Task Space Coordinates Research Articles

Learning to manipulate a whip with simple primitive actions – A simulation study

This simulation study investigated whether a 4-degrees-of-freedom (DOF) arm could strike a target with a 50-DOF whip using a motion profile similar to discrete human movements. The interactive dynamics of the multi-joint arm was modeled as a constant joint-space mechanical impedance, with values derived from experimental measurement. Targets at various locations could be hit with a single maximally smooth motion in joint-space coordinates. The arm movements that hit the targets were identified with fewer than 250 iterations. The optimal actions were essentially planar arm motions in extrinsic task-space coordinates, predominantly oriented along the most compliant direction of both task-space and joint-space mechanical impedances. Of the optimal movement parameters, striking a target was most sensitive to movement duration. This result suggests that the elementary actions observed in human motor behavior may support efficient motor control in interaction with a dynamically complex object.

Design development and control of a shape memory alloy linear actuation based XYθ motion stage

This article addresses the development and trajectory tracking analysis of the three degrees of freedom Shape memory alloy (SMA) actuation-based 4- P PR motion stage. The developed motion stage is of four legs of the PPR (Prismatic-Prismatic-Revolute) configuration, having the first prismatic joint as the active joint. SMA spring is incorporated as the linear actuator of the motion stage. The three degrees of freedom motion of the end-effector is achieved based on a new type of SMA-driven PPR joint configuration to provide two translations and one rotational motion. The advantages of the SMA as an actuator is such as lightweight, higher accuracy, and micron-level movement to establish linear motion and silent actuation. The kinematic and jacobian relations are derived for the developed motion stage. The actuation of the SMA (Nitinol) spring actuator is accomplished by the use of a programmable power supply. In addition, the close loop PID control scheme to the SMA linear actuator is investigated. The mechanism has some inherent errors, as geometric errors (kinematic error), friction between the elements of the mechanism, etc, are significant issues in tracking the trajectory of the motion stage. Thus, to address the above issues, this study incorporates the dual-loop control scheme for better trajectory tracking and error compensation of the proposed motion stage. The control method employs a redundant feedback approach, in which discrete joint space displacements and mobile platform coordinates, and task space coordinates are determined as feedback signal using suitable sensors. In this control scheme, the actual joint displacement errors are computed using the redundant feedback data and corrected the desired joint displacement trajectory to obtain the desired task space trajectory. To measure the effectiveness of the used control scheme, a real-time prototype of the proposed motion stage (4- P PR) is developed and investigated the performance of the control method using some simple geometric trajectories. It is observed from the experiments that the motion stage using SMA linear actuation technique has good tracking performance using the control scheme. The developed motion stage can be implemented in the micro-stereolithography process and micron-level positioning application.

Time-Optimal Path Following for Robotic Manipulation of Loosely Placed Objects: Modeling and Experiment

A consistent method is presented for solving the so-called general waiter problem, which resembles the general task of manipulating several objects that are loosely placed on a robot, rather than grasped or fixed otherwise. The waiter problem consists of moving a tray (mounted at the end-effector of a robot) with a number of cups, from one pose to another as fast as possible such that the cups do not slide at any time. The geometric path of the tray motion is prescribed while the attitude of the tray must vary. The basis for any optimization and realtime control is a reliable dynamic model of the robot. Therefore a parameter identification is performed using optimized persistent excitation trajectories. The optimization problem is solved with a multiple shooting method which determines the robot trajectory. For the considered wrist-partitioned robot, the motion is described by the joint coordinates of the translation part and the angles describing the orientation of the tray. This combination of joint and task space coordinates is beneficial for solving the optimal control problem (convergence is increased). The optimization accounts for the technical limitations of the robot as well as the limiting friction of the cups. Experimental results with 4 cups for a time-optimal motion are shown. A crucial aspect is the use of a model-based control strategy, along with the identified parameters.

Cooperative r-Passivity Based Control for Mechanical Systems

In this work we consider the problem of cooperative end-effector control between heterogeneous fully actuated agents when varying-time delays and/or packet loss are present. We couple agents via outputs encoded with task-space coordinates and velocities that are transformed into wave-variables to overcome the destabilising effects of the communication network. The scheme poses dynamic requirements on the agents which are locally satisfied with feedback control that integrates subtasks, such as joint-limit avoidance or local tracking, when there are redundant degrees-of-freedom. The proposed approach extends existing methods to task-space control. The approach is robust to network effects, applies to nonlinear systems and is scalable by design. The tuning task is simplified considerably by separation of the cooperative and non-cooperative control terms. We demonstrate the efficacy of the proposed approach experimentally.

Sliding Mode Control of Cable‐Driven Redundancy Parallel Robot with 6 DOF Based on Cable‐Length Sensor Feedback

The sliding mode control of the cable‐driven redundancy parallel robot with six degrees of freedom is studied based on the cable‐length sensor feedback. Under the control scheme of task space coordinates, the cable length obtained by the cable‐length sensor is used to solve the forward kinematics of the cable‐driven redundancy parallel robot in real‐time, which is treated as the feedback for the control system. First, the method of forward kinematics of the cable‐driven redundancy parallel robot is proposed based on the tetrahedron method and Levenberg‐Marquardt method. Then, an iterative initial value estimation method for the Levenberg‐Marquardt method is proposed. Second, the sliding mode control method based on the exponential approach law is used to control the effector of the robot, and the influence of the sliding mode parameters on control performance is simulated. Finally, a six‐degree‐of‐freedom position tracking experiment is carried out on the principle prototype of the cable‐driven redundancy parallel robot. The experimental results show that the robot can accurately track the desired position in six directions, which indicates that the control method based on the cable‐length sensor feedback for the cable‐driven redundancy parallel robot is effective and feasible.

Reference trajectory tracking for a multi-DOF robot arm

Abstract This paper presents the problem of tracking the generated reference trajectory by the simulation model of a multi-DOF robot arm. The kinematic transformation between task space and joint configuration coordinates is nonlinear and configuration dependent. To obtain the solution of the forward kinematics problem, the homogeneous transformation matrix is used. A solution to the inverse kinematics is a vector of joint configuration coordinates calculated using of pseudoinverse Jacobian technique. These coordinates correspond to a set of task space coordinates. The algorithm is presented which uses iterative solution and is simplified by considering stepper motors in robot arm joints. The reference trajectory in Cartesian coordinate system is generated on-line by the signal generator previously developed in MS Excel. Dynamic Data Exchange communication protocol allows sharing data with Matlab-Simulink. These data represent the reference tracking trajectory of the end effector. Matlab-Simulink software is used to calculate the representative joint rotations. The proposed algorithm is demonstrated experimentally on the model of 7-DOF robot arm system.

KINEMATIC MODELLING AND ANALYSIS OF A WIRE-ACTUATED PARALLEL MANIPULATOR

The kinematic modelling and analysis of a 4 degrees of freedom wire-actuated parallel manipulator with redundant actuation is investigated. The manipulator employs combinations of rigid links, joints and wires. Hybrid actuation of joints and wires, two actuated joints and three actuated wires, is used. Position and first and second order kinematics of the closed-loop manipulator are formulated based on matrix exponentials. The transfer of first and second order kinematic variables, i.e., wire/joint velocities and accelerations, among the manipulator task space coordinates, active and passive joint coordinates and wire lengths are provided.

Robust nonlinear task space control for 6 DOF parallel manipulator

This paper presents a robust nonlinear controller equipped with a friction estimator for a 6 degree of freedom (DOF) parallel manipulator in the task space coordinates. The requisite 6 DOF system states for the task space control are acquired by an alpha–beta tracker and a numerical forward kinematic solution. The Friedland–Park friction observer in the joint space coordinates provides friction estimates that help to improve the control performance. Finally, the RNTC turns out to outper form a nonlinear task space control and a popularly adopted PID control with the friction estimator in the joint space coordinates.

Base invariance of the manipulability index

The manipulability index suggested by Yoshikava is an important tool for the design of mechanisms and their control. It represents a quantitative measure of the functionality and the ability for realizing some tasks or groups of tasks. This index is some kind of performance measure and should be taken into consideration in the design phase of a mechanism and also in the design of control algorithms.In this paper two important properties of the manipulability index are investigated. The first part of the present work demonstrates that manipulability of a mechanism is independent of task space coordinates. In the second part, a proof of the independency of the manipulability index on the first DOF is given.This invariance is important for simplification of the mechanism's Jacobian matrix and gives excellent insight into the dependences of configuration space coordinates on this index. Moreover, it proves that the manipulability index is determined only by relative positions of the mechanism itself and by the mechanism's geometry.Finally, the properties of the manipulability index are illustrated by some examples for fundamental open kinematical chain structures.

Range identification for perspective vision systems

In this note, a new observer is developed to determine range information (and, hence, the three-dimensional (3-D) coordinates) of an object feature moving with affine motion dynamics (or the more general Ricatti motion dynamics) with known motion parameters. The unmeasurable range information is determined from a single camera provided an observability condition is satisfied that has physical significance. To develop the observer, the perspective system is expressed in terms of the nonlinear feature dynamics. The structure of the proposed observer is inspired by recent disturbance observer results. The proposed technique facilitates a Lyapunov-based analysis that is less complex than the sliding-mode based analysis derived for recent observer designs. The analysis demonstrates that the 3-D task-space coordinates of the feature point can be asymptotically identified. Simulation results are provided that illustrate the performance of the observer in the presence of noise.

Robust nonlinear control of a 6 DOF parallel manipulator : Task space approach

This paper presents a robust nonlinear controller for a 6 degree of freedom (DOF) parallel manipulator in the task space coordinates. The proposed control strategy requires information on orientations and translations in the task space unlike the joint space or link space control scheme. Although a 6 DOF sensor may provide such information in a straightforward manner, its cost calls for a more economical alternative. A novel indirect method based on the readily available length information engages as a potential candidate to replace a 6 DOF sensor. The indirect approach generates the necessary information by solving the forward kinematics and subsequently applying alpha-beta-gamma tracker. With the 6 DOF signals available, a robust nonlinear task space control (RNTC) scheme is proposed based on the Lyapunov redesign method, whose stability is rigorously proved. The performance of the proposed RNTC with the new estimation scheme is evaluated via experiments. First, the results of the estimator are compared with the rate-gyro signals, which indicates excellent agreement. Then, the RNTC with on-line estimated 6 DOF data is shown to achieve excellent control performance to sinusoidal inputs, which is superior to those of a commonly used proportional-plus-integral-plus-derivative controller with a feedforward friction compensation under joint space coordinates and the nonlinear controller under task space coordinates.

バーチャルレーダによる障害物情報提示システム

During teleoperation, when the operator's attention is concentrated in controlling the end-effector motion, it is very difficult to recognize a possible link collision. Such collision may damage the environment or the link seriously, because usually the link has no sensors. In this paper, we propose a so-called“virtual radar”which displays the collision information considering the whole manipulator at the end-effector level. The computer checks for unreachable areas due to the presence of obstacles and displays the appropriate information mapped in task-space coordinates using a 3D graphical image. This enhances the reliability of the system. However, in the case of a 6 D.O.F manipulator, collision possibility space must be a 6 dimensional one and hence it is difficult to visualize and understand. To tackle this problem, a deformed sphere and patterns on its surface are employed. We have applied this method to a 6 D.O.F. manipulator and have verified the effectiveness of the proposed approach by experiments with a real telerobotic system.

A new adaptive control algorithm for robot manipulators in task space

Adaptive control of robotic manipulators in task space coordinates is considered in this paper. A new composite adaptive control law, which uses the prediction error and tracking error to drive parameter estimation, is developed based on sliding mode and a general Lyapunov-like concept. It is shown that global stability and convergence can be achieved for the adaptive control algorithm. The algorithm has the advantage that inverse of Jacobian matrix and the bounded inverse of the estimated inertia matrix are not required. The algorithm is further modified so as to achieve robustness to bounded disturbances. A simulation example is provided to demonstrate the performance of the proposed algorithm.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A Sensitivity Analysis Based Method for Robot Calibration

A new robot kinematic calibration procedure is presented. The parameters of the kinematic model are estimated through a relationship established between the deviations in the joint variables and the deviations in the model parameters. Thus, the new method can be classified as an inverse calibration procedure. Using suitable sensitivity analysis methods, the matrix of the partial derivatives of joint variables with respect to robot parameters is calculated without having explicit expressions of joint variables as a function of task space coordinates (closed inverse kinematic solution). This matrix provides the relationship between the changes in the joint variables and the changes in the parameter values required for the calibration. Two deterministic sensitivity analysis methods are applied, namely the Direct Sensitivity Approach and the Adjoint Sensitivity Method. The new calibration procedure was successfully tested by the simulated calibrations of a two-degree-of-freedom revolute-joint planar manipulator.

Robust tracking control of rigid-link electrically-driven robots

A robust tracking controller for rigid-link electrically driven (RLED) robot manipulators operating in free-space or under motion constraints is introduced. Using models of the robot dynamics and environmental constraints, a dynamic model with decoupled position and force degrees of freedom is obtained for the mechanical subsystem with respect to a set of task-space coordinates. A robust tracking control is then formulated for the decoupled manipulator dynamics and the electrical actuator dynamics, which yields a global uniform ultimate bounded (GUUB) stability result for the position and velocity tracking error. The controller is robust with respect to parametric uncertainties and additive bounded disturbances in the RLED dynamic model. The controller requires measurement of the robot link positions, link velocities, and motor armature currents.

Implementation of robust impedance and force control

In this paper, we discuss the problem of implementing impedance control in the presence of model uncertainties and its application to robot force control. We first propose a sliding mode-based impedance controller. The implementation of the targeted impedance, and the preservation of stability in the presence of model uncertainties, are the key issues in the proposed approach. Using sliding mode control, a simple and robust algorithm is obtained so that the targeted impedance can be accurately implemented without the exact model of the robot. The controller is designed in terms of the task space coordinates. The chattering in the sliding mode control is eliminated by using a continuous function. The problem of force control is also addressed for the impedance controlled robot. An off-line estimation method of the environment model is suggested and used in the force control scheme. The proposed impedance and force control schemes have been experimentally verified on a two degree-of-freedom direct-drive robot arm. The experimental results are presented in this paper.

マニピュレータの2次調和平均型可操作性指標について

This is a mathematical study on the properties and the characteristics of the quadra-harmonic mean type manipulability index (H2).There are several essential properties of manipulability indices which ensure that an index can be conveniently applied to actual theoretical or numerical analyses of robotic arms; i.e. that the index is: (1) scalar valued; (2) based on the singular values of Jacobian matrix; (3) independent of the task space coordinates; (4) expressed as an analytic function; and that (5) the index has a closed algorithm. But few studies have paid enough attention to them.This paper discusses first the geometric meanings of the index H2, and it shows that the inverse of the index value coincides with the square mean root velocity in the joint coordinates space corresponding to the randomly given reference velocity in the task space.Second, it is proved that the index H2 has the essential properties described above. Special attention is paid to the analyticity of the index function.Furthermore, it is also proved that the value of the index H2 approximates minimal singular value of the Jacobian matrix within a neighborhood of each kinematic singular point, while it approximates the arithmetic mean of singular values within a neighborhood of each kinematically isotropic point. These approximated values express the manipulability best, but they do not have closed formulae nor simple numerical algorithms. These approximations are also illustrated graphically.

A Task Space Decoupling Approach to Hybrid Control of Manipulators

A scheme for dynamic hybrid control of robot manipulators is presented. The design is directly achieved in task space coordinates. In this way, the inherent orthogonality between force and velocity description of tasks is preserved and overspecification is avoided in the control synthesis. A nonlinear decoupling and linearizing feedback law is obtained which yields invariant control performances over time-varying tasks. The effect of a robustifying integral action is discussed. Simulation results are reported for a two-link arm.

A New Approach to Kinematic Control of Robot Manipulators

A new approach for solving the inverse kinematics problem iteratively is presented. The solution is based on the recursive estimation of a kinematics operator which maps the task space coordinates into joint coordinates. The recursive estimation is based on least square approximation. For controlling the robot, the solution (Joint coordinates) must be compensated to achieve an arbitrarily small error (in least square sense) of the desired task space coordinates. The compensation is provided by closed loop feedback of task space coordinates using an optimal control approach.

A solution to the inverse kinematics of redundant manipulators

AbstractA solution to the inverse kinematics is a set of joint coordinates which correspond to a given set of task space coordinates (position and orientation of end effector). For the class of kinematically redundant robots, the solution is generically nonunique such that special methods are required for obtaining a solution. The method addressed in the paper, introduced earlier and termed “generalized inverse,” is based on a certain partitioning of the Jacobian functional corresponding to a nonlinear relationship of the inverse kinematics type. The article presents a new algorithm for solving the inverse kinematics using the method of generalized inverse based on a modified Newton‐Raphson iterative technique. The new algorithm is efficient, converges rapidly, and completely generalizes the solution of the inverse kinematics problem for redundant robots. The method is illustrated by numerical examples.