Morse Potential Based Aggregation in Multiagent Systems with Applications to Circumnavigation and Exploration

Abstract

Swarms of autonomous vehicles, which are modeled as Multi-agent systems (MASs), have found increasing applications in search and rescue, reconnaissance missions, collaborative transportation, among many other applications of a similar nature. Exploration and collective circumnavigation are two important aspects of a practical multi-agent mission. Physics-based laws, especially those based on potential minimization, are viable candidates for such multi-agent missions where aggregation in some form is sought. In particular, a Morse potential-based Attraction Repulsion (MPAR) scheme is suited because it is a range-based implicit control scheme that under ideal conditions leads to well-defined steady-state behaviors and configurations. A number of these behaviors, like milling, double milling, flocking, rigid formation, etc. have practical applications, and hence are of interest to robotics community and mission planners. However, unlike aggregation behavior of MPAR laws under all-to-all communication, the behavior of MPAR under an incomplete neighborhood, especially in a sparse communication scenario, which happens in a scenario without centralized command center, is not well-understood. The effect of MPAR parameters and initial conditions on the stability of the final formation has also not been studied by researchers. This lack of studies makes the mechanization of MPAR in a practical mission difficult.

In this thesis, we propose an augmented network which comprises a sequence of agents connected in a directed linear topology with a \textit{Stationary Agent} at the end. This configuration under MPAR leads to useful final configurations which are valuable for collective circumnavigation and guided exploration. We demonstrate two distinct motion patterns called the unperturbed and perturbed cases. The former demonstrates bounded exploration, while the latter is shown to mimic stable collective circumnavigation. Kinematic characterization of the resultant nonlinear system is done, and analytical results on the steady-state values for circumnavigation are obtained. We next consider the special case of three followers and obtain detailed analytical results. This analysis includes a novel implicit equation approach to solve velocity ratios of swarm members in the augmented network. Subsequently, an extension to the multiple follower case is discussed. Numerical solutions for the steady-state values from the analytical expressions are also presented. Illustrative simulation results for a larger number of followers are also presented.

In the last part of the thesis, we consider a network without a stationary agent but with limited sensor and communication information and absence of a centralized command. In such cases, we show that individual swarm members do not form well-defined network structures. So, convergence results corresponding to such networks may not hold true and, hence, aggregation on such an "unstructured" network cannot be guaranteed a priori. We undertake aggregation studies under Morse Potential in a swarm system under unstructured random neighborhood considerations, for both directed and undirected graph networks. The expected swarm behavior, particularly of those corresponding to a lower neighborhood size, is markedly different from those expected from the original MPAR formulation under all-to-all communication. Through our study, we identify some patterns like swarm shedding and random droplets, which are not apparent from original MPAR formulation. A key finding is that aggregation is possible even under sparse connectivity.

This finding is key in adopting MPAR for a practical mission, especially in initial and mid-mission phases, where in the absence of detailed information about a mission scenario, MPAR can be enforced to maintain initial cohesion, and in leading a subset of the swarms to a desired target or target-rich zone within a widespread search space.