Shahab Kalantar

Distributed shape control of homogeneous swarms of autonomous underwater vehicles

In this paper, we study large formations of underwater autonomous vehicles for the purposes of exploration and sampling the ocean surface. The formations or aggregates we consider are composed of up to hundreds of robots with the capability of forming various complex shapes dictated by the shape of the region to be explored, as well as special shapes suitable for migration. The shapes are determined through bathymetric maps and described with reduced-dimensional representation techniques. The approach we propose is that of breaking up the control and coordination strategy into two decoupled problems, i.e., partitioning the aggregate into two non-overlapping sets: its boundary and its interior. The boundary uses general theory of curve evolution to form shapes while the interior passively complies, using attraction-repulsion forces, to form a uniform distribution inside the boundary. This makes the problem much more tractable than previous methods. Decision making by individual robots is entirely based on local information, autonomous underwater vehicles, formation control, swarm control.

Control of Open Contour Formations of Autonomous Underwater Vehicles

In this paper, we propose a distributed elastic behaviour for a deformable chain-like formation of small autonomous underwater vehicles with the task of forming special shapes which have been explicitly defined or are defined by some iso-contour of an environmental concentration field. In the latter case, the formation has to move in such a way as to meet certain formation parameters as well as adapt to the iso-line. We base our controller on our previous models (for manually controlled end points) using general curve evolution theory but will also propose appropriate motions for the end robots of an open chain.

Contour shaped formation control for autonomous underwater vehicles using canonical shape descriptors and deformable models

Cooperative tasks such as swarms following gradients, detecting environmental boundaries (defining natural features) and exploration by aggregates of mobile autonomous robots have gained much attention in the past few years. Aggregates come in various forms including rigid formations, involving a few robots, with clearly-defined simple shapes or swarms, with up to hundreds of robots, but with no particular shape characteristics. In the afore-mentioned tasks, a large aggregate is required to form complex shapes. When the number of robots increases, it is very difficult or even senseless to manually determine the position of each and every agent within the formation. In this paper, we concentrate on a special kind of geometric formation (open and closed contours). We use Fourier descriptors, as one of the most natural ways of representing curves, and active contour models, to make the aggregate exhibit desirable physical behaviours. We apply these kinds of formations to the case of autonomous underwater vehicles collectively exploring, mapping, and adapting to environmental features. Many of the features found in underwater landscapes are shaped as open or closed contours so that the proposed combination makes sense. In our approach, a group of mobile agents can synthesize a curve given a small set of canonical invariant descriptors.

Motion Planning for Small Formations of Autonomous Vehicles Navigating on Gradient Fields

In this paper, we present a motion planning scheme for navigation of a contour-like formation of autonomous underwater vehicles on gradient fields and subsequent convergence to desired isoclines, inspired by evolution of closed planar curves. The basic evolution behaviour is modified to include moving boundary points and incorporate safety constraints on formation parameters. Also, the whole process is decomposed into a sequence of well-behaving states. As opposed to the basic model, the regularized solution is characterized by the maximum allowable curvature rather than balance of forces determined by fixed coefficients. Nevertheless, the proposed framework subsumes the original model. Blocking states and fairness are briefly discussed.

Scale-adaptive polygonal formations of submersible vehicles and tracking isocontours

Building on the assumption that identification of a sufficient number of isoclines of an environmental field (such as the ocean bottom terrain) allows efficient reconstruction of the field, in this paper, a sequel to [1], we describe a system where a group of robots in a spacial arrangement (a regular polygon centred around a lead robot) locally construct the field (measured at the locations of the robots) inside the polygonal area using interpolation by barycentric coordinates. If the error of interpolation is small enough, the corresponding isocline of the interpolated field will match the real isocline accurately enough. Tracking this isocline in a certain direction will then allow robust traversal of field isoclines. We use the measurement at the centre of the formation to adjust the size of the polygon to obtain desired accuracy.

Optima localization by vehicle formations imitating the Nelder-Mead simplex algorithm

In this paper, we address the problem of localizing extrema points and iso-contours of ambient environmental fields (specifically, ocean bottom landscape and underwater plumes) using a networked formation of autonomous underwater vehicles. We propose the use of the Nelder-Mead extension to the basic simplex nonlinear optimization algorithm. In these robust gradient-free strategies, decisions are solely made based on field values measured by the individual vehicles, while measurements are fused and actions decided according to the algorithm. A main goal of this paper is to trigger interest in direct search methods as pertains to this type of robotic problem.

Tracking Environmental Isoclines Using Polygonal Formations of Submersible Autonomous Vehicles

Knowledge of iso-contours of the underwater terrain can be used to reconstruct it using interpolation. Identifying a set of isoclines can be more efficient and less time-intensive than sweeping a large area. In this paper, we propose a system where a small number of agile underwater vehicles cooperatively maintain a polygonal formation on a plane above the terrain and use field values measured by the individual robots to locally reconstruct the field using interpolation schemes. The formation then tracks a desired iso-contour of the field by tracking the corresponding curve on the reconstructed field.

A Formation Control Approach to Adaptation of Contour-Shaped Robotic Formations

Much research has been done in the area of robot formations. Most of them consider rigid formations where the robot aggregate forms a rigid virtual body. Relatively little has been done on deformable formations composed of rigid links as well as flexible ones. In this paper, we will examine and design controllers for a special type of robotic formations, i.e., those resembling contours. These type of formations have numerous applications in the underwater world, including adaptation to plume boundaries and isoclines of concentration fields, flock shepherding, and shape formation. We adopt general curve evolution theory as a suitable abstraction to describe the motion of such formations. We will first design controllers using simple geometrical reasoning, based on basic requirements on connectivity and mission accomplishment, and will later show that they lead to the same controller structure