Adaptive Swarm Coordination and Formation Control

1. Introduction

Many creatures in nature behave collectively and exhibit swarm behavior. Inspired by this observation, researchers have tried to set up swarm architectures to be used in the motion control and coordination of multiple mobile robot systems (Bonabeau et al., 1999). Artificial systems composed of multiple interacting agents such as robots, unmanned ground, sea or air vehicles are commonly referred to as multi-agent systems (MAS), multi-agent dynamical systems, or multi-vehicle systems. The formation control problem is a swarm coordination problem in which a group of robots are required to acquire and maintain a prescribed geometric shape during their motion from their initial locations to a desired final destination (Bullo et al., 1999), (Ren & Cao, 2010), (Shamma, 2008). Designing agent controllers which achieve such behavior is an important problem considered in the literature widely (Anderson et al., 2008), (Gazi & Passino, 2003), (Das et al., 2002), (Olfati-Saber, 2006), (Olfati-Saber & Murray, 2004), (Tanner et al., 2004), (Ren & Beard, 2008), (Bai et al., 2011), (Desai et al., 1998, 2001), (Fidan et al., 2013), (Dorigo, & Sahin, 2004), (Gazi & Passino, 2011), (Gazi & Fidan, 2007). There are various surveys and monographs on this topic including (Ren & Cao, 2010), (Sahin & Spears, 2005), (Jadbabaie et al., 2003), (Lin et al., 2005). In order to be able to control a dynamic MAS, e.g., to accomplish certain formation control tasks, one needs to consider the dynamics of each individual agent and design an individual controller for that agent, aiming to have the resultant distributed control scheme meet the MAS control goal. There are various agent dynamic models considered in the literature including single integrator, double integrator, non-holonomic, or Lagrange agent models. If the MAS is a homogeneous system, the dynamics of all the agents might be governed by the same model. In contrast, in a heterogeneous MAS, agents with different underlying dynamics can be part of the same system. From control point of view, an MAS can be viewed as a set of plant dynamics of the individual agents which are loosely coupled by the mission constraints of the problem under consideration. For example, in the formation control problem, the agent motions are constrained by the distance requirements in the desired geometric shape. Most of the approaches assume known system parameters and no uncertainty in the agent dynamics. Under this assumption various decentralized and distributed control schemes have been developed in the literature.

In real-life applications, the agents are autonomous mobile robots or vehicles with actual dynamics which are indeed more complicated than the single or double integrator models. It is also a common situation in real-life scenarios that exact values of the system parameters like mass and inertia of the vehicle are not known a priori, but their approximate values are known. In case the agent dynamics contains uncertainties, there is a need to suppress their effects using robust or adaptive strategies. There have been some attempts in this direction as well, combining the methods and tools of the adaptive and robust control literature with the MAS control algorithms.