A ZONOTOPE-BASED APPROACH FOR MANIPULABILITY STUDY OF REDUNDANT ROBOT LIMBS

2013 ◽  
Vol 10 (03) ◽  
pp. 1350023 ◽  
Author(s):  
BERTRAND TONDU
Keyword(s):  
Joint Space ◽  
Structure Model ◽  
Regional Structure ◽  
Humanoid Robotics ◽  
Volume Measure ◽  
Manipulability Measure ◽  
Joint Velocity ◽  
Serial Chains ◽  
Kinematic Efficiency ◽  
Original Formula

Kinematic efficiency of robot limbs can be analyzed by means of the manipulability concept defined by Yoshikawa. However, when it is applied to redundant serial chains, that are the most common case in humanoid robotics, Yoshikawa's manipulability measure is not able to take into account the joint velocity range of each robot joint. In order to overcome this difficulty we propose to substitute in the place of the manipulability ellipsoid a manipulability zonotope resulting from the robot Jacobian transform of the joint velocities parallelotope. The proposed manipulability zonotope notion is similar to the well-known manipulability polytope notion, but its associated volume measure can take benefit of the so-called zonotope theory. By means of a famous and powerful theorem about the cubical dissection of any zonotope, an original formula of manipulability measure is proposed from which is also derived a mean manipulability estimate associated to a given joint space working. The proposed tools are applied to a kinematic analysis of a 4R-regional structure model of the upper limb.

Natural Resolution of Ill-Posed Inverse Kinematics for Redundant Robots: A Challenge to Bernstein’s Degrees-of-Freedom Problem

2006 ◽  
Vol 18 (5) ◽  
pp. 651-660 ◽  
Author(s):  
Suguru Arimoto ◽  
◽  
Masahiro Sekimoto ◽  
Keyword(s):  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Sensory Feedback ◽  
Joint Space ◽  
Dimensional Manifold ◽  
Reaching Task ◽  
Loop Dynamics ◽  
Ill Posed ◽  
Human Limb ◽  
Joint Velocity

Over half a century ago, A. N. Bernstein observed that “dexterity” in human limb movement emerges from the involvement of multijoint motion with surplus degrees of freedom (DOF). Robotics posits that DOF redundancy in robot may enhance dexterity and versatility. Kinematic redundancy involves the problem of ill-posed inverse kinematics from task-description space to joint space. This problem is conventionally avoided by introducing an artificial performance index and uniquely determining an inverse kinematics solution by minimizing it. Instead of taking this conventional avoidance solution, we propose challenging Bernstein’s DOF problem by introducing two direct novel concepts - stability on a manifold and transferability to a submanifold - in dealing with human multijoint movement in reaching and showing that sensory feedback from task space to joint space together with adequate damping (joint velocity feedback) enables any solution to overall closed-loop dynamics to converge naturally and coordinately to a lower-dimensional manifold describing a set of joint states fulfilling a given motion task. This means that a reaching task is accomplished by sensory feedback with the appropriate choice of a stiffness parameter and damping coefficients without having to consider inverse kinematics. We also show that these concepts cope with the annoying “variability” of redundant joint motion seen typically in skilled human reaching. In conclusion, we propose a virtual spring/damper hypothesis that leads to natural control of skilled movement in redundant multijoint reaching.

A Singularity Avoiding Kinematic Solution for a Four-Jointed Robot Wrist Using Heuristic Algorithm

1992 ◽  
Author(s):  
Wei-Ming Lee
Keyword(s):  
Joint Space ◽  
Time Interval ◽  
Time Intervals ◽  
Singularity Avoidance ◽  
Numerical Result ◽  
Robot Wrist ◽  
Singular Configuration ◽  
Trajectory Generation Algorithm ◽  
Joint Velocity ◽  
Kinematic Solution

Abstract In this paper, a heuristic, singularity avoiding, trajectory generation algorithm is developed to solve the singularity problem of a four-jointed robot wrist. Starting from the inverse velocity solutions, a reduced Jacobian matrix is composed to map the system between the joint space and workspace. Six linear combinations of the joint rates are constructed to be used as a family of constraint functions. The forecasting function is very important in the whole algorithm. It is necessary to know in advance if the system is going into or near a singular configuration. The algorithm will determine through forecasting whether to switch from the current constraint function to another which possesses the smallest maximum joint velocity during the forecasting time interval. Trajectories which partially cover the wrist workspace are generated to prove singularity avoidance. The numerical result is shown in the maximum of the min-max joint velocity in different time intervals. It is indicated that the forecasting time interval will effect the singularity avoidance.

Kinematic modeling of a 7-degree of freedom spatial hybrid manipulator for medical surgery

2017 ◽  
Vol 232 (1) ◽  
pp. 12-23 ◽  
Author(s):  
Amanpreet Singh ◽  
Ekta Singla ◽  
Sanjeev Soni ◽  
Ashish Singla
Keyword(s):  
Closed Loop ◽  
Direct Method ◽  
Kinematic Model ◽  
Degree Of Freedom ◽  
Parameter Method ◽  
Kinematic Modeling ◽  
Hybrid Manipulator ◽  
Prime Objective ◽  
Joint Velocity ◽  
Serial Chains

The prime objective of this work is to deal with the kinematics of spatial hybrid manipulators. In this direction, in 1955, Denavit and Hartenberg proposed a consistent and concise method, known as D-H parameters method, to deal with kinematics of open serial chains. From literature review, it is found that D-H parameter method is widely used to model manipulators consisting of lower pairs. However, the method leads to ambiguities when applied to closed-loop, tree-like and hybrid manipulators. Furthermore, in the dearth of any direct method to model closed-loop, tree-like and hybrid manipulators, revisions of this method have been proposed from time-to-time by different researchers. One such kind of revision using the concept of dummy frames has successfully been proposed and implemented by the authors on spatial hybrid manipulators. In that work, authors have addressed the orientational inconsistency of the D-H parameter method, restricted to body-attached frames only. In the current work, the condition of body-attached frames is relaxed and spatial frame attachment is considered to derive the kinematic model of a 7-degree of freedom spatial hybrid robotic arm, along with the development of closed-loop constraints. The validation of the new kinematic model has been performed with the help of a prototype of this 7-degree of freedom arm, which is being developed at Council of Scientific & Industrial Research–Central Scientific Instruments Organisation Chandigarh to aid the surgeon during a medical surgical task. Furthermore, the developed kinematic model is used to develop the first column of the Jacobian matrix, which helps in providing the estimate of the tip velocity of the 7-degree of freedom manipulator when the first joint velocity is known.

A Unified Approach for Second-Order Control of the Manipulator With Joint Physical Constraints

2017 ◽  
Vol 9 (4) ◽  
Author(s):  
Pei Jiang ◽  
Shuihua Huang ◽  
Ji Xiang ◽  
Michael Z. Q. Chen
Keyword(s):  
Joint Space ◽  
Second Order ◽  
The Self ◽  
Dynamic Feedback ◽  
Unified Approach ◽  
Physical Constraints ◽  
Dynamic Feedback Control ◽  
Joint Limits ◽  
Joint Velocity ◽  
Self Motion

Kinematic control of manipulators with joint physical constraints, such as joint limits and joint velocity limits, has received extensive studies. Many studies resolved this problem at the second-order kinematic level, which may suffer from the self-motion instability in the presence of persistent self-motion or unboundedness of joint velocity. In this paper, a unified approach is proposed to control a manipulator with both joint limits and joint velocity limits at the second-order kinematic level. By combining the weighted least-norm (WLN) solution in the revised joint space and the clamping weighted least-norm (CWLN) solution in the real joint space, the unified approach ensures the joint limits and joint velocity limits at the same time. A time-variant clamping factor is incorporated into the unified approach to suppress the self-motion when the joint velocity diverges, or the end-effector stops, which improves the stability of self-motion. The simulations in contrast to the traditional dynamic feedback control scheme and the new minimum-acceleration-norm (MAN) scheme have been made to demonstrate the advantages of the unified approach.

scholarly journals Simulación del Modelo Matemático de la Cinemática Diferencial de Robots Seriales Planos Configuración RRR y RPR

2019 ◽  
pp. 1-8
Author(s):  
Patricio Martinez-Zamudio ◽  
Victor Gonzalez-Villela ◽  
Hector Leon-Nuñez
Keyword(s):  
Jacobian Matrix ◽  
Kinematic Model ◽  
Joint Space ◽  
Differential Model ◽  
End Effector ◽  
Model And Simulation ◽  
Serial Robot ◽  
Serial Chains ◽  
Robot Configurations ◽  
The Relationship

This article presents the model and simulation of the serial robot configurations of the types RRR and RPR, applying the theories of differential kinematics, to obtain the representation of its mathematical model (Jacobian matrix) and its simulation. The differential kinematics in robotics is the relationship between vector spaces, so it is possible to make the velocity map in the joint space in the end effector workspace. We present the differential kinematic model that is obtained from the position kinematics by differentiation techniques and with the help of the asymmetric matrix we obtain the information that is part of the Jacobian matrix, which allows us to know the velocities of the joint variables as a function of linear and angular velocity in the end effector and vice versa. The simulation of the manipulators is carried out validating the mathematical differential model; through the validation of the differential kinematics of serial chains it is possible to apply the procedure to complicated manipulator robots. The method presented here is the basis of a useful tool for solving complex robots, as in the case of redundant, parallel and hybrid serial manipulator robots.

Passivity-Based Interaction Controller and Observer for Robot Manipulators

1998 ◽  
Vol 120 (4) ◽  
pp. 516-520
Author(s):  
Bruno Siciliano ◽  
Luigi Villani
Keyword(s):  
Robot Manipulator ◽  
Industrial Robot ◽  
Force Sensor ◽  
Joint Space ◽  
Control Architecture ◽  
End Effector ◽  
Control Scheme ◽  
Open Control ◽  
Joint Velocity ◽  
Environment Regulation

This work presents the design of a passivity-based controller and observer for a robot manipulator interacting with a compliant environment. Regulation of the contact force along the constrained direction and tracking of the end-effector position along the unconstrained directions is achieved; semiglobal exponential stability is proved. The control scheme is implemented in the joint space, and experimental results are illustrated for an open control architecture industrial robot which is endowed with joint position sensors and wrist force sensor, but no joint velocity sensors.

Fast calibration of CBED patterns for quantitative analysis

1993 ◽  
Vol 51 ◽  
pp. 674-675
Author(s):  
M.A. Gribelyuk ◽  
M. Rühle
Keyword(s):  
Reciprocal Lattice ◽  
Accurate Determination ◽  
Incident Beam ◽  
Crystal Thickness ◽  
Structure Model ◽  
Beam Direction ◽  
Transmitted Beam ◽  
Reciprocal Vector ◽  
On Line

A new method is suggested for the accurate determination of the incident beam direction K, crystal thickness t and the coordinates of the basic reciprocal lattice vectors V1 and V2 (Fig. 1) of the ZOLZ plans in pixels of the digitized 2-D CBED pattern. For a given structure model and some estimated values Vest and Kest of some point O in the CBED pattern a set of line scans AkBk is chosen so that all the scans are located within CBED disks.The points on line scans AkBk are conjugate to those on A0B0 since they are shifted by the reciprocal vector gk with respect to each other. As many conjugate scans are considered as CBED disks fall into the energy filtered region of the experimental pattern. Electron intensities of the transmitted beam I0 and diffracted beams Igk for all points on conjugate scans are found as a function of crystal thickness t on the basis of the full dynamical calculation.

Sign in / Sign up

Export Citation Format

Share Document