scholarly journals Improved Performance of Asymptotically Optimal Rapidly Exploring Random Trees

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Beth Boardman ◽  
Troy Harden ◽  
Sonia Martínez
Keyword(s):  
Degrees Of Freedom ◽  
Metric Spaces ◽  
Dynamic Environments ◽  
Random Trees ◽  
Asymptotically Optimal ◽  
Euclidean Metric ◽  
The Third ◽  
Dubins Vehicle ◽  
Improved Performance ◽  
Dubins Vehicles

Three algorithms that improve the performance of the asymptotically optimal Rapidly exploring Random Tree (RRT*) are presented in this paper. First, we introduce the Goal Tree (GT) algorithm for motion planning in dynamic environments where unexpected obstacles appear sporadically. The GT reuses the previous RRT* by pruning the affected area and then extending the tree by drawing samples from a shadow set. The shadow is the subset of the free configuration space containing all configurations that have geodesics ending at the goal and are in conflict with the new obstacle. Smaller, well defined, sampling regions are considered for Euclidean metric spaces and Dubins' vehicles. Next, the Focused-Refinement (FR) algorithm, which samples with some probability around the first path found by an RRT*, is defined. The third improvement is the Grandparent-Connection (GP) algorithm, which attempts to connect an added vertex directly to its grandparent vertex instead of parent. The GT and GP algorithms are both proven to be asymptotically optimal. Finally, the three algorithms are simulated and compared for a Euclidean metric robot, a Dubins' vehicle, and a seven degrees-of-freedom manipulator.

Real Time, Near-Optimal Trajectory Planning of an Omni-Directional Vehicle

2001 ◽  
Author(s):  
Tamás Kalmár-Nagy ◽  
Pritam Ganguly ◽  
Raffaello D’Andrea
Keyword(s):  
Real Time ◽  
Optimal Trajectory ◽  
Degrees Of Freedom ◽  
Dynamic Environments ◽  
Real Time Control ◽  
Uncertain Environments ◽  
Time Control ◽  
Innovative Method ◽  
Optimal Trajectory Planning ◽  
Three Degrees Of Freedom

Abstract In this paper, we discuss an innovative method of generating near-optimal trajectories for a robot with omni-directional drive capabilities, taking into account the dynamics of the actuators and the system. The relaxation of optimality results in immense computational savings, critical in dynamic environments. In particular, a decoupling strategy for each of the three degrees of freedom of the vehicle is presented, along with a method for coordinating the degrees of freedom. A nearly optimal trajectory for the vehicle can typically be calculated in less than 1000 floating point operations, which makes it attractive for real-time control in dynamic and uncertain environments.

scholarly journals Preface

2015 ◽  
Vol 27 (4) ◽  
pp. 459-459
Author(s):  
ACHIM JUNG ◽  
GUO-QIANG ZHANG
Keyword(s):  
Lattice Theory ◽  
Process Algebra ◽  
Metric Spaces ◽  
Domain Theory ◽  
Conference Series ◽  
The Third ◽  
Language Semantics ◽  
And Mathematics ◽  
October 17 ◽  
Partial Logics

The International Symposium on Domain Theory (ISDT) is a conference series intended to be a forum for researchers in domain theory and its applications. Topics include topological and logical aspects of domains; categories of domains and powerdomains; continuous posets and their representations; partial orders, lattice theory and metric spaces; types, process algebra and concurrency; non-classical and partial logics; programming language semantics; applications in computer science and mathematics. This conference series was founded by Yingming Liu, Yixiang Chen, Klaus Keimel, and Guo-Qiang Zhang. All ISDT events have taken place in China. The first ISDT was held in Shanghai, October 17–24, 1999; the second ISDT was held in Chengdu, October 22–26, 2001; the third ISDT occurred in Xi'an, China, May 10–14, 2004; the fourth ISDT was held in Changsha, June 2–6, 2006; and the fifth ISDT took place in Shanghai, September 11–14, 2009.

scholarly journals An Asymptotically Optimal NMPC Core for Multi Degrees of Freedom Rigid Bodies

2012 ◽  
Vol 45 (17) ◽  
pp. 207-212
Author(s):  
Chyon Hae Kim ◽  
Shimon Sugawara ◽  
Shigeki Sugano
Keyword(s):  
Degrees Of Freedom ◽  
Rigid Bodies ◽  
Asymptotically Optimal

Conservation Principles for Systems With a Varying Number of Degrees-of-Freedom

1998 ◽  
Vol 65 (3) ◽  
pp. 719-726 ◽  
Author(s):  
S. Djerassi
Keyword(s):  
Angular Momentum ◽  
Degrees Of Freedom ◽  
Mechanical Energy ◽  
Equations Of Motion ◽  
Nonholonomic Systems ◽  
Linear Momentum ◽  
Dynamical Equations ◽  
The Third ◽  
Conservation Principles

This paper is the third in a trilogy dealing with simple, nonholonomic systems which, while in motion, change their number of degrees-of-freedom (defined as the number of independent generalized speeds required to describe the motion in question). The first of the trilogy introduced the theory underlying the dynamical equations of motion of such systems. The second dealt with the evaluation of noncontributing forces and of noncontributing impulses during such motion. This paper deals with the linear momentum, angular momentum, and mechanical energy of these systems. Specifically, expressions for changes in these quantities during imposition and removal of constraints are formulated in terms of the associated changes in the generalized speeds.

scholarly journals Reconfiguration Analysis of a 3-DOF Parallel Mechanism

Robotics ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 66
Author(s):  
Maurizio Ruggiu ◽  
Xianwen Kong
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Operation Mode ◽  
Parallel Mechanisms ◽  
Universal Joint ◽  
Kinematic Chains ◽  
Constraint Equations ◽  
The Third ◽  
Equilateral Triangles ◽  
Moving Platform

This paper deals with the reconfiguration analysis of a 3-DOF (degrees-of-freedom) parallel manipulator (PM) which belongs to the cylindrical parallel mechanisms family. The PM is composed of a base and a moving platform shaped as equilateral triangles connected by three serial kinematic chains (legs). Two legs are composed of two universal (U) joints connected by a prismatic (P) joint. The third leg is composed of a revolute (R) joint connected to the base, a prismatic joint and universal joint in sequence. A set of constraint equations of the 1-RPU−2-UPU PM is derived and solved in terms of the Euler parameter quaternion (a.k.a. Euler-Rodrigues quaternion) representing the orientation of the moving platform and of the Cartesian coordinates of the reference point on the moving platform. It is found that the PM may undergo either the 3-DOF PPR or the 3-DOF planar operation mode only when the base and the moving platform are identical. The transition configuration between the operation modes is also identified.

scholarly journals F-Metric, F-Contraction and Common Fixed-Point Theorems with Applications

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 586 ◽  
Author(s):  
Awais Asif ◽  
Muhammad Nazam ◽  
Muhammad Arshad ◽  
Sang Og Kim
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
The Third ◽  
Set Valued Mappings ◽  
Common Fixed Point Theorems

In this paper, we noticed that the existence of fixed points of F-contractions, in F -metric space, can be ensured without the third condition (F3) imposed on the Wardowski function F : ( 0 , ∞ ) → R . We obtain fixed points as well as common fixed-point results for Reich-type F-contractions for both single and set-valued mappings in F -metric spaces. To show the usability of our results, we present two examples. Also, an application to functional equations is presented. The application shows the role of fixed-point theorems in dynamic programming, which is widely used in computer programming and optimization. Our results extend and generalize the previous results in the existing literature.

A 3D passive dynamic biped with yaw and roll compensation

Robotica ◽  
2001 ◽  
Vol 19 (3) ◽  
pp. 275-284 ◽  
Author(s):  
M. Wisse ◽  
A. L. Schwab ◽  
R. Q. vd. Linde
Keyword(s):  
Degrees Of Freedom ◽  
High Energy ◽  
Roll Motion ◽  
Multibody Model ◽  
The Third ◽  
High Energy Efficiency ◽  
Dynamic Compensator ◽  
Third Dimension ◽  
The Stability ◽  
Natural Dynamics

Autonomous walking bipedal machines, possibly useful for rehabilitation and entertainment purposes, need a high energy efficiency, offered by the concept of ‘Passive Dynamic Walking' (exploitation of the natural dynamics of the robot). 2D passive dynamic bipeds have been shown to be inherently stable, but in the third dimension two problematic degrees of freedom are introduced: yaw and roll.We propose a design for a 3D biped with a pelvic body as a passive dynamic compensator, which will compensate for the undesired yaw and roll motion, and allow the rest of the robot to move as if it were a 2D machine. To test our design, we perform numerical simulations on a multibody model of the robot. With limit cycle analysis we calculate the stability of the robot when walking at its natural speed.The simulation shows that the compensator, indeed, effectively compensates for both the yaw and the roll motion, and that the walker is stable.

Face Detection in Peripheral Vision: Do Faces Pop Out?

Perception ◽  
1997 ◽  
Vol 26 (12) ◽  
pp. 1555-1570 ◽  
Author(s):  
Valerie Brown ◽  
Dale Huey ◽  
John M Findlay
Keyword(s):  
Visual Search ◽  
Eye Movements ◽  
Face Detection ◽  
Peripheral Vision ◽  
Opposite Polarity ◽  
Target Face ◽  
The Third ◽  
Search Tasks ◽  
Face Images ◽  
Improved Performance

We examined whether faces can produce a ‘pop-out’ effect in visual search tasks. In the first experiment, subjects' eye movements and search latencies were measured while they viewed a display containing a target face amidst distractors. Targets were upright or inverted faces presented with seven others of the opposite polarity as an ‘around-the-clock’ display. Face images were either photographic or ‘feature only’, with the outline removed. Naive subjects were poor at locating an upright face from an array of inverted faces, but performance improved with practice. In the second experiment, we investigated systematically how training improved performance. Prior to testing, subjects were practised on locating either upright or inverted faces. All subjects benefited from training. Subjects practised on upright faces were faster and more accurate at locating upright target faces than inverted. Subjects practised on inverted faces showed no difference between upright and inverted targets. In the third experiment, faces with ‘jumbled’ features were used as distractors, and this resulted in the same pattern of findings. We conclude that there is no direct rapid ‘pop-out’ effect for faces. However, the findings demonstrate that, in peripheral vision, upright faces show a processing advantage over inverted faces.

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