Observability Options Against an Adversarial Swarm - a Quantitative Analysis [video]

Abstract

In this presentation we address the problem of detecting internal cooperating strategies of an adversarial swarm by estimating a set of parameters that define a particular swarm cooperating strategy. This is a nonstandard estimation problem the estimation problem we address in this paper is not to estimate, for example, position and velocity of each member of the swarm; rather we are interested in understanding how individual agents cooperate to achieve the swarm behavior that is observed by outsiders. For a non-cooperative, adversarial swarm, this estimation problem produces unique challenges. The dynamic, evolving configuration of the swarm over time can lead to time periods where observation is effective for estimation, or it can lead to times such as when a swarm has stabilized into an equilibrium configuration when some internal strategies may be unobservable. The interactive nature of a swarm also makes relevant the impact of the observer on the swarm itself. For a swarm which reacts to obstacles or other agents, the observer may impact the movements of the swarm. This provides the opportunity for a dynamic observer to act not just as a passive data collector, but as a possible agent provocateur, provoking the swarm into more revealing behaviors. In this presentation, we explore tools for this problem using a model-based approach. We adopt a swarm model developed by Leonard et al. where authors propose an algorithm for controlling a swarm based on a potential function and virtual leaders. The potential function and virtual leaders employed can be characterized by a set of parameters. The estimation problem is then examined for the estimation of these parameters. Prior to actually designing an estimator a natural question is whether these parameters are in fact observable. The answer to this question is surprisingly nontrivial. Using the well-established notion of unobservability index we show that these parameters are indeed observable. However, in order to achieve observability the adversarial swarm must be disrupted by an intruder. In the presence of the intruder the unobservability index is shown to be good, i.e., the parameters in question are observable. Another non-trivial aspect of the problem is estimation of the parameters. Many swarm models involve parameters that represent the range limit of communication and/or range of influence among agents. These parameters introduce discontinuity into the swarm dynamics making the design of a convergent estimation algorithm very challenging. When applying standard filtering techniques such as unscented Kalman filter (UKF) to actually estimate these parameters we have discovered that the estimates often fail to converge although the parameters have shown to be observable.