A fast workspace-density-driven inverse kinematics method for hyper-redundant manipulators

Robotica ◽  
2006 ◽  
Vol 24 (5) ◽  
pp. 649-655 ◽  
Author(s):  
Yunfeng Wang
Keyword(s):  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Reference Frames ◽  
Detailed Comparison ◽  
Joint Space ◽  
Divide And Conquer ◽  
Redundant Manipulators ◽  
Breadth First Search ◽  
High Degree ◽  
Very High

Hyper-redundant manipulators have a very large number of redundant degrees of freedom. They have been recognized as a means to improve manipulator performance in complex and unstructured environments. However, the high degree of redundancy also poses new challenges when performing inverse kinematics calculations. Prior works have shown that the workspace density (generated by sampling the joint space and evaluating the frequency of occurrence of the resulting end-effector reference frames) is a valuable quantity for use in ${\cal O}(P)$ inverse kinematics algorithms. Here $P$ is the number of modules in a manipulator constructed of a serial cascade of modules. This paper develops a new “divide-and-conquer” method for inverse kinematics using the workspace density. This method does not involve a high-dimensional Jacobian matrix and offers high accuracy. And its computational complexity is only ${\cal O}({\rm log}_2\,P)$, which makes it ideal for very high degree-of-freedom systems. Numerical simulations are performed to demonstrate this new method on a planar example, and a detailed comparison with a breadth-first search method is conducted.

scholarly journals Finite-Horizon Kinetic Energy Optimization of a Redundant Space Manipulator

2021 ◽  
Vol 11 (5) ◽  
pp. 2346
Author(s):  
Alessandro Tringali ◽  
Silvio Cocuzza
Keyword(s):  
Kinetic Energy ◽  
Real Time ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Computational Time ◽  
Redundant Manipulators ◽  
Space Robotics ◽  
Optimal Method ◽  
End Effector ◽  
Global Optimal

The minimization of energy consumption is of the utmost importance in space robotics. For redundant manipulators tracking a desired end-effector trajectory, most of the proposed solutions are based on locally optimal inverse kinematics methods. On the one hand, these methods are suitable for real-time implementation; nevertheless, on the other hand, they often provide solutions quite far from the globally optimal one and, moreover, are prone to singularities. In this paper, a novel inverse kinematics method for redundant manipulators is presented, which overcomes the above mentioned issues and is suitable for real-time implementation. The proposed method is based on the optimization of the kinetic energy integral on a limited subset of future end-effector path points, making the manipulator joints to move in the direction of minimum kinetic energy. The proposed method is tested by simulation of a three degrees of freedom (DOF) planar manipulator in a number of test cases, and its performance is compared to the classical pseudoinverse solution and to a global optimal method. The proposed method outperforms the pseudoinverse-based one and proves to be able to avoid singularities. Furthermore, it provides a solution very close to the global optimal one with a much lower computational time, which is compatible for real-time implementation.

Control of a Handwriting Robot with DOF Redundancy Based on Feedback in Task Coordinates

2004 ◽  
Vol 16 (4) ◽  
pp. 381-387 ◽  
Author(s):  
Hiroe Hashiguchi ◽  
◽  
Suguru Arimoto ◽  
Ryuta Ozawa
Keyword(s):  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Sensory Feedback ◽  
Closed Loop ◽  
Joint Space ◽  
Hand Dexterity ◽  
Loop Dynamics ◽  
Additional Input ◽  
Ill Posed ◽  
Joint Motions

To enhance robot hand dexterity, it is said that the robot should be designed to have a redundant number of degrees of freedom. In redundant robotic systems, inverse kinematics from task description space to joint space becomes ill-posed, making it difficult to determine joint motions. To avoid this ill-posedness, most proposed methods introduce an additional input term calculated from an intentionally introduced artificial index of performance. We propose a 4 DOF redundant handwriting robot using novel simple control to solve the problem of ill-posedness based on sensory feedback. We demonstrate the effectiveness of proposed control in computer simulation of closed-loop dynamics with the constraint that the robot’s endpoint be always on a two-dimensional plane.

Human Modeling: Inverse Kinematics with Maximum Joint Availability

2000 ◽  
Vol 44 (38) ◽  
pp. 848-851
Author(s):  
Terrence J. Mayes ◽  
James C. Maida
Keyword(s):  
Personal Computer ◽  
Inverse Kinematics ◽  
Degree Of Freedom ◽  
Hybrid Technique ◽  
Performance Simulation ◽  
Human Modeling ◽  
High Degree ◽  
Very High

This paper describes a hybrid technique for performing inverse kinematics (IK) on redundant articulations with very high degree of freedom. Components from several different IK approaches are combined with special attention given to performance. Simulation of the algorithm on a personal computer can be done at interactive rates. Modifications to the standard IK approach are discussed and compared against previous approaches.

scholarly journals Stability and steady state of complex cooperative systems: a diakoptic approach

2019 ◽  
Vol 6 (12) ◽  
pp. 191090 ◽  
Author(s):  
Philip Greulich ◽  
Ben D. MacArthur ◽  
Cristina Parigini ◽  
Rubén J. Sánchez-García
Keyword(s):  
Degrees Of Freedom ◽  
Dependence Graph ◽  
Divide And Conquer ◽  
Connected Components ◽  
Dominant Eigenvalue ◽  
Theoretical Criterion ◽  
Strongly Connected ◽  
Cooperative Dynamics ◽  
Eigenvalue Zero ◽  
High Degree

Cooperative dynamics are common in ecology and population dynamics. However, their commonly high degree of complexity with a large number of coupled degrees of freedom renders them difficult to analyse. Here, we present a graph-theoretical criterion, via a diakoptic approach (divide-and-conquer) to determine a cooperative system’s stability by decomposing the system’s dependence graph into its strongly connected components (SCCs). In particular, we show that a linear cooperative system is Lyapunov stable if the SCCs of the associated dependence graph all have non-positive dominant eigenvalues, and if no SCCs which have dominant eigenvalue zero are connected by a path.

Research on Kinematics Analysis and Trajectory Planning of Novel EOD Manipulator

2021 ◽  
Vol 11 (20) ◽  
pp. 9438
Author(s):  
Jianwei Zhao ◽  
Tao Han ◽  
Xiaofei Ma ◽  
Wen Ma ◽  
Chengxiang Liu ◽  
...  
Keyword(s):  
Trajectory Planning ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Random Number ◽  
Polynomial Interpolation ◽  
Interpolation Method ◽  
Joint Space ◽  
Work Requirements ◽  
Multiple Degrees Of Freedom ◽  
Quintic Polynomial

To address the problems of mismatch, poor flexibility and low accuracy of ordinary manipulators in the complex special deflagration work process, this paper proposes a new five-degree-of-freedom (5-DOF) folding deflagration manipulator. Firstly, the overall structure of the explosion-expulsion manipulator is introduced. The redundant degrees of freedom are formed by the parallel joint axes of the shoulder joint, elbow joint and wrist pitching joint, which increase the flexibility of the mechanism. Aiming at a complex system with multiple degrees of freedom and strong coupling of the manipulator, the virtual joint is introduced, the corresponding forward kinematics model is established by D–H method, and the inverse kinematics solution of the manipulator is derived by analytical method. In the MATLAB platform, the workspace of the manipulator is analyzed by Monte Carlo pseudo-random number method. The quintic polynomial interpolation method is used to simulate the deflagration task in joint space. Finally, the actual prototype experiment is carried out using the data obtained by simulation. The trajectory planning using the quintic polynomial interpolation method can ensure the smooth movement of the manipulator and high accuracy of operation. Furthermore, the trajectory is basically consistent with the simulation trajectory, which can realize the work requirements of putting the object into the explosion-proof tank. The new 5-DOF folding deflagration manipulator designed in this paper has stable motion and strong robustness, which can be used for deflagration during the COVID-19 epidemic.

Natural Resolution of Ill-Posed Inverse Kinematics for Redundant Robots: A Challenge to Bernstein’s Degrees-of-Freedom Problem

2006 ◽  
Vol 18 (5) ◽  
pp. 651-660 ◽  
Author(s):  
Suguru Arimoto ◽  
◽  
Masahiro Sekimoto ◽  
Keyword(s):  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Sensory Feedback ◽  
Joint Space ◽  
Dimensional Manifold ◽  
Reaching Task ◽  
Loop Dynamics ◽  
Ill Posed ◽  
Human Limb ◽  
Joint Velocity

Over half a century ago, A. N. Bernstein observed that “dexterity” in human limb movement emerges from the involvement of multijoint motion with surplus degrees of freedom (DOF). Robotics posits that DOF redundancy in robot may enhance dexterity and versatility. Kinematic redundancy involves the problem of ill-posed inverse kinematics from task-description space to joint space. This problem is conventionally avoided by introducing an artificial performance index and uniquely determining an inverse kinematics solution by minimizing it. Instead of taking this conventional avoidance solution, we propose challenging Bernstein’s DOF problem by introducing two direct novel concepts - stability on a manifold and transferability to a submanifold - in dealing with human multijoint movement in reaching and showing that sensory feedback from task space to joint space together with adequate damping (joint velocity feedback) enables any solution to overall closed-loop dynamics to converge naturally and coordinately to a lower-dimensional manifold describing a set of joint states fulfilling a given motion task. This means that a reaching task is accomplished by sensory feedback with the appropriate choice of a stiffness parameter and damping coefficients without having to consider inverse kinematics. We also show that these concepts cope with the annoying “variability” of redundant joint motion seen typically in skilled human reaching. In conclusion, we propose a virtual spring/damper hypothesis that leads to natural control of skilled movement in redundant multijoint reaching.

scholarly journals A Solution of the Inverse Kinematics Problem for a 7-Degrees-of-Freedom Serial Redundant Manipulator Using Gröbner Bases Theory

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Sérgio Ricardo Xavier da Silva ◽  
Leizer Schnitman ◽  
Vitalino Cesca Filho
Keyword(s):  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Gröbner Bases ◽  
Grobner Bases ◽  
Operational Performance ◽  
Redundant Manipulators ◽  
Redundant Manipulator ◽  
All Solutions ◽  
Inverse Kinematics Problem ◽  
Algebraic Computing

This article presents a solution of the inverse kinematics problem of 7-degrees-of-freedom serial redundant manipulators. A 7-degrees-of-freedom (7-DoF) redundant manipulator can avoid obstacles and thus improve operational performance. However, its inverse kinematics is difficult to solve since it has one more DoF than that necessary for reaching the whole workspace, which causes infinite solutions. In this article, Gröbner bases theory is proposed to solve the inverse kinematics. First, the Denavit–Hartenberg model for the manipulator is established. Second, different joint configurations are obtained using Gröbner bases theory. All solutions are confirmed with the aid of algebraic computing software, confirming that this method is accurate and easy to be implemented.

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.

Inverse Kinematics of Redundant Manipulators Formulated as Quadratic Programming Optimization Problem Solved Using Recurrent Neural Networks: A Review

Robotica ◽  
2019 ◽  
Vol 38 (8) ◽  
pp. 1495-1512
Author(s):  
Ahmed A. Hassan ◽  
Mohamed El-Habrouk ◽  
Samir Deghedie
Keyword(s):  
Neural Networks ◽  
Quadratic Programming ◽  
Recurrent Neural Networks ◽  
Inverse Kinematics ◽  
Optimization Problem ◽  
Problem Formulation ◽  
Joint Space ◽  
Problem Solution ◽  
Redundant Manipulators ◽  
Joint Angles

SUMMARYThe Inverse Kinematics (IK) problem of manipulators can be divided into two distinct steps: (1) Problem formulation, where the problem is developed into a form which can then be solved using various methods. (2) Problem solution, where the IK problem is actually solved by producing the values of different joint space variables (joint angles, joint velocities or joint accelerations). The main focus of this paper is concentrated on the discussion of the IK problem of redundant manipulators, formulated as a quadratic programming optimization problem solved by different kinds of recurrent neural networks.

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