networks to avoid the computation of the robot inverse kinematics as well as the inverse task space-camera mapping which involves tedious calibration procedures. The feasibility of the proposed neural controller is illustrated through experiments on a planar robot.

A Fourier Series Neural Network and Its Application to System Identification

A distinctive neural network architecture, called the Fourier Series Neural Network (FSNN), is developed with particular consideration for applications in the area of system identification and control. This paper focuses on the theory of the FSNN and its application to system identification. This neural network is based on the topological structure of the multiple Fourier series, and is shown to be free of local minima. The global stability of the FSNN learning dynamics is guaranteed using the Delta learning rule. This paper demonstrates that the trained FSNN model approximates the Fourier series representation of an identified system with the network state weights approximating the coefficients of the Fourier series. This feature enables the FSNN to estimate the frequency spectrum of an unknown system, making the FSNN a powerful tool for controller design or on-line adaptive tuning based on system frequency response. The capabilities of the FSNN are demonstrated for linear and nonlinear systems by applying the FSNN to estimate the amplitude and phase spectrums of a second order linear transfer function and to model nonlinear inverse robot kinematics. These evaluations indicate that the FSNN modeling technique is applicable to both linear and nonlinear systems with multi-inputs and multi-outputs.

Application of the general elimination method in robot kinematics

A general method for solving the robot inverse kinematics problem is presented. The method is based upon the general elimination method to obtain the equivalent system of equations which are ‘triangularized’ and the solutions of the inverse kinematics problem can be solved by backsubstitutions.

Direct adaptive impedance control of robot manipulators

AbstractThis article presents an adaptive scheme for controlling the end‐effector impedance of robot manipulators. The proposed control system consists of three subsystems: a simple “filter” that characterizes the desired dynamic relationship between the end‐effector position error and the end‐effector/environment contact force, an adaptive controller that produces the Cartesian‐space control input required to provide this desired dynamic relationship, and an algorithm for mapping the Cartesian‐space control input to a physically realizable joint‐space control torque. The controller does not require knowledge of either the structure or the parameter values of the robot dynamics and is implemented without calculation of the robot inverse kinematic transformation. As a result, the scheme represents a general and computationally efficient approach to controlling the impedance of both nonredundant and redundant manipulators. Furthermore, the method can be applied directly to trajectory tracking in free‐space motion by removing the impedance filter. Computer simulation results are given for a planar four degree‐of‐freedom redundant robot under adaptive impedance control. These results demonstrate that accurate end‐effector impedance control and effective redundancy utilization can be achieved simultaneously by using the proposed controller.

Robot manipulator control for hazardous waste‐handling applications

AbstractThe U.S. Department of Energy has identified robotics as a major technology to be utilized in its program of environmental restoration and waste management, and in particular has targeted robotic handling of hazardous waste to be an essential element in this program. Successful performance of waste‐handling operations will require a robot to perform complex tasks involving both accurate positioning of its end effector and compliant contact between the end effector and the environment, and will demand that these tasks be completed in uncertain surroundings. This article focuses on the development of a robot control system capable of meeting the requirements of hazardous‐waste‐handling applications and presents as a solution an adaptive scheme for controlling the mechanical impedance of kinematically redundant manipulators. The proposed controller is capable of accurate end effector impedance control and effective redundancy utilization, does not require knowledge of the complex robot dynamic model or parameter values for the robot or the environment, and is implemented without calculation of the robot inverse kinematic transformation. Computer simulation results are given for a 4 degree of freedom redundant robot under adaptive impedance control. These results indicate that the proposed controller is capable of successfully performing tasks of importance in robotic waste‐handling applications.

Computer generation of symbolic kinematics for robot manipulators

Computer generation of symbolic solutions for the direct and inverse robot kinematics is a desired capability not previously available to robotics engineers. In this article, we present a methodology for the design of a software system capable of solving the direct and inverse kinematics for n degree of freedom (dof) manipulators in symbolic form. The inputs to the system are the Denavit-Hartenberg parameters of the manipulator. The outputs of the system are the direct and inverse kinematics solutions in symbolic form. The system consists of a symbolic processor to perform matrix and algebraic manipulations and an expert system to solve the class of nonlinear equations involved in the solution of the inverse kinematics problem. The system can be used to study robot kinematics configurations whose inverse kinematics solutions are not known to exist a priori. Two examples are included to illustrate its capabilities. The first example provides explicit analytical solutions, previously believed nonexistent, for a 3 dof manipulator. A second example is included for a robot whose inverse kinematics solution requires intensive algebraic manipulations.

A study of robot inverse kinematics based upon the solution of differential equations

This article presents an improved numerical algorithm for robot inverse kinematics which is based upon the solution of the first-order differential equations arising from the manipulator's velocity Jacobian relations. The use of the Adams-Moulton predictorcorrector scheme leads to a fourth-order trajectory following in the joint space. The implementation of a strict descent feature for the trajectory error at the end-effector level contributes to the robustness of the algorithm near singularities. The execution of this algorithm is about 2.7 times faster than that of Gupta and Kazerounian,16 with much of the speed up coming from the use of software optimizations. Several issues related to the accuracy, convergence, speed, real-time computation, and portability of this algorithm are discussed.

An adaptive scheme for robot joint trajectory generation

AbstractIt has been shown recently that robot inverse kinematic transformation can be easily carried out by using a nonlinear dynamic system called “joint space command generator.” In this paper, an adaptive version of the command generator is proposed. The main feature of this command generator is that the inverse Jacobian is estimated on‐line (using least‐squares algorithms), thus the explicit form of the inverse Jacobian is not required. Since the Jacobian is dependent on the end‐effector orientation representation, the adaptive command generator is then inherently flexible in accommodating any choice of orientation representation during Cartesian trajectory planning. The only knowledge required is the forward kinematics of the robot. Thus inverse kinematic transformation of robot trajectories can be carried out with a minimum amount of kinematic information. Extensive simulation studies of the proposed scheme have been carried out which showed that the adaptive command generator is computationally feasible and highly accurate. Different orientation representations have been tested with equal success. Some typical simulation results are presented to illustrate the performance of the adaptive command generator.

A numerical algorithm for solving robot inverse kinematics

SUMMARYAn extension of the inverse kinematics algorithm by Gupta and Kazerounian is presented. The robot kinematics is formulated by using the Zero Reference Position Method. Euler parameters and the related vector forms of the spatial rotation concatenation have been used to improve the efficiency of the velocity Jacobian computation. The joint rates are formally integrated by using a modified predictor-corrector method particularized to robot inverse kinematics – it is a strict descending, p(1)c(0 – n), variable step algorithm. The definitions of the rotational error and overall error measure have been revised. Depending upon the convergence criteria used, these modifications reduce the overall computational time by 20%.

A modular architecture for inverse robot kinematics

A modular architecture for general-purpose inverse robot kinematics is developed. The authors synthesize kinematic modules for the robot arm and wrist and develop computational blocks to describe their respective functions. They then present an analytical framework that defines the inverse kinematic problem in terms of the proper coordination of the kinematic modules to accomplish the desired robot task. In this general-purpose framework, the inverse kinematics problem is always solvable in the feasible regions of the robot workspace, irrespective of whether the solution is analytically tractable. The modular architecture is based upon a nonlinear equation solver for which the Banach fixed-point theorem provides the theoretical basis. The proposed framework allows for the mathematical definition of the region in the robot workspace where convergence to the correct solution is guaranteed. It is insensitive to the initial estimates and provides for the computation of multiple solutions. >

Quaternions Applied to Direct and Inverse Robot Kinematics Problems

The trigonometry and vectors coordinate geometry have demostra ted some deficiences like tools to manipulate a robot. The properties of quaternions and how they can be applied are exposed. An example is given to show how to use the quaternions in an arm manipulator.

A complete generalized solution to the inverse kinematics of robots

The kinematic transformation between task space and joint configuration coordinates is nonlinear and configuration dependent. A solution to the inverse kinematics is a vector of joint configuration coordinates that corresponds to a set of task space coordinates. For a class of robots closed form solutions always exist, but constraints on joint displacements cannot be systematically incorporated in the process of obtaining a solution. An iterative solution is presented that is suitable for any class of robots having rotary or prismatic joints, with any arbitrary number of degrees of freedom, including both standard and kinematically redundant robots. The solution can be obtained subject to specified constraints and based on certain performance criteria. The solution is based on a new rapidly convergent constrained nonlinear optimization algorithm which uses a modified Newton-Raphson technique for solving a system nonlinear equations. The algorithm is illustrated using as an example a kinematically redundant robot.