Abstract
This paper contributes a design of distributed controllers for flocking of mobile agents with an ellipsoidal shape and a limited communication range. A separation condition for ellipsoidal agents is first derived. Smooth step functions are then introduced. These functions and the separation condition between the ellipsoidal agents are embedded in novel pairwise potential functions to design flocking control algorithms. The proposed flocking design results in (1) smooth controllers despite of the agents’ limited communication ranges, (2) no collisions between any agents, (3) asymptotic convergence of each agent’s generalized velocity to a desired velocity, and (4) boundedness of the flock size, defined as the sum of all distances between the agents, by a constant.
Highlights
Flocking, referred to as a collective motion of a large number of self-propelled entities, has attracted a lot of attention of researchers in biology, physics, and computer science [1,2,3,4]
Local arti cial potentials between neighboring agents were used to deal with separation and cohesion problems in [12, 13, 18,19,20,21,22,23]. e leader-follower approach to a target tracking problem was used in [24, 25]
Both methods are too complicated for an application in ock control. If these methods are applied for collision avoidance, the condition, for which the minimum distance between two disks or the discriminant of their characteristic polynomial is positive, is extremely complicated to be embedded in a proper potential function for designing a ocking algorithm
Summary
Flocking, referred to as a collective motion of a large number of self-propelled entities, has attracted a lot of attention of researchers in biology, physics, and computer science [1,2,3,4]. Many agents have a nonspherical, especially long and narrow, shape If these agents are tted to spheres, there is a problem of the large conservative volume. E above discussion indicates that it is much more efficient to use an ellipsoidal approximation of the agents with a long and narrow shape for collision avoidance in designing ocking algorithms. Both methods are too complicated for an application in ock control If these methods are applied for collision avoidance, the condition, for which the minimum distance between two disks or the discriminant of their characteristic polynomial is positive, is extremely complicated to be embedded in a proper potential function for designing a ocking algorithm. E aforementioned observations motivate contributions of this paper on a design of ocking algorithms for mobile agents with an ellipsoidal shape and limited communication ranges. E aforementioned observations motivate contributions of this paper on a design of ocking algorithms for mobile agents with an ellipsoidal shape and limited communication ranges. e paper’s contributions include (1) a new condition for separation between two ellipsoids, see Section 2.1; (2) smooth step functions; (3) a new pairwise potential function for two ellipsoidal agents, see Section 4.1.1; (4) a derivation of ocking algorithms based on the pairwise potential functions, see Section 4.4
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