Inverse Kinematics of Serial Redundant Manipulators With Locked Articulations

1995 ◽  
Author(s):  
Louis Perreault ◽  
Clément M. Gosselin
Keyword(s):  
Inverse Kinematics ◽  
General Procedure ◽  
Inverse Kinematic ◽  
Redundant Manipulators ◽  
Redundant Manipulator ◽  
Inverse Kinematic Problem

Abstract This paper presents an algorithm for the solution of the inverse kinematics of a serial redundant manipulator with one (or more) locked joint(s). To this end, a general procedure is developed for the determination of the equivalent Denavit-Hartenberg parameters of a serial manipulator with locked joints. This procedure can be applied to any serial architecture. The solution of the inverse kinematic problem for the three cases which can arise is then addressed. An example of the application of the method to a SARCOS 7-DOF manipulator is also given.

Dual arm-angle parameterisation and its applications for analytical inverse kinematics of redundant manipulators

Robotica ◽  
2015 ◽  
Vol 34 (12) ◽  
pp. 2669-2688 ◽  
Author(s):  
Wenfu Xu ◽  
Lei Yan ◽  
Zonggao Mu ◽  
Zhiying Wang
Keyword(s):  
Inverse Kinematics ◽  
Reference Plane ◽  
Redundant Manipulators ◽  
Redundant Manipulator ◽  
Singularity Problem ◽  
Human Arm ◽  
Angle Method ◽  
Self Motion ◽  
Dual Arm ◽  
Configuration Control

SUMMARYAn S-R-S (Spherical-Revolute-Spherical) redundant manipulator is similar to a human arm and is often used to perform dexterous tasks. To solve the inverse kinematics analytically, the arm-angle was usually used to parameterise the self-motion. However, the previous studies have had shortcomings; some methods cannot avoid algorithm singularity and some are unsuitable for configuration control because they use a temporary reference plane. In this paper, we propose a method of analytical inverse kinematics resolution based on dual arm-angle parameterisation. By making use of two orthogonal vectors to define two absolute reference planes, we obtain two arm angles that satisfy a specific condition. The algorithm singularity problem is avoided because there is always at least one arm angle to represent the redundancy. The dual arm angle method overcomes the shortcomings of traditional methods and retains the advantages of the arm angle. Another contribution of this paper is the derivation of the absolute reference attitude matrix, which is the key to the resolution of analytical inverse kinematics but has not been previously addressed. The simulation results for typical cases that include the algorithm singularity condition verified our method.

Kinematic and Workspace Modelling of a 6-PUS Parallel Mechanism

2018 ◽  
Author(s):  
Jérôme Landuré ◽  
Clément Gosselin
Keyword(s):  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Inverse Kinematic ◽  
Degree Of Freedom ◽  
Accurate Description ◽  
Transmission Ratio ◽  
Inverse Kinematic Problem ◽  
Jacobian Matrices ◽  
Six Degree Of Freedom

This article presents the kinematic analysis of a six-degree-of-freedom six-legged parallel mechanism of the 6-PUS architecture. The inverse kinematic problem is recalled and the Jacobian matrices are derived. Then, an algorithm for the geometric determination of the workspace is presented, which yields a very fast and accurate description of the workspace of the mechanism. Singular boundaries and a transmission ratio index are then introduced and studied for a set of architectural parameters. The proposed analysis yields conceptual architectures whose properties can be adjusted to fit given applications.

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.

Posture Prediction Versus Inverse Kinematics

2001 ◽  
Author(s):  
Karim Abdel-Malek ◽  
Wei Yu ◽  
Zan Mi ◽  
E. Tanbour ◽  
M. Jaber
Keyword(s):  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Human Performance ◽  
Inverse Kinematic ◽  
Cost Functions ◽  
Optimization Approach ◽  
Final Position ◽  
Serial Robot ◽  
Posture Prediction

Abstract Inverse kinematics is concerned with the determination of joint variables of a manipulator given its final position or final position and orientation. Posture prediction also refers to the same problem but is typically associated with models of the human limbs, in particular for postures assumed by the torso and upper extremities. There has been numerous works pertaining to the determination and enumeration of inverse kinematic solutions for serial robot manipulators. Part of these works have also been directly extended to the determination of postures for humans, but have rarely addressed the choice of solutions undertaken by humans, but have focused on purely kinematic solutions. In this paper, we present a theoretical framework that is based on cost functions as human performance measures, subsequently predicting postures based on optimizing one or more of such cost functions. This paper seeks to answer two questions: (1) Is a given point reachable (2) If the point is reachable, we shall predict a realistic posture. We believe that the human brain assumes different postures driven by the task to be executed and not only on geometry. Furthermore, because of our optimization approach to the inverse kinematics problem, models with large number of degrees of freedom are addressed. The method is illustrated using several examples.

Repeatable Joint Displacement Generation for Redundant Robotic Systems

1994 ◽  
Vol 116 (1) ◽  
pp. 11-16 ◽  
Author(s):  
Y. S. Chung ◽  
M. Griffis ◽  
J. Duffy
Keyword(s):  
Joint Space ◽  
Inverse Kinematic ◽  
Torsional Stiffness ◽  
Numerical Verification ◽  
Redundant Manipulators ◽  
Redundant Manipulator ◽  
Kinematic Equation ◽  
End Effector ◽  
Prismatic Joints ◽  
Cyclic Type

This paper presents a novel, practical, and theoretically sound kinematic control strategy for serial redundant manipulators. This strategy yields repeatability in the joint space of a serial redundant manipulator whose end effector undergoes some general cyclic type motion. This is accomplished by deriving a new inverse kinematic equation that is based on springs being theoretically or conceptually located in the joints of the manipulator (torsional springs for revolute joints, translational springs for prismatic joints). Previous researchers have also derived an inverse kinematic equation for serial redundant manipulators. However, to the authors’ knowledge, the new strategy is the first to include the free angles of torsional springs and the free lengths of translational springs. This is important because it ensures the repeatability in the joint space of a serial redundant manipulator whose end effector undergoes a cyclic type motion. Numerical verification for repeatability is done in terms of Lie bracket condition. Choices for the free angle and torsional stiffness of a joint (or the free length and translational stiffness) are made based upon the mechanical limits of the joint.

scholarly journals A Fast Evaluation of Initial Configurations in Repeatable Inverse Kinematics for Redundant Manipulators

2018 ◽  
Vol 28 (3) ◽  
pp. 483-492
Author(s):  
Ignacy Duleba ◽  
Iwona Karcz-Duleba ◽  
Arkadiusz Mielczarek
Keyword(s):  
Configuration Space ◽  
Inverse Kinematics ◽  
Indirect Method ◽  
Inverse Kinematic ◽  
Initial Configuration ◽  
Redundant Manipulators ◽  
Task Space ◽  
Original Function ◽  
Fast Evaluation ◽  
Computationally Expensive

Abstract A repeatable inverse kinematic task in robot manipulators consists in finding a loop (cyclic trajectory) in a configuration space, which corresponds to a given loop in a task space. In the robotic literature, an entry configuration to the trajectory is fixed and given by a user. In this paper the assumption is released and a new, indirect method is introduced to find entry configurations generating short trajectories. The method avoids a computationally expensive evaluation of (infinite) many entry configurations for redundant manipulators (for each of them, repeatable inverse kinematics should be run). Some fast-to-compute functions are proposed to evaluate entry configurations and their correlations with resulting lengths of trajectories are computed. It appears that only an original function, based on characteristics of a manipulability subellipsoid, properly distinguishes entry configurations that generate short trajectories. This function can be used either to choose one from a few possible entry configurations or as an optimized function to compute the best initial configuration.

scholarly journals Dynamic analysis of a five degree of freedom robotic arm using MATLAB-Simulink Simscape

2021 ◽  
Vol 343 ◽  
pp. 08004
Author(s):  
Mihai Crenganis ◽  
Alexandru Barsan ◽  
Melania Tera ◽  
Anca Chicea
Keyword(s):  
Dynamic Analysis ◽  
Dynamic Model ◽  
Inverse Kinematics ◽  
Geometric Approach ◽  
Correct Choice ◽  
Inverse Kinematic ◽  
Degree Of Freedom ◽  
Robotic Arm ◽  
Inverse Kinematic Problem ◽  
Joint Torques

In this paper, a dynamic analysis for a 5 degree of freedom (DOF) robotic arm with serial topology is presented. The dynamic model of the robot is based on importing a tri-dimensional CAD model of the robot into Simulink®-Simscape™-Multibody™. The dynamic model of the robot in Simscape is a necessary and important step in development of the mechanical structure of the robot. The correct choice of the electric motors is made according to the resistant joint torques determined by running the dynamic analysis. One can import complete CAD assemblies, including all masses, inertias, joints, constraints, and tri-dimensional geometries, into the model block. The first step for executing a dynamic analysis is to resolve the Inverse Kinematics (IK) problem for the redundant robot. The proposed method for solving the inverse kinematic problem for this type of structure is based on a geometric approach and validated afterwards using SimScape Multibody. Solving the inverse kinematics problem is a mandatory step in the dynamic analysis of the robot, this is required to drive the robot on certain user-imposed trajectories. The dynamic model of the serial robot is necessary for the simulation of motion, analysis of the robot’s structure and design of optimal control algorithms.

Proper Smart Method of the Inverse Kinematic Problem

2015 ◽  
Vol 772 ◽  
pp. 455-460 ◽  
Author(s):  
Adrian Olaru ◽  
Serban Olaru ◽  
Niculae Mihai
Keyword(s):  
Inverse Kinematics ◽  
Jacobian Matrix ◽  
Inverse Kinematic ◽  
Iterative Approximation ◽  
Inverse Kinematic Problem ◽  
Space Curves ◽  
Inverse Kinematics Problem ◽  
Artificial Intelligence Algorithm ◽  
Pseudo Inverse

One of the most precise method solving the inverse kinematics problem in the redundant cases of the robots is the coupled method. The proposed method use the Iterative Pseudo Inverse Jacobian Matrix Method (IPIJMM) coupled with the proper Sigmoid Bipolar Hyperbolic Tangent Neural Network with Time Delay and Recurrent Links (SBHTNN-TDRL). One precise solution of the inverse kinematics problem is very difficult to find, when the degree of freedom increase and in many cases this is impossible because the redundant solutions. In all these cases must be used the numerical iterative approximation, like the proposed method, with artificial intelligence algorithm. The paper describe all the steps in one case study to obtain the space circle curve in different planes by using one arm type robot and the proposed method. The errors of the space movement of the robot end-effecter, after applying the proposed method, was less than 0,01. The presented method is general and it can be used in all other robots types and for all other conventional and unconventional space curves.

A new motion planning method for discretely actuated hyper-redundant manipulators

Robotica ◽  
2015 ◽  
Vol 35 (1) ◽  
pp. 101-118 ◽  
Author(s):  
Alireza Motahari ◽  
Hassan Zohoor ◽  
Moharam Habibnejad Korayem
Keyword(s):  
Genetic Algorithm ◽  
Motion Planning ◽  
Trajectory Tracking ◽  
Inverse Kinematic ◽  
Planning Problem ◽  
Redundant Manipulators ◽  
Tracking Problem ◽  
Parallel Mechanisms ◽  
Redundant Manipulator ◽  
The Common

SUMMARYA hyper-redundant manipulator is made by mounting the serial and/or parallel mechanisms on top of each other as modules. In discrete actuation, the actuation amounts are a limited number of certain values. It is not feasible to solve the kinematic analysis problems of discretely actuated hyper-redundant manipulators (DAHMs) by using the common methods, which are used for continuous actuated manipulators. In this paper, a new method is proposed to solve the trajectory tracking problem in a static prescribed obstacle field. To date, this problem has not been considered in the literature. Theremoving first collision(RFC) method, which is originally proposed for solving the inverse kinematic problems in the obstacle fields was modified and used to solve the motion planning problem. For verification, the numerical results of the proposed method were compared with the results of thegenetic algorithm(GA) method. Furthermore, a novel DAHM designed and implemented by the authors is introduced.

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