Cost Function-Free Optimization in Inverse Kinematics of Open Kinematic Chains

2015 ◽  
pp. 137-145 ◽  
Author(s):  
József K. Tar ◽  
László Nádai ◽  
Imre Felde ◽  
Imre J. Rudas
Keyword(s):  
Cost Function ◽  
Inverse Kinematics ◽  
Kinematic Chains

On the Placement of Serial Manipulators

2000 ◽  
Author(s):  
Karim Abdel-Malek ◽  
Wei Yu
Keyword(s):  
Cost Function ◽  
Inverse Kinematics ◽  
Inverse Kinematic ◽  
Working Environment ◽  
Robot Arm ◽  
Serial Manipulators ◽  
Surface Patches ◽  
Numerical Formulation ◽  
Fixed Reference ◽  
Position And Orientation

Abstract Criteria and implementation for the placement robot manipulators with the objective to reach specified target points are herein addressed. Placement of a serial manipulator in a working environment is characterized by defining the position and orientation of the manipulator’s base with respect to a fixed reference frame. The problem has become of importance in both the medical and manufacturing fields, where a robot arm must be appropriately placed with respect to targets that cannot be moved. A broadly applicable numerical formulation is presented. While other methods have used inverse kinematics solutions in their formulation for defining a locality for the manipulator base, this type of solution is difficult to implement because of the inherent complexities in determining al inverse kinematic solutions. The approach taken in this work is based on characterizing the placement forcing a cost function to impel the workspace envelope in terms of surface patches towards the target points and subject to functionality constraints, but that does not require the computation of inverse kinematics. The formulation and experimental code are demonstrated using a number of examples.

A New Algorithm for the Determination of the Workspace of Complex Planar Kinematic Chains

1995 ◽  
Author(s):  
Pascal Lê-Huu ◽  
Clément M. Gosselin
Keyword(s):  
Numerical Solution ◽  
Inverse Kinematics ◽  
Degree Of Freedom ◽  
Topological Graph ◽  
Kinematic Chains ◽  
Cartesian Space ◽  
Hybrid Manipulator ◽  
Three Degree Of Freedom ◽  
Two Degree Of Freedom

Abstract A new algorithm for the determination of the workspace of complex planar kinematic chains is presented in this paper. This algorithm is completely general since it can deal with any kind of topological graph and any set of parameters defined in a convention of notation. It uses the numerical solution of the inverse kinematics and is based on a wavefront expansion in the Cartesian space. Three examples are presented here, and lead to a dexterity mapping for two two-degree-of-freedom multi-loop manipulators and a three-degree-of-freedom hybrid manipulator.

Analysis and Simulation of a Parallel Platform with 2R-1T

2012 ◽  
Vol 562-564 ◽  
pp. 1456-1459
Author(s):  
Qi Zhi Yang ◽  
Peng Fei Zi ◽  
Long Chen ◽  
Jia Qi Zhuang
Keyword(s):  
Theoretical Calculation ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Kinematic Chains ◽  
Calculation Results ◽  
Parallel Platform ◽  
Moving Platform ◽  
Branched Chain ◽  
Changes Over Time ◽  
Spatial Degrees Of Freedom

It is described that a parallel platform with three spatial degrees of freedom; the platform is built up by parallel combination of three symmetrical (SPS) and a branched-chain (PU). It is gotten the freedom of the mechanism and the theory expression of inverse kinematics by theoretical calculation. The mechanism was modeled by Pro/E, and the model is imported with Mech/Pro to ADAMS/View for simulation. The trajectory of three kinematic chains that changes over time through computer simulation, which are got by exerting force on the moving platform, is compared with the theoretical calculation results gotten through MATLAB. The results prove that the curve of position is identical, and it testifies the correctness of the movement of the platform.

scholarly journals Inverse and Forward Kinematic Analysis of a 6-DOF Parallel Manipulator Utilizing a Circular Guide

Robotics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 31
Author(s):  
Alexey Fomin ◽  
Anton Antonov ◽  
Victor Glazunov ◽  
Yuri Rodionov
Keyword(s):  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Forward Kinematics ◽  
Rotational Angle ◽  
End Effector ◽  
Kinematic Chains ◽  
Position And Orientation ◽  
Manipulator Design ◽  
Forward Kinematic

The proposed study focuses on the inverse and forward kinematic analysis of a novel 6-DOF parallel manipulator with a circular guide. In comparison with the known schemes of such manipulators, the structure of the proposed one excludes the collision of carriages when they move along the circular guide. This is achieved by using cranks (links that provide an unlimited rotational angle) in the manipulator kinematic chains. In this case, all drives stay fixed on the base. The kinematic analysis provides analytical relationships between the end-effector coordinates and six controlled movements in drives (driven coordinates). Examples demonstrate the implementation of the suggested algorithms. For the inverse kinematics, the solution is found given the position and orientation of the end-effector. For the forward kinematics, various assembly modes of the manipulator are obtained for the same given values of the driven coordinates. The study also discusses how to choose the links lengths to maximize the rotational capabilities of the end-effector and provides a calculation of such capabilities for the chosen manipulator design.

scholarly journals Extending FABRIK with Obstacle Avoidance for Solving the Inverse Kinematics Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Songqiao Tao ◽  
Huajin Tao ◽  
Yumeng Yang
Keyword(s):  
Obstacle Avoidance ◽  
Computer Animation ◽  
Inverse Kinematics ◽  
Heuristic Method ◽  
Computational Cost ◽  
Target Position ◽  
Second Step ◽  
Kinematic Chains ◽  
Inverse Kinematics Problem ◽  
Low Computational Cost

Inverse kinematics (IK) has been extensively applied in the areas of robotics, computer animation, ergonomics, and gaming. Typically, IK determines the joint configurations of a robot model and achieves a desired end-effector position in robotics. Since forward and backward teaching inverse kinematics (FABRIK) is a forward and backward iterative method that finds updated joint positions by locating a point on a line instead of using angle rotations or matrices, it has the advantages of fast convergence, low computational cost, and visualizing realistic poses. However, the manipulators usually work in a complex environment. So, the kinematic chains are easy to produce the interference with their surrounding scenarios. To resolve the above mentioned problem, a two-step obstacle avoidance technology is proposed to extend the basic FABRIK in this study. The first step is a heuristic method that locates the updated linkage bar, the root joint, and the target position in a line, so that the interference can be eliminated in most cases. In the second step, multiple random rotation strategies are adopted to eliminate the interference that has not been eliminated in the first step. Experimental results have shown that the extending FABRIK has the obstacle avoidance ability.

Parallel Computational Algorithms for the Kinematics and Dynamics of Planar and Spatial Parallel Manipulators

1996 ◽  
Vol 118 (1) ◽  
pp. 22-28 ◽  
Author(s):  
C. M. Gosselin
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Kinematic Chains ◽  
Novel Approach ◽  
Judicious Choice ◽  
Six Degree Of Freedom ◽  
Three Degree Of Freedom

This paper introduces a novel approach for the computation of the inverse dynamics of parallel manipulators. It is shown that, for this type of manipulator, the inverse kinematics and the inverse dynamics procedures can be easily parallelized. The result is a closed-form efficient algorithm using n processors, where n is the number of kinematic chains connecting the base to the end-effector. The dynamics computations are based on the Newton-Euler formalism. The parallel algorithm arises from a judicious choice of the coordinate frames attached to each of the legs, which allows the exploitation of the parallel nature of the mechanism itself. Examples of the application of the algorithm to a planar three-degree-of-freedom parallel manipulator and to a spatial six-degree-of-freedom parallel manipulator are presented.

scholarly journals Inverse modeling of the stewart foot

2021 ◽  
Vol 12 (9) ◽  
pp. s774-s793
Author(s):  
Adriana Comanescu ◽  
Alexandra Rotaru ◽  
Liviu Marian Ungureanu ◽  
Florian Ion Tiberiu Petrescu
Keyword(s):  
Inverse Modeling ◽  
Inverse Kinematics ◽  
Robotic Systems ◽  
Kinematic Modeling ◽  
Kinematic Parameters ◽  
End Effector ◽  
Kinematic Chains ◽  
Special Character ◽  
Logical Functions

The Stewart's leg is used today in the majority of parallel robotic systems, such as the Stewart platform, but also in many other types of mechanisms and kinematic chains, in order to operate them or to transmit motion. A special character in the study of robots is the study of inverse kinematics, with the help of which the map of the motor kinematic parameters necessary to obtain the trajectories imposed on the effector can be made. For this reason, in the proposed mechanism, we will present reverse kinematic modeling in this paper. The kinematic output parameters, ie the parameters of the foot and practically of the end effector, ie those of the point marked with T, will be determined for initiating the working algorithm with the help of logical functions, "If log(ical)", with the observation that here they play the role of input parameters; it is positioned as already specified in the inverse kinematics when the output is considered as input and the input as output. The logical functions used, as well as the entire calculation program used, were written in Math Cad.

scholarly journals A General Method for Kinematic Retargeting: Adapting Poses Between Humans and Robots

2014 ◽  
Author(s):  
Tarik Tosun ◽  
Ross Mead ◽  
Robert Stengel
Keyword(s):  
Cost Function ◽  
Degrees Of Freedom ◽  
Specific Problem ◽  
Broad Class ◽  
Human Robot Interaction ◽  
Weighted Sum ◽  
Robot Interaction ◽  
Kinematic Chains ◽  
Specific Manner ◽  
General Method

This paper presents a method for kinematic retargeting that is general to a broad class of kinematic chains. Kinematic retargeting is the adaptation of a pose or motion from one kinematic embodiment to another. Our method distinguishes itself in its ability to adapt poses to new robots with very little configuration by the user. We accomplish this by defining two general metrics for retargeting and minimizing a cost function which is the weighted sum of these two metrics. This allows the method to automatically adapt poses between source and target chains that have different link lengths and degrees of freedom. These capabilities address a specific problem in Human-Robot Interaction (HRI), where behaviors are often defined in a robot-specific manner. The ability to automatically adapt behaviors from humans to new robots, and from one robot to another, will facilitate experimental repeatability. Through simulation and experiments, we demonstrate that our method is effective in adapting poses across chains with different numbers of joints, and in adapting socially expressive gestures from a human to two very different robots.

EFFICIENT INVERSE KINEMATICS COMPUTATION BASED ON REACHABILITY ANALYSIS

2012 ◽  
Vol 09 (04) ◽  
pp. 1250035 ◽  
Author(s):  
NIKOLAUS VAHRENKAMP ◽  
TAMIM ASFOUR ◽  
RÜDIGER DILLMANN
Keyword(s):  
Data Structures ◽  
Inverse Kinematics ◽  
Humanoid Robot ◽  
Integrated Approach ◽  
Humanoid Robots ◽  
Reachability Analysis ◽  
Cluttered Environments ◽  
Kinematic Chains ◽  
Base Position ◽  
Bimanual Grasping

In this work we show how precomputed reachability information can be used to efficiently solve complex inverse kinematics (IK) problems such as bimanual grasping or re-grasping for humanoid robots. We present an integrated approach which generates collision-free IK solutions in cluttered environments while handling multiple potential grasping configurations for an object. Therefore, the spatial reachability of the robot's workspace is efficiently encoded by discretized data structures and sampling-based techniques are used to handle arbitrary kinematic chains. The algorithms are employed for single-handed and bimanual grasping tasks with fixed robot base position and methods are developed that allow to efficiently incorporate the search for suitable robot locations. The approach is evaluated in different scenarios with the humanoid robot ARMAR-III.

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