Minimizing The Maximum Distance Traveled To Form Patterns With Systems of Mobile Robots

In the pattern formation problem, robots in a system must self-coordinate to form a given pattern, regardless of translation, rotation, uniform-scaling, and/or reflection. In other words, a valid final configuration of the system is a formation that is \textit{similar} to the desired pattern. While there has been no shortage of research in the pattern formation problem under a variety of assumptions, models, and contexts, we consider the additional constraint that the maximum distance traveled among all robots in the system is minimum. Existing work in pattern formation and closely related problems are typically application-specific or not concerned with optimality (but rather feasibility). We show the necessary conditions any optimal solution must satisfy and present a solution for systems of three robots. Our work also led to an interesting result that has applications beyond pattern formation. Namely, a metric for comparing two triangles where a distance of $0$ indicates the triangles are similar, and $1$ indicates they are \emph{fully dissimilar}.

Quality Amplification of Error Prone Navigation for Swarms of Micro Aerial Vehicles (with Detailed Simulations)

We present an error tolerant path planning algorithm for Micro Aerial Vehicles (MAV) swarms. We assume a MAV navigation system without relying on GPS-like techniques. The MAV find their navigation path by using their sensors and cameras, in order to identify and follow a series of visual landmarks. The visual landmarks lead the MAV towards the target destination. MAVs are assumed to be unaware of the terrain and locations of the landmarks. Landmarks are also assumed to hold a-priori information, whose interpretation (by the MAVs) is prone to errors. We distinguish two types of errors, namely, recognition and advice. Recognition errors are due to misinterpretation of sensed data and a-priori information or confusion of objects (e.g., due to faulty sensors). Advice errors are due to outdated or wrong information associated to the landmarks (e.g., due to weather conditions). Our path planning algorithm proposes swarm cooperation. MAVs communicate and exchange information wirelessly, to minimize the {\em recognition} and {\em advice} error ratios. By doing this, the navigation system experiences a quality amplification in terms of error reduction. As a result, our solution successfully provides an adaptive error tolerant navigation system. Quality amplification is parametetrized with regard to the number of MAVs. We validate our approach with theoretical proofs and numeric simulations.