Motion Planning for Small Formations of Autonomous Vehicles Navigating on Gradient Fields
Proceedings of the International Symposium on Underwater Technology, Tokyo, Japan, 2007
Shahab Kalantar & Uwe R. Zimmer
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.
The need to deploy large numbers of autonomous vehicles to safely monitor underwater phenomena, which are usually of considerable spatial extent, is currently a driving impetus for many research efforts. These monitoring tasks include, among others, characterizing diffusion processes (e.g., temperature and salinity ) through the evolution of their isoclines, monitoring flows of one kind or another over iso-baths, identification of iso-tachs of flow fields, and delineation of boundaries of plumes or biological concentrations. Due to inevitable uncertainties associated with measurements, any kind of imposed structure on the shape of vehicle formations can be of great help. Generally speaking, suitable formations will have to be deformable rather than rigid. They should have the capability to lose potential energy to get into the right shape and gain potential energy under the influence of ambient field gradients. Candidate formations are either dense networks (for area coverage ,) those resembling chains (for isocline tracking ,,) or both  (swarms with boundary). We will consider curved formations with open ends. The proposed strategy will ultimately be implemented on Serafina robots developed in our lab (figure 1). We will only consider the planar case where the robots are stabilized to navigate on an imaginary plane. In the following, we will precisely formulate the problem.
In this paper, we proposed a framework for planning the motion of a group of planar autonomous agents in a chain formation for the purposes of adaptation to level curves of environmental fields using local measurements and communication. The framework is composed of a hybrid supervisory automaton, a block generating the basic behaviour according to a discrete implementation of the original curve evolution scheme, a governor block constraining the basic behaviour to admissible regions (ensuring formation safety within some user-determined bounds) and three blocks modifying the basic behaviour (to ensure fairness of the system). The overall strategy is to make the formation smooth enough before exposing it to external forces and then decrease the internal force when safely close to the iso-cline.
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