A numerically stable algorithm for analytic inverse kinematics of 7-DoF S-R-S manipulators with joint limit avoidance

2021 ◽  
pp. 1-15
Author(s):  
Junchen Wang ◽  
Chunheng Lu ◽  
Yinghao Zhang ◽  
Zhen Sun ◽  
Yu Shen
Keyword(s):  
Inverse Kinematics ◽  
Joint Angle ◽  
State Of The Art ◽  
Joint Angles ◽  
Stable Algorithm ◽  
Angle Space ◽  
Joint Limits ◽  
Self Motion ◽  
Configuration Control ◽  
Joint Limit

Abstract This paper presents a numerically stable algorithm for analytic inverse kinematics of 7-DoF S-R-S manipulators with joint limit avoidance. The arm angle is used to represent the self-motion manifold within a global arm configuration. The joint limits are analytically mapped to the arm angle space for joint limit avoidance. To profile the relation between the joint angle and arm angle, it is critical to characterize the singular arm angle for each joint. In the-state-of-the art methods, the existence of the singular arm angle is triggered by comparing a discriminant with zero given a threshold. We will show this leads to numerical issues since the threshold is inconsistent among different target poses, leading to incorrect range of the arm angle. These issues are overcome by associating indeterminate joint angles of tangent joints with angles of 0 or pi of cosine joints, rather than using an independent threshold for each joint. The closed-form algorithm in C++ code to perform numerically stable inverse kinematics of 7-DoF S-R-S manipulators with global arm configuration control and joint limit avoidance is also given.

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

Robotica ◽  
2015 ◽  
Vol 34 (12) ◽  
pp. 2669-2688 ◽  
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.

Joint angle variations analyses of the two link planar manipulator in welding by using inverse kinematics

Robotica ◽  
2005 ◽  
Vol 24 (3) ◽  
pp. 355-363 ◽  
Author(s):  
S. Bulut ◽  
M. B. Terzioǧlu
Keyword(s):  
Angular Velocity ◽  
Data Collection ◽  
Inverse Kinematics ◽  
Joint Angle ◽  
Joint Angles ◽  
End Effector ◽  
Fortran 90

In this paper, the joint angles of a two link planar manipulator are calculated by using inverse kinematics equations together with some geometric equalities. For a given position of the end-effector the joint angle and angular velocity of the links are derived. The analyses contains many equations which have to be solved. However, the solutions are rather cumbersome and complicated, therefore a program is written in Fortran 90 in order to do, the whole calculation and data collection. The results are given at the end of this paper.

Inverse Solution and Optimal Concept Rethink from Human Operation to Industrial Redundant Manipulator

2014 ◽  
Vol 541-542 ◽  
pp. 1140-1145 ◽  
Author(s):  
Mei Ling Wang ◽  
Min Zhou Luo ◽  
Xin Lin
Keyword(s):  
Real Time ◽  
Computational Efficiency ◽  
Inverse Kinematics ◽  
Joint Angle ◽  
Inverse Solution ◽  
Joint Movement ◽  
Redundant Manipulator ◽  
Joint Angles ◽  
Human Arm ◽  
Dual Arm

More and more dual arm robots with redundant manipulator are introduced in industrial fields. Here we focus on this special structure with 7-DOF redundant manipulator, an exhibit analytical and optimal concept was proposed. The formula derivations of inverse kinematics showed that when the redundant joint angle has been obtained, the remaining six joint angles can be derived analytically, and there are eight sets of inverse solution for one giving redundant joint angle. Reversed thinking the joint movement habits, patterns, and frequency of human arm operations, an optimal concept was presented to gain a real time computational efficiency of a direct inverse solution while also achieving the purpose of application.

scholarly journals Learning of Obstacle Avoidance with Redundant Manipulator by Hierarchical SOM

2011 ◽  
Vol 15 (5) ◽  
pp. 525-531
Author(s):  
Yuichi Kobayashi ◽  
◽  
Takahiro Nomura
Keyword(s):  
Reinforcement Learning ◽  
Obstacle Avoidance ◽  
Inverse Kinematics ◽  
Joint Angle ◽  
Hand Position ◽  
Redundant Manipulator ◽  
Motion Generation ◽  
Joint Angles ◽  
Vision Sensors ◽  
Configuration Information

This paper proposes a method of obstacle avoidance motion generation for a redundant manipulator with a Self-OrganizingMap (SOM) and reinforcement learning. To consider redundancy, two types of SOMs - a hand position map and a joint angle map - are combined. Multiple joint angles corresponding to the same hand position are memorized in the proposed map. Preserved redundant configuration information is used to generate motions based on tasks and situations, while resolving inverse kinematics problems with a redundant manipulator. The proposed map is applied to planning motion control using reinforcement learning in an unknown environment, where collision with obstacles is detected only directly by tactile sensing. The feasibility of the proposed framework was verified by simulation and experiments with an arm robot with force and a vision sensors.

scholarly journals Hand posture comparison in Synergy Space

2017 ◽  
Author(s):  
Nayan Bhatt ◽  
Varadhan SKM
Keyword(s):  
Degrees Of Freedom ◽  
Joint Angle ◽  
Similarity Index ◽  
Movement Control ◽  
Human Movement ◽  
Hand Posture ◽  
Joint Angles ◽  
Angle Space ◽  
The Central Nervous System ◽  
Kinematic Transformation

In studies of human movement control, an important question is how the central nervous system (CNS) controls movements in the presence of a large number of degrees of freedom (DoFs) at all levels of the control architecture. It is known that CNS groups the multiple DoFs into representative functional units also called synergies for simplification of the task. Hence, comparing two different hand postures in the synergy space, rather than joint angle space may provide insightful information about efforts needed (in terms of synergy components) to transform from one hand posture to another hand posture. Working with synergy space may also provide information about how CNS deals with system with multiple DoFs. We developed an index called posture similarity index (PSI) which measures the similarity of two postures by projecting hand posture from the joint angles into the synergy space. A large value of PSI represents high similarity between postures whereas a lower value represents less similarity between postures. This index uses principle of synergies and nicely captures effort required for kinematic transformation. Using this index as a feature, possible set of representative postures can be identified. The other hand postures can be derived from a possible set of representative postures with relatively less efforts for kinematic transformation.

scholarly journals Genome-Wide Association Studies Based on Equine Joint Angle Measurements Reveal New QTL Affecting the Conformation of Horses

Genes ◽  
2019 ◽  
Vol 10 (5) ◽  
pp. 370 ◽  
Author(s):  
Annik Imogen Gmel ◽  
Thomas Druml ◽  
Rudolf von Niederhäusern ◽  
Tosso Leeb ◽  
Markus Neuditschko
Keyword(s):  
Joint Angle ◽  
Association Studies ◽  
Genome Wide Association ◽  
Cranial Morphology ◽  
Genome Wide Association Studies ◽  
Joint Angles ◽  
Mineral Density ◽  
Mixed Effect ◽  
Stifle Joint ◽  
Genome Wide

The evaluation of conformation traits is an important part of selection for breeding stallions and mares. Some of these judged conformation traits involve joint angles that are associated with performance, health, and longevity. To improve our understanding of the genetic background of joint angles in horses, we have objectively measured the angles of the poll, elbow, carpal, fetlock (front and hind), hip, stifle, and hock joints based on one photograph of each of the 300 Franches-Montagnes (FM) and 224 Lipizzan (LIP) horses. After quality control, genome-wide association studies (GWASs) for these traits were performed on 495 horses, using 374,070 genome-wide single nucleotide polymorphisms (SNPs) in a mixed-effect model. We identified two significant quantitative trait loci (QTL) for the poll angle on ECA28 (p = 1.36 × 10−7), 50 kb downstream of the ALX1 gene, involved in cranial morphology, and for the elbow joint on ECA29 (p = 1.69 × 10−7), 49 kb downstream of the RSU1 gene, and 75 kb upstream of the PTER gene. Both genes are associated with bone mineral density in humans. Furthermore, we identified other suggestive QTL associated with the stifle joint on ECA8 (p = 3.10 × 10−7); the poll on ECA1 (p = 6.83 × 10−7); the fetlock joint of the hind limb on ECA27 (p = 5.42 × 10−7); and the carpal joint angle on ECA3 (p = 6.24 × 10−7), ECA4 (p = 6.07 × 10−7), and ECA7 (p = 8.83 × 10−7). The application of angular measurements in genetic studies may increase our understanding of the underlying genetic effects of important traits in equine breeding.

scholarly journals Experimental and Numerical Study of Fracture Behavior of Rock-Like Material Specimens with Single Pre-Set Joint under Dynamic Loading

Materials ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 2690
Author(s):  
Bo Pan ◽  
Xuguang Wang ◽  
Zhenyang Xu ◽  
Lianjun Guo ◽  
Xuesong Wang
Keyword(s):  
Crack Initiation ◽  
Crack Propagation ◽  
Joint Angle ◽  
Simulation Software ◽  
Dissipated Energy ◽  
Energy Structure ◽  
Joint Angles ◽  
Crack Penetration ◽  
Before And After ◽  
The Impact

The Split Hopkinson Pressure Bar (SHPB) is an apparatus for testing the dynamic stress-strain response of the cement mortar specimen with pre-set joints at different angles to explore the influence of joint attitudes of underground rock engineering on the failure characteristics of rock mass structure. The nuclear magnetic resonance (NMR) has also been used to measure the pore distribution and internal cracks of the specimen before and after the testing. In combination with numerical analysis, the paper systematically discusses the influence of joint angles on the failure mode of rock-like materials from three aspects of energy dissipation, microscopic damage, and stress field characteristics. The result indicates that the impact energy structure of the SHPB is greatly affected by the pre-set joint angle of the specimen. With the joint angle increasing, the proportion of reflected energy moves in fluctuation, while the ratio of transmitted energy to dissipated energy varies from one to the other. NMR analysis reveals the structural variation of the pores in those cement specimens before and after the impact. Crack propagation direction is correlated with pre-set joint angles of the specimens. With the increase of the pre-set joint angles, the crack initiation angle decreases gradually. When the joint angles are around 30°–75°, the specimens develop obvious cracks. The crushing process of the specimens is simulated by LS-DYNA software. It is concluded that the stresses at the crack initiation time are concentrated between 20 and 40 MPa. The instantaneous stress curve first increases and then decreases with crack propagation, peaking at different times under various joint angles; but most of them occur when the crack penetration ratio reaches 80–90%. With the increment of joint angles in specimens through the simulation software, the changing trend of peak stress is consistent with the test results.

A Model of the Human Spine: Forward and Inverse Kinematics

1992 ◽  
Author(s):  
Sunil Kumar Agrawal ◽  
Siyan Li ◽  
Glen Desmier
Keyword(s):  
Range Of Motion ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Joint Angles ◽  
Human Spine ◽  
Forward And Inverse Kinematics ◽  
Position And Orientation ◽  
Three Degrees Of Freedom ◽  
Adjacent Vertebra

Abstract The human spine is a sophisticated mechanism consisting of 24 vertebrae which are arranged in a series-chain between the pelvis and the skull. By careful articulation of these vertebrae, a human being achieves fine motion of the skull. The spine can be modeled as a series-chain with 24 rigid links, the vertebrae, where each vertebra has three degrees-of-freedom relative to an adjacent vertebra. From the studies in the literature, the vertebral geometry and the range of motion between adjacent vertebrae are well-known. The objectives of this paper are to present a kinematic model of the spine using the available data in the literature and an algorithm to compute the inter vertebral joint angles given the position and orientation of the skull. This algorithm is based on the observation that the backbone can be described analytically by a space curve which is used to find the joint solutions..

Gyroscope-Free Link Parameter Measurement Using Accelerometers and Magnetometer

2014 ◽  
Author(s):  
Vishesh Vikas ◽  
Carl D. Crane
Keyword(s):  
Angular Velocity ◽  
Joint Angle ◽  
Inertial Sensors ◽  
Angular Acceleration ◽  
Parameter Measurement ◽  
Joint Angles ◽  
Symmetry Constraint ◽  
Estimation Techniques ◽  
Angular Velocities ◽  
Joint Parameters

Knowledge of joint angles, angular velocities is essential for control of link mechanisms and robots. The estimation of joint angles and angular velocity is performed using combination of inertial sensors (accelerometers and gyroscopes) which are contactless and flexible at point of application. Different estimation techniques are used to fuse data from different inertial sensors. Bio-inspired sensors using symmetrically placed multiple inertial sensors are capable of instantaneously measuring joint parameters (joint angle, angular velocities and angular acceleration) without use of any estimation techniques. Calibration of inertial sensors is easier and more reliable for accelerometers as compared to gyroscopes. The research presents gyroscope-less, multiple accelerometer and magnetometer based sensors capable of measuring (not estimating) joint parameters. The contribution of the improved sensor are four-fold. Firstly, the inertial sensors are devoid of symmetry constraint unlike the previously researched bio-inspired sensors. However, the accelerometer are non-coplanarly placed. Secondly, the accelerometer-magnetometer combination sensor allows for calculation of a unique rotation matrix between two link joined by any kind of joint. Thirdly, the sensors are easier to calibrate as they consist only of accelerometers. Finally, the sensors allow for calculation of angular velocity and angular acceleration without use of gyroscopes.

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