We have pursued a minimalist approach to a multi-agent rendezvous problem. Using a simple agent model with a ternary output sensor, a three level quantized control, and a Dubins car model, we have shown that a group of these constrained agents can still achieve guaranteed rendezvous behavior without coordinates, communication, or even distinguishability. Furthermore, by exploiting the geometric constraints on internal angles of polygons, we have shown that the convergence behavior of the system is precisely predictable based on the parameters of the individual agents. Our simulation indicates that the bounds derived in the theorems may be close to tight. Moreover, when simulated sensing error is introduced by providing the vehicles with randomly wrong feedback 20% of the time, the simplistic system still behaves as predicted in simulation.
An interesting problem arises from our investigation of the rendezvous problem: For agents on a pursuit cycle, a regular polygon appears to be the ``preferred'' formation (the agents seem to form it without much effort). Although we are able to avoid global dynamics arguments used in [28], a better understanding of how our system evolves over time will help explain why this is the case. This understanding could also lead to more accurate lower bounds on the time that rendezvous takes for a given arrangement of agents. Another related open problem is prescribing the location of rendezvous, which is theoretically appealing and useful for practical purposes.
Going beyond the paper, we want to approach the following questions: 1) Is it possible for an even simpler agent model to rendezvous? By simpler we mean that one or more of sensing and control are strictly less powerful, holding the rest of the agent model unchanged. 2) Are there any other tasks achievable with similar simple agents? For example, we see that it is possible for the agents to get into clusters; can they form a regular lattice structure? Can we get them to follow prescribed paths up to homotopy?
Even though we focus on the rendezvous task in this paper, our motivation in this work lies with a more general goal: Investigating what task classes are possible with minimal amount of information. For a given task, there seems to be an intrinsic relation among the required strengths of the sensors and the controller of an agent. For example, an agent can move to and touch an object to learn its shape; alternatively, it can take a picture and extract the same information. Thus, there must be some equivalence between those two agent models. A firm grasp of this relation will not only help pin down the most basic requirements for a given task, but also offer powerful design guidance for better autonomous systems.