Polynomial Inverse Kinematic Solution of the Jaco Robot

2014 ◽  
Author(s):  
Clément Gosselin ◽  
Hanwei Liu
Keyword(s):  
Polynomial Solution ◽  
Solution Process ◽  
Inverse Kinematic ◽  
Degree Polynomial ◽  
Inverse Kinematic Problem ◽  
End Effector ◽  
Numerical Examples ◽  
Position And Orientation ◽  
Kinematic Solution

This article presents a polynomial solution to the inverse kinematic problem of the 6R serial Jaco robot. The solution is specifically tailored to the Jaco robot, which is not wrist-partitioned. The derivation of the univariate 16-degree polynomial is presented, starting from the direct kinematic equations providing the position and orientation of the end-effector as a function of the joint variables. Upon calculation of the roots of the polynomial, all joint variables are obtained by backsubstitution, leading to a unique set of joint variables for each of the roots. Also, it is shown that for certain configurations, the 16-degree polynomial contains only terms of even powers while all terms are not zero in general. Two numerical examples are given to demonstrate the effectiveness of the solution process.

scholarly journals Analytical inverse kinematics for 5-DOF humanoid manipulator under arbitrarily specified unconstrained orientation of end-effector

Robotica ◽  
2014 ◽  
Vol 33 (4) ◽  
pp. 747-767 ◽  
Author(s):  
Masayuki Shimizu
Keyword(s):  
Analytical Method ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Singularity Analysis ◽  
Inverse Kinematic ◽  
Inverse Kinematic Problem ◽  
Target Orientation ◽  
End Effector ◽  
Position And Orientation

SUMMARYThis paper proposes an analytical method of solving the inverse kinematic problem for a humanoid manipulator with five degrees-of-freedom (DOF) under the condition that the target orientation of the manipulator's end-effector is not constrained around an axis fixed with respect to the environment. Since the number of the joints is less than six, the inverse kinematic problem cannot be solved for arbitrarily specified position and orientation of the end-effector. To cope with the problem, a generalized unconstrained orientation is introduced in this paper. In addition, this paper conducts the singularity analysis to identify all singular conditions.

Alternative Inverse Kinematic Equations for General RRP and RRR Regional Structures of Manipulators

1996 ◽  
Author(s):  
Peregrine E. J. Riley
Keyword(s):  
Degrees Of Freedom ◽  
Joint Angle ◽  
Inverse Kinematic ◽  
Intersection Point ◽  
Degree Polynomial ◽  
Six Degrees Of Freedom ◽  
Common Intersection ◽  
Position And Orientation ◽  
Spatial Positioning ◽  
Orientational Structure

Abstract Many manipulators with six degrees of freedom are constructed with two distinct sections, a regional structure for spatial positioning, and an orientational structure having a common intersection point for the joint axes. With this arrangement, inverse kinematic solutions for position and orientation may be found separately. While solutions for general three link manipulators have been available since the work of Pieper in 1969, this paper presents new forms of the inverse kinematic equations for general RRP and RRR regional structures. Cartesian coordinates of the F-surface (generated by movement of the outer two joints) together with the outer joint angle are used as the equation variables. In addition, a second degree polynomial approxiamation of the equation may be used for quick iteration to a solution. It is hoped that these new equations will be useful by themselves and in workspace regions where solutions using equations in terms of the joint variables are numerically inaccurate or impossible.

scholarly journals A novel solution of inverse kinematic for 6R robot manipulator with offset joint based on screw theory

2020 ◽  
Vol 17 (3) ◽  
pp. 172988142092564
Author(s):  
Zhiwei Liao ◽  
Gedong Jiang ◽  
Fei Zhao ◽  
Xuesong Mei ◽  
Yang Yue
Keyword(s):  
Joint Angle ◽  
Screw Theory ◽  
Robot Manipulator ◽  
Inverse Kinematic ◽  
Transformation Matrix ◽  
Inverse Kinematic Problem ◽  
End Effector ◽  
Closed Form Solutions ◽  
Specific Configuration ◽  
Kinematic Approach

This article proposes a novel inverse kinematic approach with translation transformation matrix based on screw theory to solve the inverse kinematic problem for 6R robot manipulator with offset joint. The translation transformation matrix is introduced to convert the 6R robot manipulator with offset joint to a new configuration with intersecting axes, and the mapping relationship from the end effector to the joint angle is established along with the Paden–Kahan subproblems. The eight closed solutions of the specific configuration are deduced, which automatically eliminate the singularity solutions. Moreover, the precision and efficiency of the proposed method are verified through a numerical example. Unlike other approaches, the presented algorithm not only inherits the superior accuracy of the other geometric approaches but also exhibits an outperform efficiency. Finally, the method is generalized to other 6R robots, which has closed-form solutions to further verify its versatility. The presented study provides some basis for further investigations, such as trajectory planning and motion control, which provides a new tool on the analysis and application of this kind of robot manipulator.

Probabilistic Approach for Digital Human Kinematic and Dynamic Reliabilities

2012 ◽  
Author(s):  
Jared Gragg ◽  
Jingzhou (James) Yang ◽  
Guolai Yang
Keyword(s):  
Equations Of Motion ◽  
Probabilistic Approach ◽  
Inverse Kinematic ◽  
Digital Human Modeling ◽  
Inverse Kinematic Problem ◽  
End Effector ◽  
Dynamic Reliability ◽  
Human Modeling ◽  
Digital Human ◽  
Recursive Dynamics

Traditionally, deterministic methods have been applied in digital human modeling (DHM). Transforming the deterministic approach of digital human modeling into a probabilistic approach is natural since there is inherent uncertainty and variability associated with DHM problems. Typically, deterministic studies in this field ignore this uncertainty or try to limit the uncertainty by employing optimization procedures. Due to the variability in the inputs, a deterministic study may not be enough to account for the uncertainty in the system. Probabilistic design techniques allow the designer to predict the likelihood of an outcome while also accounting for uncertainty, in contrast to deterministic studies. The purpose of this study is to incorporate probabilistic approaches to a deterministic DHM problem that has already been studied, analyzing human kinematics and dynamics. The problem is transformed into a probabilistic approach where the human kinematic and dynamic reliabilities are determined. The kinematic reliability refers to the probability that the human end-effector position (and/or orientation) falls within a specified distance from the desired position (and/or orientation) in an inverse kinematic problem. The dynamic reliability refers to the probability that the human end-effector position (and/or velocity) falls within a specified distance from the desired position (and/or velocity) along a specified trajectory in the workspace. The dynamic equations of motion for DHM are derived by the Lagrangian backward recursive dynamics formulation.

Analysis of Hyper-Redundant Manipulators

1999 ◽  
Author(s):  
Farshid Maghami Asl ◽  
Hashem Ashrafiuon ◽  
C. Nataraj
Keyword(s):  
Inverse Kinematic ◽  
Redundant Manipulators ◽  
Full Extension ◽  
Inverse Dynamic ◽  
Inverse Kinematic Problem ◽  
New Approach ◽  
Robust Solution ◽  
Numerical Examples ◽  
Planar Manipulators ◽  
Joint Velocity

Abstract A new approach to solve the inverse kinematic problem for hyper-redundant planar manipulators following any desired path is presented. The method is singularity free and provides a robust solution even in the event of mechanical failure of some of the robot actuators. The approach is based on defining virtual layers and dividing them into virtual/real three-link or four-link sub-robots. It starts by solving the inverse kinematic problem for the sub-robot located in the lowest virtual layer, which is then used to solve the inverse kinematic equations for the sub-robots located in the upper virtual layers. An algorithm is developed which provides a singularity-free solution up to full extension through a configuration index. The configuration index can be interpreted as the average of the determinants of the Jacobians of the sub-robots. The equations for the velocities and accelerations of the manipulator are solved by extending the same approach where it is realized that the value of configuration index is critical in maintaining joint velocity continuity. The inverse dynamic problem of the robot is also solved to obtain the torques required for the robot actuators to accomplish its task. Computer simulations of several hyper-redundant manipulators using the proposed method are presented as numerical examples.

A Method for Determining and Correcting Robot Position and Orientation Errors Due to Manufacturing

1988 ◽  
Vol 110 (1) ◽  
pp. 3-10 ◽  
Author(s):  
P. L. Broderick ◽  
R. J. Cipra
Keyword(s):  
Closed Form Solution ◽  
Difficult Problem ◽  
Inverse Kinematic ◽  
Form Solution ◽  
Correct Position ◽  
Forward Solution ◽  
Simple Task ◽  
Position And Orientation ◽  
Robot Position ◽  
Kinematic Solution

A method is presented for calibration of a robot to correct position and orientation errors due to manufacturing. The method is based on the shape matrix robot kinematic description. Each joint is individually and successively moved in order to explicitly calculate the shape matrix of each link. In addition, methods to correct for the errors in both the forward and inverse kinematic solutions are presented. The modification of the forward solution is a simple task. The modification of the inverse kinematic solution is a difficult problem and is achieved by an iterative technique which supplements the closed-form solution. An example of the calibration and inverse solution is presented to show the improvement in the accuracy of the robot.

A Complete Solution for the Inverse Kinematic Problem of the General 6R Robot Manipulator

1991 ◽  
Vol 113 (4) ◽  
pp. 481-486 ◽  
Author(s):  
H. Y. Lee ◽  
C. Woernle ◽  
M. Hiller
Keyword(s):  
Robot Manipulator ◽  
Complete Solution ◽  
Kinematic Chain ◽  
Polynomial Equation ◽  
Inverse Kinematic ◽  
Inverse Kinematic Problem ◽  
End Effector ◽  
Polynomial Degree ◽  
Half Angle

The inverse kinematic problem of the general 6R robot manipulator is completely solved by means of a 16th degree polynomial equation in the tangent of the half-angle of a revolute joint. An algorithm is developed to compute the desired joint angles of all possible configurations of the kinematic chain for a given position of the end-effector. Examples for robots with maximal 16 different configurations show that the polynomial degree 16 is the lowest possible for the general 6R robot manipulator. Further, a numerical method for the determination of the boundaries of the workspace and its subspaces with different numbers of configurations is developed. These boundaries indicate the singular positions of the end-effector.

Complex Robotic Inverse Kinematic Solutions

1993 ◽  
Vol 115 (3) ◽  
pp. 509-514 ◽  
Author(s):  
E. D. Pohl ◽  
H. Lipkin
Keyword(s):  
Robotic Manipulators ◽  
Inverse Kinematic ◽  
Complex Numbers ◽  
Error Minimization ◽  
Important Criterion ◽  
Real Numbers ◽  
End Effector ◽  
Industrial Manipulators ◽  
Complex Joint ◽  
Kinematic Solution

A new method exploiting complex numbers in the inverse kinematic solution of serial robotic manipulators is presented. If a prescribed end effector location is outside of the manipulator workspace, complex joint values result. While they cannot be implemented physically, they may be mapped to real numbers. The result approximates the prescribed location. For many industrial manipulators, mapped solutions may be explained using spherical and planar dyads. An important criterion characterizes error minimization properties, and is illustrated for a 3R regional robot.

Inverse Kinematic Solutions of Free-Floating Closed-Chain Planar Manipulators

1991 ◽  
Author(s):  
Sunil Kumar Agrawal ◽  
R. Garimella
Keyword(s):  
Center Of Mass ◽  
Solution Procedure ◽  
Inverse Kinematic ◽  
Joint Angles ◽  
End Effector ◽  
Planar Manipulators ◽  
Closed Chain ◽  
Fixed Base ◽  
Inverse Solutions ◽  
Position And Orientation

Abstract This paper deals with inverse solutions of free-floating closed-chain planar manipulators. The problem, in essence, is to compute the joint angles given the position and orientation of the end-effector. For free-floating planar manipulators, in the absence of external forces and couples, the linear and angular momentum are conserved. This makes the solution procedure and the number of inverse solutions for free-floating manipulators different from those of corresponding fixed-base manipulators. In order to illustrate this, we present the inverse kinematics of a free-floating planar manipulator whose end-effector is coupled to a base link by two R-R-R series chains. From the analysis, we conclude that for a given position and orientation of the end-effector, the location of the center of mass of the mechanism, and the orientation of the base link, upto 16 solutions of the joint angles are possible. To contrast, a fixed base manipulator of the same structure has a maximum of four solutions.

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