scholarly journals An Efficient Collision Detection Method for Computing Discrete Logarithms with Pollard's Rho

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Ping Wang ◽  
Fangguo Zhang
Keyword(s):  
Collision Detection ◽  
Detection Method ◽  
Detection Algorithm ◽  
Point Method ◽  
Expected Number ◽  
Distinguished Point ◽  
Discrete Logarithms ◽  
Cyclic Groups ◽  
Space Requirements ◽  
Generic Algorithms

Pollard's rho method and its parallelized variant are at present known as the best generic algorithms for computing discrete logarithms. However, when we compute discrete logarithms in cyclic groups of large orders using Pollard's rho method, collision detection is always a high time and space consumer. In this paper, we present a new efficient collision detection algorithm for Pollard's rho method. The new algorithm is more efficient than the previous distinguished point method and can be easily adapted to other applications. However, the new algorithm does not work with the parallelized rho method, but it can be parallelized with Pollard's lambda method. Besides the theoretical analysis, we also compare the performances of the new algorithm with the distinguished point method in experiments with elliptic curve groups. The experiments show that the new algorithm can reduce the expected number of iterations before reaching a match from 1.309Gto 1.295Gunder the same space requirements for the single rho method.

Robot Collision Detection Without External Sensors Based on Time-Series Analysis

2020 ◽  
Vol 143 (4) ◽  
Author(s):  
Tie Zhang ◽  
Peizhong Ge ◽  
Yanbiao Zou ◽  
Yingwu He
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Collision Detection ◽  
Degrees Of Freedom ◽  
Detection Method ◽  
Industrial Robot ◽  
Detection Algorithm ◽  
Detection Accuracy ◽  
External Torque ◽  
Series Analysis

Abstract To ensure the human safety in the process of human–robot cooperation, this paper proposes a robot collision detection method without external sensors based on time-series analysis (TSA). In the investigation, first, based on the characteristics of the external torque of the robot, the internal variation of the external torque sequence during the movement of the robot is analyzed. Next, a time-series model of the external torque is constructed, which is used to predict the external torque according to the historical motion information of the robot and generate a dynamic threshold. Then, the detailed process of time-series analysis for collision detection is described. Finally, the real-machine experiment scheme of the proposed real-time collision detection algorithm is designed and is used to perform experiments with a six degrees-of-freedom (6DOF) articulated industrial robot. The results show that the proposed method helps to obtain a detection accuracy of 100%; and that, as compared with the existing collision detection method based on a fixed symmetric threshold, the proposed method based on TSA possesses smaller detection delay and is more feasible in eliminating the sensitivity difference of collision detection in different directions.

An Accurate Collision Detection Method for Cable Simulation

2013 ◽  
Vol 347-350 ◽  
pp. 3571-3575
Author(s):  
Shi Fu Xie ◽  
Li Yuan Ma ◽  
Peng Yuan Liu
Keyword(s):  
Collision Detection ◽  
Detection Method ◽  
Computational Cost ◽  
Detection Algorithm ◽  
New Method ◽  
Collision Resolution ◽  
Force Method ◽  
Shortest Distance ◽  
Resolution Scheme ◽  
Cable Segment

In this paper, we present a fast and robust collision detection (CD) and resolution scheme for deformable cable using a new method based on the shortest distance of cable segment axis. We employ a bounding sphere hierarchy (BVH) by exploiting the topology of cable for reducing the collision detection query space. After searching the collision through the bounding sphere hierarchy, the collision detection algorithm will find the two segments which are close enough to require an exact collision check. Furthermore, the exact collision state is decided by our proposed method. Penalty force method is applied to the collision resolution. The comparative experiments show that the proposed method performs more accurate than existing algorithms for deformable cable simulation without substantial computational cost.

scholarly journals Research on Collision Detection Method of Contact On-line Measurement

2021 ◽  
Vol 2095 (1) ◽  
pp. 012079
Author(s):  
Hongfang Qi ◽  
Runqi Guo
Keyword(s):  
Collision Detection ◽  
Detection Method ◽  
Structural Characteristics ◽  
Detection Algorithm ◽  
Discrete Method ◽  
Simple Geometry ◽  
Line Measurement ◽  
On Line ◽  
Grid Division ◽  
Speed And Accuracy

Abstract In order to avoid collision and improve the safety of on-line measurement, a contact on-line measurement collision detection method is studied. Firstly, according to the structural characteristics of the probe and workpiece, the dynamic collision detection between the probe and workpiece is transformed into static collision detection by using the discrete method, and then the grid division of the collision detection space is carried out by using the space division method. Finally, the dynamic collision detection between the probe and workpiece is transformed into the intersection judgment between simple geometry, and according to different collision accuracy requirements, Hierarchical collision detection combining rough detection and fine detection is carried out. Experimental results show that the hierarchical collision detection algorithm has high detection speed and accuracy.

scholarly journals Detection method for auto guide vehicle’s walking deviation based on image thinning and Hough transform

2019 ◽  
Vol 52 (3-4) ◽  
pp. 252-261 ◽  
Author(s):  
Xiaohua Cao ◽  
Daofan Liu ◽  
Xiaoyu Ren
Keyword(s):  
Hough Transform ◽  
Detection Method ◽  
Detection Algorithm ◽  
Visual Navigation ◽  
Guide Line ◽  
Actual Environment ◽  
Lane Line ◽  
Image Thinning ◽  
High Level ◽  
Refinement Algorithm

Auto guide vehicle’s position deviation always appears in its walking process. Current edge approaches applied in the visual navigation field are difficult to meet the high-level requirements of complex environment in factories since they are easy to be affected by noise, which results in low measurement accuracy and unsteadiness. In order to avoid the defects of edge detection algorithm, an improved detection method based on image thinning and Hough transform is proposed to solve the problem of auto guide vehicle’s walking deviation. First, the image of lane line is preprocessed with gray processing, threshold segmentation, and mathematical morphology, and then, the refinement algorithm is employed to obtain the skeleton of the lane line, combined with Hough detection and line fitting, the equation of the guide line is generated, and finally, the value of auto guide vehicle’s walking deviation can be calculated. The experimental results show that the methodology we proposed can deal with non-ideal factors of the actual environment such as bright area, path breaks, and clutters on road, and extract the parameters of the guide line effectively, after which the value of auto guide vehicle’s walking deviation is obtained. This method is proved to be feasible for auto guide vehicle in indoor environment for visual navigation.

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