Finite-Time Formation Control without Collisions for Multiagent Systems with Communication Graphs Composed of Cyclic Paths

Abstract

This paper addresses the formation control problem without collisions for multiagent systems. A general solution is proposed for the case of any number of agents moving on a plane subject to communication graph composed of cyclic paths. The control law is designed attending separately the convergence to the desired formation and the noncollision problems. First, a normalized version of the directed cyclic pursuit algorithm is proposed. After this, the algorithm is generalized to a more general class of topologies, including all the balanced formation graphs. Once the finite-time convergence problem is solved we focus on the noncollision complementary requirement adding a repulsive vector field to the previous control law. The repulsive vector fields display an unstable focus structure suitably scaled and centered at the position of the rest of agents in a certain radius. The proposed control law ensures that the agents reach the desired geometric pattern in finite time and that they stay at a distance greater than or equal to some prescribed lower bound for all times. Moreover, the closed-loop system does not exhibit undesired equilibria. Numerical simulations and real-time experiments illustrate the good performance of the proposed solution.

Motion Coordination Problems with Collision Avoidance for Multi-Agent Systems

“…This proof is detailed in Ref. [17]. It is worth mentioning that, geometrically, the worst case occurs when an agent is surrounded by other six agents.…”

“…The goal of this chapter is to design decentralised control strategies that allow motion coordination for multi-agent systems avoiding collisions between agents. The non-collision strategy is based on previous works [16,17]. We use bounded control strategies based on sigmoid functions adding a repulsive vector field.…”

A General Solution to the Formation Control Problem Without Collisions for First-Order Multi-Agent Systems

“…[14][15][16] Finally, a new strategy has been used recently which consists in designing the repulsive component of the control law in such a way that every agent regards an unstable counterclockwise focus on the location of any other possible colliding agent or obstacle. 10,11,17 As a result, no undesired equilibrium points appear and it can be proved that agents not only avoid collisions but also they stay at a distance greater than or equal to a predefined bound.…”

“…[5][6][7] Several solutions to this problem have been proposed. [8][9][10][11] In a first approach, collisions can be predicted, but not avoided, from initial conditions. 12,13 This can be useful if such initial conditions can be selected properly.…”

Containment problem with time-varying formation and collision avoidance for multiagent systems

“…The collision avoidance strategy is based on previous works. 25,26 The main difference is that in this work we consider the formation tracking problem. Moreover, in this work we use bounded control strategies based on sigmoid functions instead of normalizing them, adding a repulsive vector field.…”