Search

A team of non-holonomic constant-speed under-actuated unmanned aerial vehicles (UAVs) with lower-limited turning radii travel in 3D. The space hosts an unknown and unpredictably varying scalar environmental field. A space direction is given; this direction and the coordinate along it are conditionally termed as the “vertical” and “altitude”, respectively. All UAVs should arrive at the moving and deforming isosurface where the field assumes a given value. They also should evenly distribute themselves over a pre-specified range of the “altitudes” and repeatedly encircle the entirety of the isosurface while remaining on it, each at its own altitude. Every UAV measures only the field intensity at the current location and both the Euclidean and altitudinal distances to the objects (including the top and bottom of the altitudinal range) within a finite range of visibility and has access to its own speed and the vertical direction. The UAVs carry no communication facilities, are anonymous to one another, and cannot play distinct roles in the team. A distributed control law is presented that solves this mission under minimal and partly inevitable assumptions. This law is justified by a mathematically rigorous global convergence result; computer simulation tests confirm its performance.

In this paper, the design of a data-rate constrained observer for a dynamical system is presented. This observer is designed to function both in discrete time and continuous time. The system is connected to a remote location via a communication channel which can transmit limited amounts of data per unit of time. The objective of the observer is to provide estimates of the state at the remote location through messages that are sent via the channel. The observer is designed such that it is robust toward losses in the communication channel. Upper bounds on the required communication rate to implement the observer are provided in terms of the upper box dimension of the state space and an upper bound on the largest singular value of the system’s Jacobian. Results that provide an analytical bound on the required minimum communication rate are then presented. These bounds are obtained by using the Lyapunov dimension of the dynamical system rather than the upper box dimension in the rate. The observer is tested through simulations for the Lozi map and the Lorenz system. For the Lozi map, the Lyapunov dimension is computed. For both systems, the theoretical bounds on the communication rate are compared to the simulated rates.