Formation control of mobile agents using local potential functions

Non-Collision Conditions in Multi-Agent Virtual Leader-Based Formation Control

“…1 has been chosen because it renders symmetric expressions for the distance between any pair of agents. Another topology rendering the same kind of symmetry is the socalled undirected complete graph [18], where every agent detects the position of the rest of the agents. We have chosen the former topology because it requires less communication channels between agents.…”

“…In [18], it is shown that the undesired equilibria are unstable for a complete graph formation strategy, however, they are not explicitly calculated. In [19,20], some "navigation functions" are designed with attractive and repulsive behaviour.…”

“…This occurs because the robots can be trapped in undesired equilibrium points. The analysis to calculate these equilibria and the trajectories which do not converge to the desired formation is very complex [18]. A complete survey of convergence and collision avoidance based on APF and RPF was presented in our previous work [28].…”

“…Other formation schemes are based on formation graphs which represent specific interagent communication channels to achieve a specific geometric pattern [9,10,29]. Some tools of graph theory and linear systems are used to prove the convergence to the desired formation for special formation graphs such as the complete formation graph (i.e., where every agent measures the position of the rest of the group [18]), cyclic pursuit [13], undirected graphs [21], leaders-followers graphs (i.e., where all robots have communication with one or more group leaders [11,12]), etc. In this paper, we utilize a formation graph where one agent is considered as a virtual leader.…”

Convergence and Collision Avoidance in Formation Control: A Survey of the Artificial Potential Functions Approach

“…However, the main drawback of mixing APF and RPF is the appearance of equilibria where the composite vector field vanishes and the robots can get trapped at undesired equilibrium points. Therefore, a proof of global convergence to the desired formation for all initial conditions becomes quite involved because the analysis to calculate these equilibria and the trajectories which do not converge to the desired formation is very complex (Do (2006)). This chapter analyzes the global convergence and non-collisions strategies of formation strategies based on Artificial Potential Functions on the context of formation graphs for the case of point robots or omnidirectional robots.…”