Inverse Kinematics Solutions for General Spatial Linkages

1987 ◽  
Author(s):  
M. Tucker ◽  
N. D. Perreira
Keyword(s):  
Inverse Kinematics ◽  
Robot Control ◽  
Degrees Of Freedom ◽  
General Purpose ◽  
Inverse Solution ◽  
Six Degrees Of Freedom ◽  
Inverse Kinematics Problem ◽  
Spatial Linkages ◽  
Pseudo Inverse ◽  
Solution Techniques

Abstract A procedure for obtaining solutions to the general inverse kinematics problem for both position and velocity is presented. Solutions to this problem are required for improved robot control and linkage synthesis. The procedure requires obtaining the inverse of the actual robot linkage Jacobian. A procedure to detect the presence of singularities in the Jacobians and their causes are given. Inverse solution techniques applicable to robots with less than, equal to, or greater than six degrees of freedom and their implementation to robots with various types of singularities is outlined. For each case, the implementation of both the complete Moore-Penrose inverse and a robot specific pseudo inverse are included. Although it is not necessary to use the complete Moore-Penrose inverse on any particular robot, it can be used to obtain generic inverse routines for general purpose applications.

3D Modeling and Closed-Form Inverse Kinematics Solution for 6dof Surgical Robot

2013 ◽  
Vol 455 ◽  
pp. 533-538
Author(s):  
Edris Farah ◽  
Shao Gang Liu
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Closed Form Solution ◽  
Inverse Kinematic ◽  
Form Solution ◽  
Surgical Robot ◽  
Decoupling Method ◽  
Six Degrees Of Freedom ◽  
Inverse Kinematics Problem

Since robots began to inter the medical fields, more research efforts and more attention have been given to this kind of robots. In this paper six degrees of freedom surgical robot was studied. The Denavit-Hartenberg parameters of the robot have been computed and 3D model has been built by using open source robotics toolbox. The paper also discussed a closed form solution for the inverse kinematics problem by using inverse kinematic decoupling method.

Realization of a 6-DOF Manipulator With an Unconventional Topological Structure

2008 ◽  
Author(s):  
Keisuke Arikawa
Keyword(s):  
Topological Structure ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Kinematic Structure ◽  
Spherical Joint ◽  
Active Joint ◽  
Six Degrees Of Freedom ◽  
Inverse Kinematics Problem ◽  
Skeletal Model ◽  
And Control

We propose a six-degrees-of-freedom manipulator with an unconventional topological structure. Because of the complex kinematic structure, it might seem that we cannot actually build such a manipulator. However, we show that we can construct a working model and control its hand configuration. First, we discuss the mobility of the proposed manipulator, and present the conditions imposed on the kinematic structure and the active joint selection. Then, we derive a numerical solution of the inverse kinematics problem by making the best use of the mechanical features, and present the simulation results of trajectory tracking of the hand configuration obtained using the solution. Next, under static equilibrium, we derive the conditions for the singular configurations, where the hand cannot support specific force moments. Finally, we construct an equivalent spherical joint that has a large movable range, and we present a working skeletal model of the proposed manipulator using the joints.

Inverse kinematics of six-degree of freedom “general” and “special” manipulators using symbolic computation

Robotica ◽  
1994 ◽  
Vol 12 (5) ◽  
pp. 421-430 ◽  
Author(s):  
C. Mavroidis ◽  
F. B. Ouezdou ◽  
P. Bidaud
Keyword(s):  
Trivial Solution ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Six Degrees Of Freedom ◽  
Industrial Manipulator ◽  
Revolute Joints ◽  
Closure Equation ◽  
Inverse Kinematics Problem ◽  
A Chain ◽  
Six Degree Of Freedom

SUMMARYThis paper presents an algorithm that solves the inverse kinematics problem of all six degrees of freedom manipulators, “general” or “special”. A manipulator is represented by a chain of characters that symbolizes the position of prismatic and revolute joints in the manipulator and the special geometry that may exist between its joint axes. One form of the loop closure equation is chosen and the Raghavan and Roth method is used to obtain symbolically a square matrix. The determinant of this matrix yields the characteristic polynomial of the manipulator in one of the kinematic variables. As an example of the use of this algorithm we present the solution to the inverse kinematics problem of the GMF Arc Mate welding manipulator. In spite of its geometry, this industrial manipulator has a non-trivial solution to its inverse kinematics problem.

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.

Dynamics of redundant robots – inverse solutions

Robotica ◽  
1986 ◽  
Vol 4 (4) ◽  
pp. 263-267 ◽  
Author(s):  
Ronald L. Huston ◽  
Timothy P. King
Keyword(s):  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Solution Algorithm ◽  
Redundant Robot ◽  
Redundant Robots ◽  
Revolute Joints ◽  
Inverse Kinematics Problem ◽  
Inverse Solutions ◽  
Natural Dynamics ◽  
Least Energy

SUMMARYThe dynamics of “simple, redundant robots” are developed. A “redundant” robot is a robot whose degrees of freedom are greater than those needed to perform a given kinetmatic task. A “simple” robot is a robot with all joints being revolute joints with axes perpendicular or parallel to the arm segments. A general formulation, and a solution algorithm, for the “inverse kinematics problem” for such systems, is presented. The solution is obtained using orthogonal complement arrays which in turn are obtained from a “zero-eigenvalues” algorithm. The paper concludes with an assertion that this solution, called the “natural dynamics solution,” is optimal in that it requires the least energy to drive the robot.

Performance-Oriented Design of Inverse Kinematics Algorithms: Extended Jacobian Approximation of the Jacobian Pseudo-Inverse

2012 ◽  
Vol 4 (2) ◽  
Author(s):  
Joanna Karpińska ◽  
Krzysztof Tchoń
Keyword(s):  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Ritz Method ◽  
Approximation Error ◽  
Robotic Manipulators ◽  
Error Functional ◽  
Free Representation ◽  
Pseudo Inverse ◽  
Jacobian Inverse ◽  
Jacobian Algorithm

For redundant robotic manipulators, we study the design problem of Jacobian inverse kinematics algorithms of desired performance. A specific instance of the problem is addressed, namely the optimal approximation of the Jacobian pseudo-inverse algorithm by the extended Jacobian algorithm. The approximation error functional is derived for the coordinate-free representation of the manipulator’s kinematics. A variational formulation of the problem is employed, and the approximation error is minimized by means of the Ritz method. The optimal extended Jacobian algorithm is designed for the 7 degrees of freedom (dof) POLYCRANK manipulator. It is concluded that the coordinate-free kinematics representation results in more accurate approximation than the coordinate expression of the kinematics.

Impedance Control: An Approach to Manipulation: Part II—Implementation

1985 ◽  
Vol 107 (1) ◽  
pp. 8-16 ◽  
Author(s):  
Neville Hogan
Keyword(s):  
Feedback Control ◽  
Inverse Kinematics ◽  
Control Algorithm ◽  
Degrees Of Freedom ◽  
Impedance Control ◽  
Dynamic Interaction ◽  
End Point ◽  
Inverse Kinematics Problem ◽  
Theoretical Reasoning ◽  
Redundant Actuators

This three-part paper presents an approach to the control of dynamic interaction between a manipulator and its environment. Part I presented the theoretical reasoning behind impedance control. In Part II the implementation of impedance control is considered. A feedback control algorithm for imposing a desired cartesian impedance on the end-point of a nonlinear manipulator is presented. This algorithm completely eliminates the need to solve the “inverse kinematics problem” in robot motion control. The modulation of end-point impedance without using feedback control is also considered, and it is shown that apparently “redundant” actuators and degrees of freedom such as exist in the primate musculoskeletal system may be used to modulate end-point impedance and may play an essential functional role in the control of dynamic interaction.

A complete analytical solution to the inverse kinematics of the Pioneer 2 robotic arm

Robotica ◽  
2005 ◽  
Vol 23 (1) ◽  
pp. 123-129 ◽  
Author(s):  
John Q. Gan ◽  
Eimei Oyama ◽  
Eric M. Rosales ◽  
Huosheng Hu
Keyword(s):  
Analytical Solution ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Robotic Manipulators ◽  
Robotic Arm ◽  
Effective Solution ◽  
Robotic Arms ◽  
Unstructured Environment ◽  
Inverse Kinematics Problem

For robotic manipulators that are redundant or with high degrees of freedom (dof), an analytical solution to the inverse kinematics is very difficult or impossible. Pioneer 2 robotic arm (P2Arm) is a recently developed and widely used 5-dof manipulator. There is no effective solution to its inverse kinematics to date. This paper presents a first complete analytical solution to the inverse kinematics of the P2Arm, which makes it possible to control the arm to any reachable position in an unstructured environment. The strategies developed in this paper could also be useful for solving the inverse kinematics problem of other types of robotic arms.

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