Control Communication Complexity of Distributed Actions

Recent papers have treated {\em control communication complexity} in the context of information-based, multiple agent control systems including nonlinear systems of the type that have been studied in connection with quantum information processing. The present paper continues this line of investigation into a class of two-agent distributed control systems in which the agents cooperate in order to realize common goals that are determined via independent actions undertaken individually by the agents. A basic assumption is that the actions taken are unknown in advance to the other agent. These goals can be conveniently summarized in the form of a {\em target matrix}, whose entries are computed by the control system responding to the choices of inputs made by the two agents. We show how to realize such target matrices for a broad class of systems that possess an input-output mapping that is bilinear. One can classify control-communication strategies, known as {\em control protocols}, according to the amount of information sharing occurring between the two agents. Protocols that assume no information sharing on the inputs that each agent selects and protocols that allow sufficient information sharing for identifying the common goals are the two extreme cases. Control protocols will also be evaluated and compared in terms of cost functionals given by integrated quadratic functions of the control inputs. The minimal control cost of the two classes of control protocols are analyzed and compared. The difference in the control costs between the two classes reflects an inherent trade-off between communication complexity and control cost.Comment: 34 pages, 1 figure, To appear in the IEEE Trans. Automatic Contro

The control theory of motion-based communication: problems in teaching robots to dance

The paper describes results on two components of a research program focused on motion-based communication mediated by the dynamics of a control system. Specifically we are interested in how mobile agents engaged in a shared activity such as dance can use motion as a medium for transmitting certain types of messages. The first part of the paper adopts the terminology of motion description languages and deconstructs an elementary form of the well-known popular dance, Salsa, in terms of four motion primitives (dance steps). Several notions of dance complexity are introduced. We describe an experiment in which ten performances by an actual pair of dancers are evaluated by judges and then compared in terms of proposed complexity metrics. An energy metric is also defined. Values of this metric are obtained by summing the lengths of motion segments executed by wheeled robots replicating the movements of the human dancers in each of the ten dance performances. Of all the metrics that are considered in this experiment, energy is the most closely correlated with the human judges' assessments of performance quality. The second part of the paper poses a general class of dual objective motion control problems in which a primary objective (artistic execution of a dance step or efficient movement toward a specified terminal state) is combined with a communication objective. Solutions of varying degrees of explicitness can be given in several classes of problems of communicating through the dynamics of finite dimensional linear control systems. In this setting it is shown that the cost of adding a communication component to motions that steer a system between prescribed pairs of states is independent of those states. At the same time, the optimal encoding problem itself is shown to be a problem of packing geometric objects, and it remains open. Current research is aimed at solving such communication-through-action problems in the context of the motion control of mobile robots.Support for this work is gratefully acknowledged to ODDR&E MURI07 Program Grant Number FA9550-07-1-0528, the National Science Founda tion ITR Program Grant Number DMI-0330171, and the Office of Naval Research, and by ODDR&E MURI10 Program Grant Number N00014-10- 1-0952. (FA9550-07-1-0528 - ODDRE MURI07; DMI-0330171 - National Science Foundation ITR Program; Office of Naval Research; N00014-10-1-0952 - ODDRE MURI10

Applied Dynamics and Geometric Mechanics

This one week workshop was organized around several central subjects in applied dynamics and geometric mechanics. The specific organization with afternoons free for discussion led to intense exchanges of ideas. Bridges were forged between researchers representing different fields. Links were established between pure mathematical ideas and applications. The meeting was not restricted to any particular application area. One of the main goals of the meeting, like most others in this series for the past twenty years, has been to facilitate cross fertilization between various areas of mathematics, physics, and engineering. New collaborative projects emerged due to this meeting. The workshop was well attended with participants from Europe, North America, and Asia. Young researchers (doctoral students, postdocs, junior faculty) formed about 30% of the participants