scholarly journals Investigation of Cyclicity of Kinematic Resolution Methods for Serial and Parallel Planar Manipulators

Robotics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 9
Author(s):  
Maurizio Ruggiu ◽  
Andreas Müller
Keyword(s):  
Objective Function ◽  
Inverse Kinematics ◽  
Joint Space ◽  
Point Of View ◽  
Initial Configuration ◽  
Local Optimum ◽  
Closed Path ◽  
Redundancy Resolution ◽  
Projected Gradient Method ◽  
Inverse Kinematics Problem

Kinematic redundancy of manipulators is a well-understood topic, and various methods were developed for the redundancy resolution in order to solve the inverse kinematics problem, at least for serial manipulators. An important question, with high practical relevance, is whether the inverse kinematics solution is cyclic, i.e., whether the redundancy solution leads to a closed path in joint space as a solution of a closed path in task space. This paper investigates the cyclicity property of two widely used redundancy resolution methods, namely the projected gradient method (PGM) and the augmented Jacobian method (AJM), by means of examples. Both methods determine solutions that minimize an objective function, and from an application point of view, the sensitivity of the methods on the initial configuration is crucial. Numerical results are reported for redundant serial robotic arms and for redundant parallel kinematic manipulators. While the AJM is known to be cyclic, it turns out that also the PGM exhibits cyclicity. However, only the PGM converges to the local optimum of the objective function when starting from an initial configuration of the cyclic trajectory.

scholarly journals Hybrid Taguchi DNA Swarm Intelligence for Optimal Inverse Kinematics Redundancy Resolution of Six-DOF Humanoid Robot Arms

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Hsu-Chih Huang ◽  
Sendren Sheng-Dong Xu ◽  
Huan-Shiuan Hsu
Keyword(s):  
Swarm Intelligence ◽  
Inverse Kinematics ◽  
Humanoid Robot ◽  
Robot Arm ◽  
Redundancy Resolution ◽  
Closed Form Solutions ◽  
Robot Arms ◽  
Inverse Kinematics Problem ◽  
Six Dof ◽  
Six Degree Of Freedom

This paper presents a hybrid Taguchi deoxyribonucleic acid (DNA) swarm intelligence for solving the inverse kinematics redundancy problem of six degree-of-freedom (DOF) humanoid robot arms. The inverse kinematics problem of the multi-DOF humanoid robot arm is redundant and has no general closed-form solutions or analytical solutions. The optimal joint configurations are obtained by minimizing the predefined performance index in DNA algorithm for real-world humanoid robotics application. The Taguchi method is employed to determine the DNA parameters to search for the joint solutions of the six-DOF robot arms more efficiently. This approach circumvents the disadvantage of time-consuming tuning procedure in conventional DNA computing. Simulation results are conducted to illustrate the effectiveness and merit of the proposed methods. This Taguchi-based DNA (TDNA) solver outperforms the conventional solvers, such as geometric solver, Jacobian-based solver, genetic algorithm (GA) solver and ant, colony optimization (ACO) solver.

scholarly journals Joint Space Redundancy Resolution of Serial Link Manipulator: An Inverse Kinematics and Continuum Structure Numerical Approach

2020 ◽  
Author(s):  
Toshit Jain ◽  
Jinesh Kumar Jain ◽  
Debanik Roy
Keyword(s):  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Complex Structure ◽  
Initial Approximation ◽  
Joint Space ◽  
Primary Objective ◽  
Target Point ◽  
Redundancy Resolution ◽  
Redundant Manipulator ◽  
Serial Link

Automatic control to any of robot manipulators, some kind of issues are being observed. A numerical method for solution generation to the inverse kinematics problem of redundant robotic manipulators is presented to obtain the smoothest algorithm as possible, leading to a robust iterative method. After the primary objective of the reachability of end-effectors to the target point is achieved, the aim is set to resolve the redundant degrees of freedom of redundant manipulator. This method is numerically stable since it converges to the correct answer with virtually any initial approximation, and it is not sensitive to the singular configurations of the manipulator. In addition, this technique is computationally effective and able to apply for serial manipulators with any DOF applications. A planar 3R-DOF serial link redundant manipulator is considered as exemplar problem for solving. Also, the continuum approach for resolving more complex structure with variable DoF is illustrated here and their brief applicability to support surgeries and adaptive use of artificial linkage moments is also calculated.

Another Approach for Redundancy Resolution of a 7 DOF Robotic Arm

2015 ◽  
Vol 762 ◽  
pp. 305-311
Author(s):  
Mihai Crenganis ◽  
Octavian Bologa
Keyword(s):  
Fuzzy Logic ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Robotic Arm ◽  
Cad Model ◽  
Redundancy Resolution ◽  
The Real ◽  
Kinematics Simulation ◽  
Inverse Kinematics Problem ◽  
Mathematical Equations

In this paper we have presented a method to solve the inverse kinematics problem of a redundant robotic arm with seven degrees of freedom and a human like workspace based on mathematical equations, Fuzzy Logic implementation and Simulink models. For better visualization of the kinematics simulation a CAD model that mimics the real robotic arm was created into SolidWorks® and then the CAD parts were converted into SimMechanics model.

On the inverse kinematics of an a priori unknown general 6R-Robot

Robotica ◽  
2012 ◽  
Vol 31 (3) ◽  
pp. 455-463 ◽  
Author(s):  
Friedemann Groh ◽  
Konrad Groh ◽  
Alexander Verl
Keyword(s):  
Inverse Kinematics ◽  
A Priori ◽  
Point Of View ◽  
Motion Group ◽  
Euclidean Motion Group ◽  
Inverse Kinematics Problem ◽  
Representation Point ◽  
Euclidean Motion

SUMMARYThis paper looks at the inverse kinematics problem of an a priori unknown 6R-Robot from the representation point of view. It describes a new representation of the Euclidean motion group. With this representation, the inverse kinematics problem can be treated entirely numerical. No symbolical methods are required.

scholarly journals Computing Robust Inverse Kinematics Under Uncertainty

2019 ◽  
Author(s):  
Anirban Sinha ◽  
Nilanjan Chakraborty
Keyword(s):  
Inverse Kinematics ◽  
Joint Space ◽  
Redundant Manipulators ◽  
Task Space ◽  
Success Rates ◽  
Redundant Manipulator ◽  
Space Error ◽  
Inverse Kinematics Problem ◽  
Robotic Tasks ◽  
Present Simulation

Abstract Robotic tasks, like reaching a pre-grasp configuration, are specified in the end effector space or task space, whereas, robot motion is controlled in joint space. Because of inherent actuation errors in joint space, robots cannot achieve desired configurations in task space exactly. Furthermore, different inverse kinematics (IK) solutions map joint space error set to task space differently. Thus for a given task with a prescribed error tolerance, all IK solutions will not be guaranteed to successfully execute the task. Any IK solution that is guaranteed to execute a task (possibly with high probability) irrespective of the realization of the joint space error is called a robust IK solution. In this paper we formulate and solve the robust inverse kinematics problem for redundant manipulators with actuation uncertainties (errors). We also present simulation and experimental results on a 7-DoF redundant manipulator for two applications, namely, a pre-grasp positioning and a pre-insertion positioning scenario. Our results show that the robust IK solutions result in higher success rates and also allows the robot to self-evaluate how successful it might be in any application scenario.

scholarly journals An Adaptive Second Order Sliding Mode Inverse Kinematics Approach for Serial Kinematic Chain Robot Manipulators

Robotics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 4
Author(s):  
Wael Mohammed Elawady ◽  
Yassine Bouteraa ◽  
Ahmed Elmogy
Keyword(s):  
Inverse Kinematics ◽  
Jacobian Matrix ◽  
Sliding Mode ◽  
Robot Manipulators ◽  
Kinematic Chain ◽  
Joint Space ◽  
Second Order ◽  
Inverse Kinematics Problem ◽  
Almost All ◽  
Second Order Sliding Mode

The problem of inverse kinematics is essential to consider while dealing with the robot’s mechanical structure in almost all applications. Since the solution of the inverse kinematics problem is very complex, many research efforts have been working towards getting the approximate solution of this problem. However, for some applications, working with the approximate robot’s model is neither sufficient nor efficient. In this paper, an adaptive inverse kinematics methodology is developed to solve the inverse kinematics problem in such a way that compensate for unknown uncertainty in the Jacobian matrix of the serial kinematic chain robot manipulators. The proposed methodology is based on continuous second order sliding mode strategy (CSOSM-AIK). The salient advantage of the CSOSM-AIK approach is that it does not require the availability of the kinematics model or Jacobian matrix of the robot manipulators from joint space variables to Cartesian space variables. The global stability of the closed-loop system with CSOSM-AIK methodology is proven using the Lyapunov theorem. In order to demonstrate the robustness and effectiveness of the proposed methodology, some simulations are conducted.

Opinion Dynamics Optimization by Varying Susceptibility to Persuasion via Non-Convex Local Search

2021 ◽  
Vol 16 (2) ◽  
pp. 1-34
Author(s):  
Rediet Abebe ◽  
T.-H. HUBERT Chan ◽  
Jon Kleinberg ◽  
Zhibin Liang ◽  
David Parkes ◽  
...  
Keyword(s):  
Local Search ◽  
Objective Function ◽  
Iterative Process ◽  
Large Scale ◽  
Opinion Dynamics ◽  
Theoretical Models ◽  
Global Optimum ◽  
Local Optimum ◽  
Opinion Formation ◽  
Long Line

A long line of work in social psychology has studied variations in people’s susceptibility to persuasion—the extent to which they are willing to modify their opinions on a topic. This body of literature suggests an interesting perspective on theoretical models of opinion formation by interacting parties in a network: in addition to considering interventions that directly modify people’s intrinsic opinions, it is also natural to consider interventions that modify people’s susceptibility to persuasion. In this work, motivated by this fact, we propose an influence optimization problem. Specifically, we adopt a popular model for social opinion dynamics, where each agent has some fixed innate opinion, and a resistance that measures the importance it places on its innate opinion; agents influence one another’s opinions through an iterative process. Under certain conditions, this iterative process converges to some equilibrium opinion vector. For the unbudgeted variant of the problem, the goal is to modify the resistance of any number of agents (within some given range) such that the sum of the equilibrium opinions is minimized; for the budgeted variant, in addition the algorithm is given upfront a restriction on the number of agents whose resistance may be modified. We prove that the objective function is in general non-convex. Hence, formulating the problem as a convex program as in an early version of this work (Abebe et al., KDD’18) might have potential correctness issues. We instead analyze the structure of the objective function, and show that any local optimum is also a global optimum, which is somehow surprising as the objective function might not be convex. Furthermore, we combine the iterative process and the local search paradigm to design very efficient algorithms that can solve the unbudgeted variant of the problem optimally on large-scale graphs containing millions of nodes. Finally, we propose and evaluate experimentally a family of heuristics for the budgeted variant of the problem.

scholarly journals Research on the inverse kinematics of manipulator using an improved self-adaptive mutation differential evolution algorithm

2021 ◽  
Vol 18 (3) ◽  
pp. 172988142110144
Author(s):  
Qianqian Zhang ◽  
Daqing Wang ◽  
Lifu Gao
Keyword(s):  
Differential Evolution ◽  
Objective Function ◽  
Inverse Kinematics ◽  
Differential Evolution Algorithm ◽  
Weight Coefficient ◽  
Adaptive Mutation ◽  
Feasible Region ◽  
Serial Manipulators ◽  
De Algorithm ◽  
Self Adaptive

To assess the inverse kinematics (IK) of multiple degree-of-freedom (DOF) serial manipulators, this article proposes a method for solving the IK of manipulators using an improved self-adaptive mutation differential evolution (DE) algorithm. First, based on the self-adaptive DE algorithm, a new adaptive mutation operator and adaptive scaling factor are proposed to change the control parameters and differential strategy of the DE algorithm. Then, an error-related weight coefficient of the objective function is proposed to balance the weight of the position error and orientation error in the objective function. Finally, the proposed method is verified by the benchmark function, the 6-DOF and 7-DOF serial manipulator model. Experimental results show that the improvement of the algorithm and improved objective function can significantly improve the accuracy of the IK. For the specified points and random points in the feasible region, the proportion of accuracy meeting the specified requirements is increased by 22.5% and 28.7%, respectively.

scholarly journals Study on the Inverse Kinematics Problem of Robot (2nd Report)

1997 ◽  
Vol 63 (5) ◽  
pp. 699-703
Author(s):  
Xiaohai JIN ◽  
Sachio SHIMIZU ◽  
Nobuyuki FURUYA
Keyword(s):  
Inverse Kinematics ◽  
Inverse Kinematics Problem
Sign in / Sign up

Export Citation Format

Share Document