Achieving a desired collective centroid by a formation of agents moving in a controllable force field
TL;DR: In this article, an all-to-all coupled planar motion model is proposed to solve the problem of a formation of agents trying to achieve a desired stationary or moving collective centroid.
Abstract: In this paper, we study the problem of a formation of agents trying to achieve a desired stationary or moving collective centroid. The agents are assumed to be moving in a force field which is controlled externally. The stabilization of the collective centroid to a fixed desired location results in a balanced formation of the agents about that point. Similarly, the centroid of the system of agents may be required to move along a certain given trajectory. For this, the centroid of the formation must converge to the desired trajectory. To solve this problem, we propose an all-to-all coupled planar motion model that explicitly incorporates an additional control pertaining to the external force field. Simulation results are presented to support the theoretical findings.
Cites background from "Achieving a desired collective cent..."
...Furthermore, some recent papers – have discussed the control problem of a group of unit-speed agents to achieve different collective tasks, e....
...Examples include behavior-based , leader-follower , virtual-structure , potential-field , graph-based , and other swarm-based algorithms [9, 13, 21]....
Cites background or result from "Achieving a desired collective cent..."
...In a similar context, the authors in  and  propose a steering control which operates with homogeneous control gains, and depends on both positions and heading angles of the agents  or only on the heading angles of the agents with an additional external force applied to them ....
...Unlike  and , in the present work, the proposed feedback control uses heterogeneous control gains that ensures the robustness of the system against variations in the homogeneous control gains caused by physical implementation (by means of some electrical circuitry)....
...However, unlike  and , in this paper, we generalize existing results and propose a more realistic steering control law which uses heterogeneous control gains....
...Also, ∣ṙc− ṙre f ∣∣ = 1 only if θk = θc, ∀ k , ....
...by using the property 〈z1,cz2〉= c〈z1,z2〉, where c ∈R ....
...U̇(θ ) = N 〈 ṙc− ṙre f ,− N N ∑ k=1 ieiθk 〈 ṙc− ṙre f , ieiθk 〉〉 (17) Since 〈z1,z2 + z3〉= 〈z1,z2〉+〈z1,z3〉 for z1,z2,z3 ∈C , U̇(θ ) in (16) is rewritten as...
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