FABRIK-R: An Extension Developed Based on FABRIK for Robotics Manipulators

In this article we present a technique that enhances an inverse kinematics (IK) solver such that when the results are applied to a computer character, we can generate a level of individualization tailored to both the character and the environment, e.g., a walking motion can become "stiffer" or can be turned into a limping motion. Since the technique is based on an IK solver, we also have the desirable effect of solving retargetting issues when mapping motion data between characters. As the individualization aspect of our technique is very tightly coupled with the inverse kinematics solver, we can achieve both the individualization and retargetting of characters in real time.

Robotic manipulation in surgical applications often demands the surgical instrument to pivot around a fixed point, known as remote center of motion (RCM). The RCM constraint ensures that the pivot point of the surgical tool remains stationary at the incision port, preventing tissue damage and bleeding. Precisely and efficiently controlling tool positioning and orientation under this constraint poses a complex Inverse Kinematics (IK) problem that must be solved in real-time to ensure patient safety and minimize complications. To address this problem, we propose PivotIK, an efficient IK solver that combines efficient evolutionary exploration with multi-objective Jacobian-based optimization. PivotIK can track desired tool poses accurately while satisfying the RCM constraint in real-time. We evaluated PivotIK through simulations and real-world experiments using redundant robotic manipulators with multi-degree-of-freedom surgical instruments. We compare PivotIK with other IK solvers in terms of solve rates, computation times, tracking errors, and RCM errors under various scenarios, including unconstrained and RCM-constrained trajectories. Our results show that PivotIK achieves superior performance, solving the IK problem in less than 1 ms with errors below 0.01 and 0.1 mm for tracking and RCM, respectively. Our real-world experiments confirm the effectiveness of PivotIK in ensuring smooth trajectory tracking and RCM compliance. PivotIK offers a promising solution for real-time IK for robotic manipulation under RCM constraints in surgical applications.

The inverse kinematics (IK) problem is a fundamental problem in robotic manipulation. Traditional, Jacobian-based solutions to this problem are known to scale poorly with the number of degrees of freedom (DOF) in the manipulator, necessitating novel IK solutions for high-DOF manipulators. Metaheuristic optimization algorithms such as Particle Swarm Optimization (PSO) are a promising alternative approach to traditional IK techniques due to their strong performance on difficult and high-DOF problems in many diverse domains. Previous applications of PSO to the IK problem have focused on specific classes (e.g., planar) or models of manipulators or specific IK subproblems (e.g., position only IK). Furthermore, the experimental validation of these techniques has considered only manipulators with seven or fewer degrees of freedom and taken place almost exclusively in simulation. In this paper, we (1) generalize previous work to derive a fitness function that can be minimized to solve the full position and orientation IK problem for any serial manipulator while respecting joint limits and avoiding self-collisions, (2) present the first statistical analysis of PSO as a high-DOF IK solver on simulated manipulators with up to 180 DOF using this fitness function, and (3) present an important validation of PSO-based IK using this fitness function on real-world hardware on a difficult precision manipulation task.

The main objectives of the present work are to model and implement a control system of five degrees of freedom (5 DOF) humanoid arm by using an exoskeleton system with 3 DOF. The exoskeleton system is used to transport the movements of the human’s arm to the controller to control the humanoid arm by using sensors at each target joint to measure the angular displacement of it. To achieve this target, a kinematic analysis of the 5 DOF arm robot has been carried out including the forward, and solving the inverse kinematics. In addition, heterogeneous teleoperation based on forward and inverse kinematic between the humanoid arm and the exoskeleton model has been performed. Also, an experimental set up has been arranged to include the sensors considered (angular displacement sensors), control unit, signal-processing boards, and the actuators (servo motors of the humanoid arm robots). The control experiments have been conducted based on PID control. Keywords : Forward kinematic, inverse kinematic, teleoperation, humanoid robot Cite this Article Elsamanty M, Sayed M, Abdr Aboo S. Heterogeneous Teleoperation Model for Controlling 3D Printed Humanoid Robot Arm with 5 DOF using 3 DOF Exoskeleton. Journal of Control & Instrumentation. 2019; 10(2): 1–15p.

Many small and large industries use robot arms to establish a range of tasks such as picking and placing, and painting in today's world. However, to complete these tasks, one of the most critical problems is to obtain the desire position of the robot arm's end-effector. There are two methods for analyzing the robot arm: forward kinematic analysis and inverse kinematic analysis. This study aims to model the forward and inverse kinematic of an open-source 4 degrees of freedom (DoF) articulated robotic arm. A kinematic model is designed and further evaluated all the joint parameters to calculate the end-effector's desired position. Forward kinematic is simple to design, but as for the inverse kinematic, a closed-form solution is needed. The developed kinematic model's performance is assessed on a simulated robot arm, and the results were analyzed if the errors were produced within the accepted range. At the end of this study, forward kinematic and inverse kinematic solutions of a 4-DoF articulated robot arm are successfully modeled, which provides the theoretical basis for the subsequent analysis and research of the robot arm.

The Inverse Kinematics (IK) algorithms implemented in the open-source Orocos Kinematics and Dynamics Library (KDL) are arguably the most widely-used generic IK solvers worldwide. However, KDL's only joint-limit-constrained IK implementation, a pseudoinverse Jacobian IK solver, repeatedly exhibits false-negative failures on various humanoid platforms. In order to find a better IK solver for generic manipulator chains, a variety of open-source, drop-in alternatives have been implemented and evaluated for this paper. This article provides quantitative comparisons, using multiple humanoid platforms, between an improved implementation of the KDL inverse Jacobian algorithm, a set of sequential quadratic programming (SQP) IK algorithms that use a variety of quadratic error metrics, and a combined algorithm that concurrently runs the best performing SQP algorithm and the improved inverse Jacobian implementation. The best alternative IK implementation finds solutions much more often than KDL, is faster on average than KDL for typical manipulation chains, and (when desired) allows tolerances on each Cartesian dimension, further improving speed and convergence when an exact Cartesian pose is not possible and/or necessary.

The solution of the inverse kinematics in robotics is very important, and it becomes more difficult in robotic manipulators with many degrees of freedom. There are several methods of solution such as algebraic, kinematic decoupling, numerical and recently metaheuristics. This paper proposes the particle swarm metaheuristics characterized by having inertia weight and acceleration coefficients of the particles that vary exponentially in each iteration of the algorithm allowing an adaptively exploration, besides the objective function to minimize considers both the position and orientation error using direct kinematics. The proposed PSO algorithm avoid to fall into wrong joint angles configurations and have better performance in comparison to the conventional algorithm improving its repeatability.

This paper deals with real-time implementation of visual-motor control of a 7 degree of freedom (DOF) robot manipulator using self-organized map (SOM) based learning approach. The robot manipulator considered here is a 7 DOF PowerCube manipulator from Amtec Robotics. The primary objective is to reach a target point in the task space using only a single step movement from any arbitrary initial configuration of the robot manipulator. A new clustering algorithm using Kohonen SOM lattice has been proposed that maintains the fidelity of training data. Two different approaches have been proposed to find an inverse kinematic solution without using any orientation feedback. In the first approach, the inverse Jacobian matrices are learnt from the training data using function decomposition. It is shown that function decomposition leads to significant improvement in accuracy of inverse kinematic solution. In the second approach, a concept called sub-clustering in configuration space is suggested to provide multiple solutions for the inverse kinematic problem. Redundancy is resolved at position level using several criteria. A redundant manipulator is dexterous owing to the availability of multiple configurations for a given end-effector position. However, existing visual motor coordination schemes provide only one inverse kinematic solution for every target position even when the manipulator is kinematically redundant. Thus, the second approach provides a learning architecture that can capture redundancy from the training data. The training data are generated using explicit kinematic model of the combined robot manipulator and camera configuration. The training is carried out off-line and the trained network is used on-line to compute the joint angle vector to reach a target position in a single step only. The accuracy attained is better than the current state of art.

This paper proposes a new kinematic structure of a redundant serial robot arm and presents forward and inverse kinematic analysis. This is a new structure developed based on the robot IRB 2400 of ABB. The new structure consists of six revolute joints and two prismatic joints. The proposed robot arm has only seven degrees of freedom because the structure has a constraint between two revolute joints. Two prismatic joints help to expand workspaces of manipulator from small to very large. The paper describes in details about forward and inverse kinematics. Forward kinematics is derived based on DH Convention while inverse kinematics is calculated based on an objective function to minimize motions of a revolute joint and two prismatic joints. The simulation results on Matlab software indicated that the joint positions and velocities of a redundant serial robot arm matched well the trajectories in Cartesian Space.

A fuzzy self-organizing map (SOM) network is proposed in this paper for visual motor control of a 7 degrees of freedom (DOF) robot manipulator. The inverse kinematic map from the image plane to joint angle space of a redundant manipulator is highly nonlinear and ill-posed in the sense that a typical end-effector position is associated with several joint angle vectors. In the proposed approach, the robot workspace in image plane is discretized into a number of fuzzy regions whose center locations and fuzzy membership values are determined using a Fuzzy C-Mean (FCM) clustering algorithm. SOM network then learns the inverse kinematics by on-line by associating a local linear map for each cluster. A novel learning algorithm has been proposed to make the robot manipulator to reach a target position. Any arbitrary level of accuracy can be achieved with a number of fine movements of the manipulator tip. These fine movements depend on the error between the target position and the current manipulator position. In particular, the fuzzy model is found to be better as compared to Kohonen self-organizing map (KSOM) based learning scheme proposed for visual motor control. Like existing KSOM learning schemes, the proposed scheme leads to a unique inverse kinematic solution even for a redundant manipulator. The proposed algorithms have been successfully implemented in real-time on a 7 DOF PowerCube robot manipulator, and results are found to concur with the theoretical findings.

Six degrees-of-freedom (DoF) robot manipulators are dynamically coupled and highly nonlinear multi-variable systems. Calculating the optimal joint angles from the operational space (i.e. inverse kinematics) and designing the optimal joint controller parameters are two important research topics. This paper proposes a 3-stage Particle Swarm Optimization (PSO)-based methodology for solving the inverse kinematics and optimizing the controller parameters. In the first stage, a PSO algorithm solves the inverse kinematics problem by minimizing a multi-objective cost function in the operational space (i.e. the error in the end-effector’s pose) and therefore finds the optimal joint angles. In the second stage, polynomial functions generate the desired trajectory between the initial and final poses in the joint space. Finally, a second PSO algorithm tunes six proportional-derivative (PD) controllers, one for each joint, to track the desired trajectory by minimizing another multi-objective cost function in the joint space. Two case studies, based on six DoF Puma 560, validate the performance of the proposed methodology. Simulation results show that the proposed 3-stage methodology provides fast and accurate results as the PSO algorithms are effective in solving the inverse kinematics problem and tuning the optimal PD parameters.

This paper presents the design and analysis of a novel five degrees-of- freedom (DOF) parallel kinematic manipulator (PKM) for part-handling, sorting, general positioning, and robotic machining applications. The 2- R(Pa-IQ)RR, R(Pa-IQ)R manipulator has two rotational DOFs, one parasitic rotation, and three translational DOFs. In comparison with other 5- and 6- DOF PKMs, this PKM possesses three pairs of coplanar legs that contain nested kinematic chains, and it makes exclusive use of revolute and prismatic joints. The inverse kinematic analysis is a novel extension of the geometric (vector) method with the analysis of inner and outer kinematic chains. The forward kinematic analysis was solved using the Newton Raphson (NR) method. The results of the forward and inverse kinematic analyses were validated with SolidWorks ® and MATLAB ® simulations.

In this paper, the possibility of bilateral delta robot with micro-macro control to enhance human ability and transfer experience of operator is considered. Human's hand movement usually occur in three dimension space with high speed and small impendence from hand's mass which is not capable with conventional serial robot that have slow speed and heavy moving part. As a result, parallel delta robot with properties of high speed and light moving part is chosen to suit human's hand behavioral. Micro-macro bilateral or scaling bilateral robot is a robot that scale the position or force from master robot to smaller slave robot. Convectional micro-macro in joint space or motor space bilateral system is not enough to control the task space of the delta robot due to non-linearity of delta robot kinematic. As a result, a micro-macro task space for delta robot in xyz plane by transform joint space into task space using inverse and forward kinematic of delta robot is proposed. Delta robot have rigid body properties which is necessary for detail work and can be considered appropriate micro-macro bilateral manipulator. However, direct kinematics of delta robot have around 40 solutions due to the complexity of pair of spherical joint that may present difficulty in design and manufacturing. Disturbance force is estimated by disturbance observer and scaled by conventional micro-macro method. The experiment and simulation is carry out to verify the proposed method.

In this paper, the mechanism and kinematics of the six degree of freedom joint manipulator PUMA560 where contains the forward kinematics, inverse kinematics and trajectory planning problems of PUMA560 are analyzed by the standard D-H method, and the forward and inverse kinematics transformation formula is derived. The manipulator was modeled with Robotics Toolbox, and the forward kinematics, inverse kinematics solutions and trajectory planning were simulated which can obtain the required data in MATLAB. This paper studies the changes of the main kinematic indexes of the robot in the process of operation, which intuitively reflects the motion state of each rod and end working part of the robot, and provides a theoretical basis for the specific development and control strategy of the manipulator.

Abstract. The similarity recognition of kinematic chains (KCs) is helpful for improving the efficiency of configuration synthesis, which has been paid more and more attention in recent years. The existing recognition methods are divided into the definition method and feature constant method. Among them, the definition method is difficult to adopt in practice because of its long operation time, especially when the number of similar vertices in KCs is large. In this paper, the new concepts of a loop tree (LT) and a loop tree matrix (LTM) have been proposed, which improve the efficiency of similarity recognition. This method is applied on the complete structure of the following: 8-link with 1 DOF (degree of freedom), 9-link with 2 DOF, 10-link with 1 DOF, 12-link with 1 DOF, 13-link with 2 DOF, 14-link with 3 DOF, 15-link with 4 DOF planar single-joint KCs, and contracted graphs with up to six independent loops. All results are verified by the definition method to prove the good applicability, reliability, and efficiency of the proposed method. Simultaneously, the application case of the similarity recognition in a mechanism creation is given to provide a reference for an innovative design.