On a Three Dimensional Vision Based Collision Avoidance Model

Abstract

Abstract. This paper presents a three dimensional collision avoidance approach for aerial vehicles inspired by coordinated behaviors in biological groups. The proposed strategy aims to enable a group of vehicles to converge to a common destination point avoiding collisions with each other and with moving obstacles in their environment. The interaction rules lead the agents to adapt their velocity vectors through a modification of the relative bearing angle and the relative elevation. Moreover the model satisfies the limited field of view constraints resulting from individual perception sensitivity.From the proposed individual based model, a mean-field kinetic model is derived. Simulations are performed to show the effectiveness of the proposed model.

A New Collision Avoidance Model with Random Batch Resolution Strategy

“…Compared to [29], our collision-interaction force is much more smooth. Moreover, similarly as the Lemma 2.9 and the Lemma 2.12 in [29], we can show that αij will increase exponentially if rules in (3) is taken. Thus the collision can be avoided in most cases.…”

“…In this section, our interest is modelling the motion of individuals without colliding with each other or obstacles in two-dimensional space. Following the same framework as in [29], the model consists of two phases:…”

“…The collision-interaction force. The collision-interaction force is inspired from [29], where a force, being perpendicular to the particle velocity, is imposed depending on the potential collision risk. More precisely, two particles are considered to have a potential collision risk if, under the assumption (A2), the MD is small enough and the TTI is nonnegative.…”

“…In spite of limited sensing capability and physiological constraints, such biological groups have outstanding performance of maintaining optimized group structure and avoiding collisions. Motivated by research on animals' behavior, many widely used models have been constructed, such as optimal control models [18], traffic following models [23] and vision-based models [29,28,10].…”

“…The model in this paper belongs to the class of vision-based models, where each agent has a limited sensing capability. To achieve the aim, we inspire the ideas from vision-based models in [29,28], where the particles, with limited sensor called "vision cone", are considered equal and follow the same simple rules to observe, detect, and react for collision avoidance. It is noted that the model in [29] is a Newtonian system constructed for threedimensional space and each particle only changes its orientation to avoid collisions, maintaining the magnitude of its velocity.…”