Generalization of the collision cone approach for motion safety in 3-D environments

Abstract

Avoidance of collision between moving objects in a 3-D environment is fundamental to the problem of planning safe trajectories in dynamic environments. This problem appears in several diverse fields including robotics, air vehicles, underwater vehicles and computer animation. Most of the existing literature on collision prediction assumes objects to be modelled as spheres. While the conservative spherical bounding box is valid in many cases, in many other cases, where objects operate in close proximity, a less conservative approach, that allows objects to be modelled using analytic surfaces that closely mimic the shape of the object, is more desirable. In this paper, a collision cone approach (previously developed only for objects moving on a plane) is used to determine collision between objects, moving in 3-D space, whose shapes can be modelled by general quadric surfaces. Exact collision conditions for such quadric surfaces are obtained and used to derive dynamic inversion based avoidance strategies.

Collision Avoidance of Hexacopter UAV Based on LiDAR Data in Dynamic Environment

“…In this study, the collision cone method is adopted as the basis of the collision detection and avoidance logic [33,34]. Let us assume that n c data points are accumulated by the LiDAR, and that the position vector of the k-th obstacle data point in the NED coordinate system is defined as r n o,k .…”

“…In this study, an enhanced collision avoidance algorithm based on the collision cone approach [33,34] is proposed to deal with a three-dimensional dynamic environment. A hexacopter is considered as the flying platform [35].…”

Three-Dimensional Velocity Obstacle Method for Uncoordinated Avoidance Maneuvers of Unmanned Aerial Vehicles

“…The vertices in each avoidance-plane are derived by solving equation (11) for z φ vo = 0, for every β. The resulting velocity obstacle conic section, denoted as VO P φ , is therefore simplified into a polygon formed by a finite set of vertices, {x vo , y vo } on the limiting curves.…”

“…The vertices that form the VO P φ section in each Avoidance Plane P φ are derived by solving the x φ vo and y φ vo in equation (11), for z vo = 0. The following equation gives the value of a:…”

“…These methods rely on the instantaneous situation detection to quickly calculate the avoidance maneuver, instead of depending on predetermined data or extensive iteration that might be optimized, but processed slower, such as in Local Path Planning methods 3,4 or Dynamic Programming. 5 Several reactive avoidance methods can be found in the literature, including the Potential Field method, [6][7][8][9] and Geometric guidance methods such as the Collision Cone 10,11 or the Velocity Obstacle method. [12][13][14][15][16][17][18][19][20][21][22][23] Since they are less computationally intensive, these reactive methods are promising in providing a fast avoidance solution in a dynamic environment.…”