scholarly journals Euclidean metrics for motion generation on SE(3)

2002 ◽  
Vol 216 (1) ◽  
pp. 47-60 ◽  
Author(s):  
C Belta ◽  
V Kumar
Keyword(s):  
Ad Hoc ◽  
Trajectory Generation ◽  
Rigid Bodies ◽  
Second Step ◽  
Computationally Efficient ◽  
Motion Generation ◽  
Euclidean Group ◽  
Screw Motions ◽  
Euclidean Metrics ◽  
Generation Problem

Previous approaches to trajectory generation for rigid bodies have been either based on the so-called invariant screw motions or on ad hoc decompositions into rotations and translations. This paper formulates the trajectory generation problem in the framework of Lie groups and Riemannian geometry. The goal is to determine optimal curves joining given points with appropriate boundary conditions on the Euclidean group. Since this results in a two-point boundary value problem that has to be solved iteratively, a computationally efficient, analytical method that generates near-optimal trajectories is derived. The method consists of two steps. The first step involves generating the optimal trajectory in an ambient space, while the second step is used to project this trajectory onto the Euclidean group. The paper describes the method, its applications and its performance in terms of optimality and efficiency.

MotionGen: An iOS and Android App for Planar Four-Bar Motion Generation

2016 ◽  
Author(s):  
Anurag Purwar ◽  
Shrinath Deshpande ◽  
Q. J. Ge
Keyword(s):  
Rigid Bodies ◽  
Geometric Constraints ◽  
Motion Generation ◽  
Unified Framework ◽  
Approximate Synthesis ◽  
Unified Algorithm ◽  
Android App ◽  
Google Android ◽  
High Utility ◽  
Generation Problem

MotionGen is an indigenously developed app for Apple iOS and Google Android platforms to help mechanism designers solve planar four-bar motion generation problem. The app is a computer implementation of authors’ recent work in developing a unified framework for the synthesis and simulation of planar four-bar mechanisms for the motion generation problem. Simplicity, high-utility, and wide-spread adoption of planar four-bar linkages have made them one of the most studied topics in Kinematics leading to development of algorithms and theories that deal with path-, function-, and motion generation-problems. Yet to date, there have been no attempts to develop efficient computational algorithms amenable to real-time computation of both type and dimensions of planar four-bar mechanisms for a given motion. MotionGen solves this problem effectively by extracting the geometric constraints of a given motion to provide the best dyad-types as well as dimensions of a total of up to six four-bar linkages. The unified algorithm also admits additional practical constraints, such as imposition of fixed- and moving-pivot and -line locations along with mixed exact- and approximate-synthesis scenarios. In that regard, its synthesis capabilities set it apart from other softwares of its ilk. However, its simulation approach also departs from more traditional methods, which typically involves assembling four rigid bodies and then designating fixed and moving links. Instead, the MotionGen requires users to assemble only two of the geometric constraints of mechanical dyads for quick prototyping of planar four-bar linkages. The app is equipped with an intuitive graphical user interface that allows a fluid dialog with the user to facilitate rapid manipulation and visualization of linkages.

A New Trajectory-Generation Scheme for Overhead Cranes With High-Speed Load Hoisting

2004 ◽  
Author(s):  
Ho-Hoon Lee ◽  
Del Segura ◽  
Yi Liang
Keyword(s):  
High Speed ◽  
High Performance ◽  
Trajectory Generation ◽  
Control Law ◽  
Mathematical Tool ◽  
Lyapunov Stability Theorem ◽  
Overhead Cranes ◽  
Time Control ◽  
Load Swing ◽  
Generation Problem

This paper proposes a new trajectory-generation scheme for a high-performance anti-swing control of overhead cranes, where the trajectory-generation problem is solved as a kinematic problem. First, a new anti-swing control law is designed based on the load-swing dynamics, for which the Lyapunov stability theorem is used as a mathematical tool. Then a new trajectory-generation scheme is proposed based on the anti-swing control law and typical crane operation in practice. For g iven hoisting motions, trolley-traveling trajectory references are computed based on the concept of minimum-time control, and then anti-swing trajectories are generated based on the trajectory references through the anti-swing control law. The new trajectory-generation scheme generates a typical anti-swing trajectory in industry with high-speed load hoisting. The effectiveness of the proposed trajectory-generation scheme is shown by generating high-performance anti-swing trajectories with high hoisting speed and hoisting ratio.

Contact-space resolution model for a physically consistent view of simultaneous collisions in articulated-body systems: theory and experimental results

2020 ◽  
Vol 39 (10-11) ◽  
pp. 1239-1258
Author(s):  
Shameek Ganguly ◽  
Oussama Khatib
Keyword(s):  
System Dynamics ◽  
Rigid Body ◽  
Degrees Of Freedom ◽  
Null Space ◽  
Rigid Bodies ◽  
Computationally Efficient ◽  
Space Resolution ◽  
Resolution Model ◽  
Space Dynamics ◽  
Contact Space

Multi-surface interactions occur frequently in articulated-rigid-body systems such as robotic manipulators. Real-time prediction of contact-interaction forces is challenging for systems with many degrees of freedom (DOFs) because joint and contact constraints must be enforced simultaneously. While several contact models exist for systems of free rigid bodies, fewer models are available for articulated-body systems. In this paper, we extend the method of Ruspini and Khatib and develop the contact-space resolution (CSR) model by applying the operational space theory of robot manipulation. Through a proper choice of contact-space coordinates, the projected dynamics of the system in the contact space is obtained. We show that the projection into the dynamically consistent null space preserves linear and angular momentum in a subspace of the system dynamics complementary to the joint and contact constraints. Furthermore, we illustrate that a simultaneous collision event between two articulated bodies can be resolved as an equivalent simultaneous collision between two non-articulated rigid bodies through the projected contact-space dynamics. Solving this reduced-dimensional problem is computationally efficient, but determining its accuracy requires physical experimentation. To gain further insights into the theoretical model predictions, we devised an apparatus consisting of colliding 1-, 2-, and 3-DOF articulated bodies where joint motion is recorded with high precision. Results validate that the CSR model accurately predicts the post-collision system state. Moreover, for the first time, we show that the projection of system dynamics into the mutually complementary contact space and null space is a physically verifiable phenomenon in articulated-rigid-body systems.

scholarly journals A Bi-Directional Carrier Sense Collision Avoidance Neighbor Discovery Algorithm in Directional Wireless Ad Hoc Sensor Networks

Sensors ◽  
2019 ◽  
Vol 19 (9) ◽  
pp. 2120
Author(s):  
Annan Yang ◽  
Bo Li ◽  
Zhongjiang Yan ◽  
Mao Yang
Keyword(s):  
Collision Avoidance ◽  
Ad Hoc ◽  
Engineering Application ◽  
Second Step ◽  
Neighbor Discovery ◽  
The Past ◽  
Carrier Sense ◽  
Ad Hoc Sensor Networks ◽  
Neighbor Discovery Protocol ◽  
Common Defect

From the perspective of media protocol control and routing of directional wireless ad hoc sensors networks, neighbor discovery protocol is an important problem to be solved first. In the past period of time, some methods have been studied on neighbor discovery protocol, but they have a common defect of link collision. The collision is caused by mutual interference of multiple transmitting nodes which are in one reception beam of the receiving node. To solve this problem, we propose a neighbor discovery algorithm using a bi-directional carrier sense collision avoidance and multi subchannels based on a scan-based algorithm (BD-SBA). Based on a scan-based algorithm (SBA), bi-directional carrier sense of the BD-SBA algorithm is performed in the first broadcast step which can reduce the collision of broadcasting the scanning request (SREQ) frames. In the second step (the reply step), the mechanism of multiple subchannels and multiple slots is applied to reduce the collision of the scanning response (SRES) frames. From the analysis and simulation, we can see that nodes using proposed algorithm can discover their neighbor nodes in fewer time. Moreover, the proposed algorithm has better performance for different beamwidths and densely distributed scenes. So it has great significance in engineering application.

Elimination of Branch, Grashof, and Order Defects in Path-Angle Generation and Function Generation Synthesis

1979 ◽  
Vol 101 (3) ◽  
pp. 428-437 ◽  
Author(s):  
K. J. Waldron ◽  
E. N. Stevensen
Keyword(s):  
Motion Generation ◽  
Function Generation ◽  
And Function ◽  
Generation Problem

Path-Angle Generation and Function Generation synthesis problems are restated as Plane-Position (or Motion Generation) problems, enabling the use of the classical Burmester technique and recent extensions that permit the avoidance of Branch, Grashof, and Order defects. An example of the solution of a Path-Angle Generation problem is given.

Trajectory Generation for Redundant Manipulator using Virus-Evolutionary Genetic Algorithm with Subpopulations

1997 ◽  
Vol 1 (2) ◽  
pp. 155-161
Author(s):  
Takemasa Arakawa ◽  
◽  
Toshio Fukuda ◽  
Naoyuki Kubota ◽  
Keyword(s):  
Genetic Algorithm ◽  
Genetic Information ◽  
Energy Optimization ◽  
Trajectory Generation ◽  
Redundant Manipulators ◽  
Redundant Manipulator ◽  
Theory Of Evolution ◽  
Evolutionary Genetic ◽  
Generation Problem ◽  
Virus Theory

In this paper, we apply a virus-evolutionary genetic algorithm with subpopulations (VEGAS) to a trajectory generation problem for redundant manipulators through energy optimization. VEGAS is based on the virus theory of evolution and VEGAS has some subpopulations that usually evolve independently. In the same subpopulation, a virus infects host individuals. And a virus sometimes immigrates from one subpopulation to another. The genetic information from one subpopulation propagates in another subpopulation only through immigration of the virus. The energy-optimized collision-free trajectory was found successfully using VEGAS.

A Model for Assessing the Shape of Solder Joints in the Presence of PCB and Package Warpage

2005 ◽  
Vol 128 (3) ◽  
pp. 184-191 ◽  
Author(s):  
Mahidhar Rayasam ◽  
Terrace B. Thompson ◽  
Ganesh Subbarayan ◽  
C. Gurumurthy ◽  
J. R. Wilcox
Keyword(s):  
Solder Joints ◽  
Equilibrium Configuration ◽  
Circuit Board ◽  
Second Step ◽  
Computationally Efficient ◽  
Test Vehicle ◽  
Step Procedure ◽  
Solder Volume ◽  
Restoring Forces ◽  
Material Volume

Our goals in this paper are to develop and demonstrate a computationally efficient methodology for assessing the effect of circuit board warpage, component warpage, and solder volume variation on the shape of the solder joints in area array packages. The effect of warpage is analyzed using a two-step procedure in the present paper. In the first step, the restoring forces and moments (in the molten state of solder droplet) that result from a given solder joint height, solder material volume, pad diameter, and pad inclination are predicted using the surface tension theory. In the second step of the analysis, the forces and moments at individual solder joints caused by varying solder heights and pad tilts are combined to predict the equilibrium configuration of the package. A program written in the MATHEMATICA® environment was developed to implement the above-described methodology. The developed procedure was validated on an experimental test vehicle with nine solder joints. The heights of solder joints computed by the program matched the experimentally measured heights to within ±5% error. Further, the general capabilities of the modeling procedure are demonstrated by assuming complex combinations of package and PCB warpage.

Finite Position Synthesis of 5-SS Platform Linkages Including Partially Specified Joint Locations

2017 ◽  
Author(s):  
Xin Ge ◽  
Anurag Purwar ◽  
Q. J. Ge
Keyword(s):  
Linear Structure ◽  
Motion Generation ◽  
Numerical Examples ◽  
Moving Points ◽  
Unified Algorithm ◽  
Moving Platform ◽  
Position Synthesis ◽  
Partial Specification ◽  
Generation Problem ◽  
Novel Algorithm

A 5-SS platform linkage generates a one-degree-of-freedom motion of a moving platform such that each of five moving points on the platform is constrained on a sphere, or in its degenerated case, on a plane. It has been well established a 5-SS platform linkage can be made to guide though seven positions exactly. This paper investigates the cases when the number of given positions are less than seven that allows for partial specification of locations of the moving points. A recently developed novel algorithm with linear structure in the design equations has been extended for the solution of the problem. The formulation of this expanded motion generation problem unifies the treatment of the input positions and constraints on the moving and fixed joints associated with the 5-SS platform linkage. Numerical examples are provided to show the effectiveness of the unified algorithm.

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