Kinematics and Singularity Analysis of a 7-DOF Redundant Manipulator

A new method of kinematic analysis and singularity analysis is proposed for a 7-DOF redundant manipulator with three consecutive parallel axes. First, the redundancy angle is described according to the self-motion characteristics of the manipulator, the position and orientation of the end-effector are separated, and the inverse kinematics of this manipulator is analyzed by geometric methods with the redundancy angle as a constraint. Then, the Jacobian matrix is established to derive the conditions for the kinematic singularities of the robotic arm by using the primitive matrix method and the block matrix method. Then, the kinematic singularities conditions in the joint space are mapped to the Cartesian space, and the singular configuration is described using the end poses and redundancy angles of the robotic arm, and a singularity avoidance method based on the redundancy angles and end pose is proposed. Finally, the correctness and feasibility of the inverse kinematics algorithm and the singularity avoidance method are verified by simulation examples.

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

10.20944/preprints202005.0162.v1 ◽

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.

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Spherical trigonometry constrained kinematics for a dexterous robotic hand with an articulated palm

Robotica ◽

10.1017/s0263574715000399 ◽

2015 ◽

Vol 34 (12) ◽

pp. 2788-2805 ◽

Cited By ~ 3

Author(s):

Evangelos Emmanouil ◽

Guowu Wei ◽

Jian S. Dai

Keyword(s):

Point Clouds ◽

Joint Space ◽

Singularity Analysis ◽

Spherical Triangle ◽

Design Criteria ◽

Robotic Hand ◽

Spherical Trigonometry ◽

Joint Angles ◽

Singularity Avoidance ◽

Spherical Triangles

SUMMARYThis work presents a method based on spherical trigonometry for computing all joint angles of the spherical metamorphic palm. The spherical palm is segmented into spherical triangles which are then solved and combined to fully solve the palm configuration. Further, singularity analysis is investigated with the analysis of each spherical triangle the palm is decomposed. Singularity-avoidance-based design criteria are then presented. Finally, point clouds are generated that represent the joint space of the palm as well as the workspace of the hand with the advantage of an articulated palm is shown.

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Singularity analysis and avoidance of a planar parallel mechanism with kinematic redundancy under a fixed orientation

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406220976712 ◽

2020 ◽

pp. 095440622097671

Author(s):

Haibo Qu ◽

Lanqing Hu ◽

Sheng Guo

Keyword(s):

Inverse Kinematics ◽

Parallel Mechanism ◽

Singularity Analysis ◽

Kinematic Redundancy ◽

Comparison Analysis ◽

Singularity Avoidance ◽

Singular Configurations ◽

Fixed Orientation ◽

Free Transition ◽

Singular Configuration

In this paper, the singularity of a planar mechanism with kinematic redundancy is studied. First, the architecture of the mechanism and the concept schematic diagram for singularity avoidance are stated. Next, inverse kinematics model of the planar parallel mechanism with kinematic redundancy is established. For determining the unique inverse solution of the mechanism under certain initial installation configuration, a comparison analysis based on the strategy tree and the virtual prototype is performed. Then, based on the obtained Jacobian matrices and the singular condition, the workspace-singularity map and two singular configurations of the mechanism are drawn. Finally, with the obtained workspace-singularity map, a singularity-free transition layer and an aisle can be found to perform to singularity avoidance, even if the initial designed trajectory passing through the second kind of singularity. Three tasks are carried out to illustrate that the workspace boundary and singular configuration can be changed by adjusting the kinematic redundant actuated parameter.

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Computing Robust Inverse Kinematics Under Uncertainty

Volume 5A: 43rd Mechanisms and Robotics Conference ◽

10.1115/detc2019-97945 ◽

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.

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Planning Manipulation and Grasping Tasks With a Redundant Arm

Volume 6: 35th Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2011-47453 ◽

2011 ◽

Cited By ~ 1

Author(s):

Steven R. Gray ◽

Joseph M. Romano ◽

Jordan Brindza ◽

Soonkyum Kim ◽

Katherine J. Kuchenbecker ◽

...

Keyword(s):

Software Architecture ◽

Inverse Kinematics ◽

Hardware Implementation ◽

Joint Space ◽

Target Object ◽

State Machine ◽

Robotic Arm ◽

Autonomous Manipulation ◽

Manipulation Task ◽

Position And Orientation

This paper presents an approach to analysis and planning for autonomous manipulation tasks using a commercially available robotic arm and hand. We discuss hardware implementation, software architecture, and state machine behaviors. The inverse kinematics of the seven-degree-of-freedom manipulator are analytically derived with special attention to deterministically resolving the redundancy at the position level. Appropriate grasps are generated given the perceived position and orientation of the target object. Planning for the arm is accomplished in joint space using an RRT* implementation. Our implementation is able to detect an arbitrarily placed object in the workspace, generate a plan for the arm and hand avoiding obstacles, and execute the planned manipulation task. To show the efficacy of our approach, we present experiments in which the system autonomously grasps a canteen and a flashlight.

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MIMO adaptive control with ∊-modification and on-line singularity avoidance method for hyper-redundant robotic arm

2016 IEEE National Aerospace and Electronics Conference (NAECON) and Ohio Innovation Summit (OIS) ◽

10.1109/naecon.2016.7856801 ◽

2016 ◽

Author(s):

Xingsheng Xu ◽

Raul Ordonez

Keyword(s):

Adaptive Control ◽

Robotic Arm ◽

Singularity Avoidance ◽

Line Singularity ◽

On Line

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Trial mountain climbing algorithm for solving the inverse kinematics of redundant manipulator

Journal of Central South University of Technology ◽

10.1007/s11771-002-0043-x ◽

2002 ◽

Vol 9 (4) ◽

pp. 285-288 ◽

Cited By ~ 3

Author(s):

You-hang Zhou ◽

Qing-hua He ◽

Bo-lu Deng

Keyword(s):

Inverse Kinematics ◽

Redundant Manipulator ◽

Mountain Climbing

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The inverse kinematics solutions of a 7 DOF robotic arm using Fuzzy Logic

2012 7th IEEE Conference on Industrial Electronics and Applications (ICIEA) ◽

10.1109/iciea.2012.6360783 ◽

2012 ◽

Cited By ~ 4

Author(s):

Mihai Crenganis ◽

Radu Breaz ◽

Gabriel Racz ◽

Octavian Bologa

Keyword(s):

Fuzzy Logic ◽

Inverse Kinematics ◽

Robotic Arm

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

Robotica ◽

10.1017/s0263574715000284 ◽

2015 ◽

Vol 34 (12) ◽

pp. 2669-2688 ◽

Cited By ~ 7

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.

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