A fast Monte Carlo algorithm for collision probability estimation

Abstract

Abstract-In order to navigate safely, it is important to detect and to react to a potentially dangerous situation. Such a situation can be underlined by a judicious use of the locations and the uncertainties of both the navigating vehicle and the obstacles. We propose to build an estimation of the collision probability from the environment perception with its probabilistic modeling. The probability of collision is computed from a sum of integral of a product of Gaussians. The integrals takes into account the uncertain configurations and the volume of both the vehicle and the obstacles.

Collisions as Information Sources in Densely Packed Multi-Robot Systems Under Mean-Field Approximations

“…In many cases, Monte Carlo based techniques have been used to obtain estimates of the collision probabilities, e.g., [16], while the majority of the analytical techniques developed compute the probability of collision along a specific path taken through the workspace in the presence of stationary or moving obstacles, e.g., [15,30].…”

Bayesian environment representation, prediction, and criticality assessment for driver assistance systems

“…Although, following (6.37), the trajectories of the vehicles can be drawn independently of each other, the specification of the Monte Carlo estimate in this more general form is advantageous as it then becomes directly obvious that only a single summation over simultaneously drawn samples from both individual distributions, p(x E,k:k+T P ) and p(x V i ,k:k+T P ), is required. This approach is termed Fast Monte Carlo in [138] and further elaborated and justified in [71]. This way, much fewer samples are needed to obtain the same estimation error compared to a naive double summation over individual trajectory samples.…”

An Ordinal Model of Risk Based on Mariner's Judgement

“…In addition, Perera et al (Perera et al, 2012) have applied both fuzzy inference and Bayesian methods in order to assess risk of collision and to take evasive action and Goerland et al ) present a comprehensive rule based expert system with fuzzy inference where the knowledge domain has been defined by consultation with professional mariners. Furthermore, a number of probabilistic approaches have been proposed that take account of unknown factors in order to predict risk and possible trajectories; see (Belkhouche and Bendjilali, 2013) or (Lambert et al, 2008) and Simsir et al (Simsir et al, 2014) for the application of Artificial Neural Networks for predicting positions of vessels in a collision alert system. These methods add a layer of sophistication to the geometric approach.…”

“…(Belkhouche and Bendjilali, 2013, Lambert et al, 2008, Plamen Angelov and Michael Everett, 2008. Amongst this research, there is a broad consensus concerning the needs to acquire a precise representation of the environment surrounding the craft and, most importantly, of processing the acquired data for assessing risk of collision before any decision can be made.…”