Inverse Kinematics of Discretely Actuated Ball-Joint Manipulators Using Workspace Density

2015 ◽  
Author(s):  
Hui Dong ◽  
Taosha Fan ◽  
Zhijiang Du ◽  
Gregory Chirikjian
Keyword(s):  
Fourier Transform ◽  
Computational Complexity ◽  
Inverse Kinematics ◽  
Solution Space ◽  
Rotation Group ◽  
Ball Joint ◽  
End Effector ◽  
Numerical Examples ◽  
One Dimensional ◽  
Elegant Form

We present a workspace-density-based (WSDB) method to solve the inverse kinematics of discretely actuated ball-joint manipulators. Intuitively speaking, workspace density measures the flexibility of a robotic manipulator when the end-effector is fixed at a certain pose or position. We use the SE(3) Fourier transform to derive the workspace density for ball-joint manipulators and show that the workspace density has a concise and elegant form. Then we show that the state for each joint is determined by maximizing the workspace density of subsequent sub-manipulators. We demonstrate our method with several numerical examples. In particular, we show that our method can provide a solution that approximately minimizes the deviation of the end-effector and its computational complexity is linear with respect to the number of joints. Hence our method is very efficient in solving the inverse kinematics of redundant discretely actuated ball-joint manipulators. In addition, we prove that the solution space of our method is reduced from the rotation group SO(3) to a one-dimensional interval.

scholarly journals Beam-Doppler Unitary ESPRIT for Multitarget DOA Estimation

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Cai Wen ◽  
Yan Zhou ◽  
Mingliang Tao ◽  
Jianxin Wu ◽  
Jinye Peng
Keyword(s):  
Fourier Transform ◽  
Computational Complexity ◽  
Doa Estimation ◽  
Critical Issue ◽  
Radar System ◽  
Estimation Accuracy ◽  
Invariance Property ◽  
Multitarget Tracking ◽  
Numerical Examples ◽  
System A

High-resolution direction of arrival (DOA) estimation is a critical issue for mainbeam multitarget tracking in ground-based or airborne early warning radar system. A beam-Doppler unitary ESPRIT (BD-UESPRIT) algorithm is proposed to deal with this problem. Firstly, multiple snapshots without spatial aperture loss are obtained by using the technique of time-smoothing. Then the conjugate centrosymmetric discrete Fourier transform (DFT) matrix is used to transform the extracted data into beam-Doppler domain. Finally, the rotational invariance property of the space-time beam is exploited to estimate DOA of the target. The DOA estimation accuracy is improved greatly because the proposed algorithm takes full advantage of temporal information of the signal. Furthermore, the computational complexity of the presented algorithm is reduced dramatically, because the degree of freedom after beam transformation is very small and most of the operations are implemented in real-number domain. Numerical examples are given to verify the effectiveness of the proposed algorithm.

Conservative solute transport with periodic velocity and sinusoidal source concentration in semi-infinite porous media: An analytical solution

2014 ◽  
Vol 6 (1) ◽  
pp. 1024-1031
Author(s):  
R R Yadav ◽  
Gulrana Gulrana ◽  
Dilip Kumar Jaiswal
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Laplace Transformation ◽  
Seepage Velocity ◽  
Transformation Technique ◽  
Numerical Examples ◽  
One Dimensional ◽  
Porous Domain ◽  
Conservative Solute Transport ◽  
Source Concentration

The present paper has been focused mainly towards understanding of the various parameters affecting the transport of conservative solutes in horizontally semi-infinite porous media. A model is presented for simulating one-dimensional transport of solute considering the porous medium to be homogeneous, isotropic and adsorbing nature under the influence of periodic seepage velocity. Initially the porous domain is not solute free. The solute is initially introduced from a sinusoidal point source. The transport equation is solved analytically by using Laplace Transformation Technique. Alternate as an illustration; solutions for the present problem are illustrated by numerical examples and graphs.

scholarly journals On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 78
Author(s):  
Haifa Bin Jebreen ◽  
Fairouz Tchier
Keyword(s):  
Differential Equation ◽  
Galerkin Method ◽  
Linear Ordinary Differential Equation ◽  
Time Interval ◽  
Hyperbolic Partial Differential Equation ◽  
Time Step ◽  
Numerical Examples ◽  
One Dimensional ◽  
The Stability ◽  
The Galerkin Method

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

scholarly journals Finite-Horizon Kinetic Energy Optimization of a Redundant Space Manipulator

2021 ◽  
Vol 11 (5) ◽  
pp. 2346
Author(s):  
Alessandro Tringali ◽  
Silvio Cocuzza
Keyword(s):  
Kinetic Energy ◽  
Real Time ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Computational Time ◽  
Redundant Manipulators ◽  
Space Robotics ◽  
Optimal Method ◽  
End Effector ◽  
Global Optimal

The minimization of energy consumption is of the utmost importance in space robotics. For redundant manipulators tracking a desired end-effector trajectory, most of the proposed solutions are based on locally optimal inverse kinematics methods. On the one hand, these methods are suitable for real-time implementation; nevertheless, on the other hand, they often provide solutions quite far from the globally optimal one and, moreover, are prone to singularities. In this paper, a novel inverse kinematics method for redundant manipulators is presented, which overcomes the above mentioned issues and is suitable for real-time implementation. The proposed method is based on the optimization of the kinetic energy integral on a limited subset of future end-effector path points, making the manipulator joints to move in the direction of minimum kinetic energy. The proposed method is tested by simulation of a three degrees of freedom (DOF) planar manipulator in a number of test cases, and its performance is compared to the classical pseudoinverse solution and to a global optimal method. The proposed method outperforms the pseudoinverse-based one and proves to be able to avoid singularities. Furthermore, it provides a solution very close to the global optimal one with a much lower computational time, which is compatible for real-time implementation.

A Hybrid Self-Stressed Cable-Driven Mechanism

2008 ◽  
Author(s):  
Saeed Behzadipour
Keyword(s):  
Static Loading ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Tensile Force ◽  
Cable System ◽  
End Effector ◽  
Stiffness Analysis ◽  
Cable Length ◽  
Cable Drive ◽  
Forward And Inverse Kinematics

A new hybrid cable-driven manipulator is introduced. The manipulator is composed of a Cartesian mechanism to provide three translational degrees of freedom and a cable system to drive the mechanism. The end-effector is driven by three rotational motors through the cables. The cable drive system in this mechanism is self-stressed meaning that the pre-tension of the cables which keep them taut is provided internally. In other words, no redundant actuator or external force is required to maintain the tensile force in the cables. This simplifies the operation of the mechanism by reducing the number of actuators and also avoids their continuous static loading. It also eliminates the redundant work of the actuators which is usually present in cable-driven mechanisms. Forward and inverse kinematics problems are solved and shown to have explicit solutions. Static and stiffness analysis are also performed. The effects of the cable’s compliance on the stiffness of the mechanism is modeled and presented by a characteristic cable length. The characteristic cable length is calculated and analyzed in representative locations of the workspace.

Kinematics of a Fully-Decoupled Remote Center-of-Motion Parallel Manipulator for Minimally Invasive Surgery

2012 ◽  
Vol 6 (2) ◽  
Author(s):  
Chin-Hsing Kuo ◽  
Jian S. Dai
Keyword(s):  
Minimally Invasive Surgery ◽  
Minimally Invasive ◽  
Invasive Surgery ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Surgical Instruments ◽  
End Effector ◽  
Minimally Invasive Surgical ◽  
Inverse Kinematics Problem

A crucial design challenge in minimally invasive surgical (MIS) robots is the provision of a fully decoupled four degrees-of-freedom (4-DOF) remote center-of-motion (RCM) for surgical instruments. In this paper, we present a new parallel manipulator that can generate a 4-DOF RCM over its end-effector and these four DOFs are fully decoupled, i.e., each of them can be independently controlled by one corresponding actuated joint. First, we revisit the remote center-of-motion for MIS robots and introduce a projective displacement representation for coping with this special kinematics. Next, we present the proposed new parallel manipulator structure and study its geometry and motion decouplebility. Accordingly, we solve the inverse kinematics problem by taking the advantage of motion decouplebility. Then, via the screw system approach, we carry out the Jacobian analysis for the manipulator, by which the singular configurations are identified. Finally, we analyze the reachable and collision-free workspaces of the proposed manipulator and conclude the feasibility of this manipulator for the application in minimally invasive surgery.

Parametric Design of a Spherical Eight-Bar Linkage Based on a Spherical Parallel Manipulator

2008 ◽  
Vol 1 (1) ◽  
Author(s):  
Gim Song Soh ◽  
J. Michael McCarthy
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Parametric Design ◽  
Degree Of Freedom ◽  
Kinematics Analysis ◽  
End Effector ◽  
Arbitrary Base ◽  
Three Degree Of Freedom ◽  
Spherical Parallel Manipulator

This paper presents a procedure that determines the dimensions of two constraining links to be added to a three degree-of-freedom spherical parallel manipulator so that it becomes a one degree-of-freedom spherical (8, 10) eight-bar linkage that guides its end-effector through five task poses. The dimensions of the spherical parallel manipulator are unconstrained, which provides the freedom to specify arbitrary base attachment points as well as the opportunity to shape the overall movement of the linkage. Inverse kinematics analysis of the spherical parallel manipulator provides a set of relative poses between all of the links, which are used to formulate the synthesis equations for spherical RR chains connecting any two of these links. The analysis of the resulting spherical eight-bar linkage verifies the movement of the system.

Adding flexibility to the links of a rigid-link dynamic model of an articulated robot

Robotica ◽  
1989 ◽  
Vol 7 (2) ◽  
pp. 165-168 ◽  
Author(s):  
A. Bodner
Keyword(s):  
Computational Complexity ◽  
Dynamic Model ◽  
Euler Equations ◽  
Inverse Dynamics ◽  
Small Degree ◽  
End Effector ◽  
Rigid Link ◽  
Link Model ◽  
Articulated Robot ◽  
Special Case

SUMMARYA method was developed that takes into account flexibility of robot links in the inverse dynamics calculations. This method uses the Newton-Euler equations and is applicable for special case systems that allow for only a small degree of flexibility. Application of the method should improve the accuracy of the position of the end effector during motion of the robot.The results of this study show that the method can be based entirely on an existing rigid-link model with only minimal changes required as additions. The computational complexity of the method is discussed briefly as well and indicates an increase of computations of slightly more than a factor of two as compared to a rigid-link model for the same robot geometry.

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