FPR—Fast Path Risk Algorithm to Evaluate Collision Probability

Collision Probability Estimation

As small satellites become more common and are assigned increasingly sophisticated missions, their role in proximity operations is also increased. An estimate of the current relative state (position, velocity and often attitude) as well as a prediction of the future relative state is important in close proximity operations. However, it is often insufficient to rely solely on this estimate to pr...

A canonical path approach to bounding collision time for Pollard’s Rho algorithm

We show how to apply the canonical path method to a non-reversible Markov chain with no holding probability: a random walk used in Pollard’s Rho algorithm for discrete logarithm. This is used to show that the Pollard Rho method for finding the discrete logarithm on a cyclic group G requires O( √ |G| (log |G|)3/2) steps until a collision occurs and discrete logarithm is possibly found, not far f...

Shortest Path Problem with Gamma Probability Distribution Arc Length

We propose a dynamic program to find the shortest path in a network having gamma probability distributions as arc lengths. Two operators of sum and comparison need to be adapted for the proposed dynamic program. Convolution approach is used to sum two gamma probability distributions being employed in the dynamic program.

Developing Macro-level Collision Prediction Models to Evaluate

Collision Probability based Safe Path Planning for Mobile Robots in Changing Environments

Automatic path planning has many applications in robotics, computer-aided design(CAD) and industrial manipulation. The property of safety is vital but seldom taken into consideraion by typical path planning. In this paper, collision probability is introduced as an evaluation of crowd degree of environments to get a safer path. The smaller collision probability a node has, the more possibly the ...