CHARDD Kickoff Meeting, Princeton University, September 13, 2007 Toward a Theory of Protocols for Communication Through Action John Baillieul C.I.S.E. and Intelligent Mechatonics Laboratory Boston University Boston, MA

CHARDD Kickoff Meeting, Princeton University, September 13, 2007 Integration with Center Themes Cognitive psychology thrust: The dynamics of choice among multiple alternatives: Key problem: Understand the tradeoff between decision time (DT) (= reaction time, RT) and error rate (ER). Optimizing the parsimoniousness of computational effort Maximum reward rate (RR)(= maximum # of correct task executions per unit time)

CHARDD Kickoff Meeting, Princeton University, September 13, 2007 Prior Work that Informs the Research From DAAD : The Boston University Center for Communicating Networked Control Systems The Data-Rate Theorem Theorem: Suppose the system G(s) is controlled using a data- rate constrained feedback channel. Suppose, moreover, G has k right half-plane poles 1,…, k. Then there is a critical data- rate such that the system can be stabilized if and only if the channel capacity R>R c. G(s)G(s)

CHARDD Kickoff Meeting, Princeton University, September 13, 2007 Integration with Center Themes Optimally parsimonious use of resources in control---e.g. speed vs. accuracy tradeoffs: G(s) Bluetooth radio Air Packets: 17 bytes payload Air Packets: ≤ 366 bits total

CHARDD Kickoff Meeting, Princeton University, September 13, 2007 From DAAD : The Boston University Center for Communicating Networked Control Systems Prior Work that Informs the Research Necessary and Sufficient Conditions for Stable Rigidity with Minimal Sensing Theorem: (Hendrickx et al., 2006) An acyclic formation graph correspondingto a stably rigid formation under a corresponding distributed relative distance control law is isostatic if and only if (i) one vertex (the leader) has out-valence 0; (ii) one vertex (the first-follower) has out-valence 1 and is adjacent to the leader vertex; and (iii) all other vertices have out-valence equal to 2

CHARDD Kickoff Meeting, Princeton University, September 13, 2007 Prior Work that Informs the Research The construction dynamics of isostatic rigid formations. JB and Lester McCoy, “The Combinatorial Graph Theory of Structured Formations,” CDC, 2007.

CHARDD Kickoff Meeting, Princeton University, September 13, 2007 Integration with Center Themes The search for robustly parsimonious connection patterns is a big deal in networked control systems. See The Technology of Networked Control Systems: Special Issue of the Proceedings of the IEEE, Vol. 95:1, January, 2007

CHARDD Kickoff Meeting, Princeton University, September 13, 2007 Problem Statement Develop a theory of control systems in which primary control objectives are met while using excess control authority to communicate among system agents.

CHARDD Kickoff Meeting, Princeton University, September 13, 2007 Approach Identify classes of controlled dynamical systems where it seems natural and interesting to design dynamical responses which achieve a primary control objective while to encoding additional information that is beyond what is needed to achieve the primary objective Develop theories of action-mediated communication together with sets of experiments to test and refine those theories. Develop approaches to decentralized control in which controllers communicate with each other through the performance of a shared task.

CHARDD Kickoff Meeting, Princeton University, September 13, 2007 Goals Design protocols for communication through motions that will allow teams of humans and robots to: Move about as a group in a variety of environments with the ability to alter motions on the fly based on both sensor feedback and the relative motions of members of the groups Collaborate in the performance of tasks without needing to communicate over classical communications channels (RF or optical). Understand the tradeoffs between reliability and security in action-mediated communication

CHARDD Kickoff Meeting, Princeton University, September 13, 2007 The Simplest Communication Through Action Problem By means of the input u, steer the output y so as to: 1.Achieve an output objective while 2.Simultaneously communicating a message from u to y.

CHARDD Kickoff Meeting, Princeton University, September 13, 2007 Two Agents Communicating Through Action Problem Both agents u and v collaboratively steer the output y so as to: 1.Achieve a prescribed output objective while 2.Simultaneously communicating messages to each other.

CHARDD Kickoff Meeting, Princeton University, September 13, 2007 Multiplexed Communication in Input/Output Networks

CHARDD Kickoff Meeting, Princeton University, September 13, 2007 Motivation from Finite Dimensional Linear Systems

CHARDD Kickoff Meeting, Princeton University, September 13, 2007 The null-space of L can be used for communication. Communication in Terminal Endpoint Linear Control Problems

CHARDD Kickoff Meeting, Princeton University, September 13, 2007 Terminal Endpoint Control with Communication steers the system from 0 to x 1 and communicates the message

CHARDD Kickoff Meeting, Princeton University, September 13, 2007 MessageEncoder G(s)G(s) u y objective + y signal Decoder Received message Control with Communication Design considerations: Consistent with primary control objective Low energy Reliability Stealth/security

CHARDD Kickoff Meeting, Princeton University, September 13, 2007 Reliable Control with Communication

CHARDD Kickoff Meeting, Princeton University, September 13, 2007 Double Integrator Example Choices of Fourier bases:

CHARDD Kickoff Meeting, Princeton University, September 13, 2007 Optimal Communication with the Double Integrator Cosine series with binary coefficients more reliably encode messages in that the average Hamming distance is larger. Open problems: 1.Reliable coding as the solution of an optimization problem 2.Optimal sampling for reliable decoding 3.Coding for noisy environments (channels) 4.Communication and vehicle motion control problems

CHARDD Kickoff Meeting, Princeton University, September 13, 2007 Problems in Communication Complexity

CHARDD Kickoff Meeting, Princeton University, September 13, 2007 Wong’s Problem Alice and Bob use a control process to collaboratively compute the value f(  ), with Alice choosing  and Bob choosing . AliceBob

CHARDD Kickoff Meeting, Princeton University, September 13, 2007 Next Steps Immediate future research goals: 1.For a variety of control system settings, study the problem of multiple agents having control inputs u 1,u 2,… which they select independently to jointly influence an output y. 2.How does the game change is we try to minimize state or output excursions while at the same time maintaining a reliable communication link? (Connection with risk/reward research.) 3.Infinite horizon games can be considered, but com- munication costs must be cost per unit time. 4.Redo the receding horizon target seeking game of next presentation with communication explicitly included.

CHARDD Kickoff Meeting, Princeton University, September 13, 2007