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Bruce A. Francis, emeritus professor at the University of Toronto and recipient of the 2014 Hendrik Bode Lecture Prize, shares some of his experiences. [ABSTRACT FROM PUBLISHER]

In the formation control problem for autonomous robots, a distributed control law steers the robots to the desired target formation. A local stability result of the target formation can be derived by methods of linearization and center manifold theory or via a Lyapunov-based approach. Besides the target formation, the closed-loop dynamics of the robots feature various other undesired invariant sets such as nonrigid formations. This note addresses a global stability analysis of the closed-loop formation control dynamics. We pursue a differential geometric approach and derive purely algebraic conditions for local stability of invariant embedded submanifolds. These theoretical results are then applied to the well-known example of a cyclic triangular formation and result in instability of all invariant sets other than the target formation. [ABSTRACT FROM PUBLISHER]

If a smooth, closed, and embedded curve is deformed along its normal vector field at a rate proportional to its curvature, it shrinks to a circular point. This curve evolution is called Euclidean curve shortening and the result is known as the Gage-Hamilton-Grayson theorem. Motivated by the rendezvous problem for mobile autonomous robots, we address the problem of creating a polygon shortening flow. A linear scheme is proposed that exhibits several analogues to Euclidean curve shortening: The polygon shrinks to an elliptical point, convex polygons remain convex, and the perimeter of the polygon is monotonically decreasing. [ABSTRACT FROM AUTHOR]

The feasibility problem is studied of achieving a specified formation among a group of autonomous unicycles by local distributed control. The directed graph defined by the information flow plays a key role. It is proved that formation stabilization to a point is feasible if and only if the sensor digraph has a globally reachable node. A similar result is given for formation stabilization to a line and to more general geometric arrangements. [ABSTRACT FROM AUTHOR]

Inspired by the so-called `tugs" problem front mathematics, we study the geometric formations of multivehicle systems under cyclic pursuit. First, we introduce the notion of cyclic pursuit by examining a system of identical linear agents in the plane. This idea is then extends to a system of wheeled vehicles, each subject to a single nonholonomic constraint (i.e., unicycles), which is the principal focus of this paper. The pursuit framework is particularly simple in that the n identical vehicles are ordered such that vehicle i pursues vehicle i + 1 modulo n. In this paper, we as- suine each vehicle has the same constant forward speed. We show that the system's equilibrium formations are generalized regular polygons and it is exposed how the multiivehicle system's global behavior can be shaped through appropriate controller gain assignments. We then study the local stability of these equilibrium polygons, revealing which formations are stable and which are not. [ABSTRACT FROM AUTHOR]

The problem of achieving a specified formation among a group of mobile autonomous agents by distributed control is studied. If convergence to a point is feasible, then more general formations are achievable too, so the focus is on convergence to a point (the agreement problem). Three formation strategies are studied and convergence is proved under certain conditions. Also, motivated by the question of whether collisions occur, formation evolution is studied. [ABSTRACT FROM AUTHOR]

The use of networks in control systems to connect controllers and sensors/actuators has become common practice in many applications. This new technology has also posed a theoretical control problem of how to use the limited data rate of the network effectively. In this paper, we consider a system where its sensor and actuator are connected by a finite data rate channel. A design method to stabilize a continuous-time, linear plant using a switching controller is proposed. In particular, to prevent the actuator from fast switching, or chattering, which can not only increase the necessary data rate but also damage the system, we employ a dwell-time switching scheme. It is shown that a systematic partition of the state-space enables us to reduce the complexity of the design problem. [ABSTRACT FROM AUTHOR]

Studies the problem of checking the consistency of a coprime factor plant/uncertainty model with experimental data obtained from frequency response measurements. Assumption of the frequency response data as noise-free for multi-input/multi-output plants; Use of a matrix-valued Nevanlinna-Pick interpolation technique to solve the problem.

Presents the acceptance speech for the recipient of the CS Society IEEE Field Award in Control. [ABSTRACT FROM PUBLISHER]