chardd kickoff meeting, princeton university, september 13, 2007 toward a theory of protocols for...

CHARDD Kickoff Meeting, Princeton University, September 13, 2007

Toward a Theory of Protocols for Communication Through Action

John BaillieulC.I.S.E. and

Intelligent Mechatonics LaboratoryBoston UniversityBoston, MA 02215

[email protected]://people.bu.edu/johnb

http://iml.bu.eduhttp://www.bu.edu/systems


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)


Prior Work that Informs the ResearchFrom DAAD19-01-1-0465: 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>Rc.

€

Rc = log2 e ⋅(Re(λ1) +L + Re(λ k ))

G(s)



Optimally parsimonious use of resources in control---e.g. speed vs. accuracy tradeoffs:

G(s)

Bluetooth radio Bluetooth radio

Air Packets: 17 bytes payload

Air Packets: ≤ 366 bits total


From DAAD19-01-1-0465: The Boston University Center for Communicating Networked Control Systems

Prior Work that Informs the ResearchNecessary and Sufficient Conditions for Stable Rigidity

with Minimal SensingTheorem: (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


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.



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


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.

QuickTime™ and aDV/DVCPRO - NTSC decompressor

are needed to see this picture.


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.


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


The Simplest Communication Through Action Problem

By means of the input u, steer the output y so as to:1. Achieve an output objective while2. Simultaneously communicating a message from u to y.


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 while2. Simultaneously communicating messages to each other.


Multiplexed Communication in Input/Output Networks


Motivation from Finite Dimensional Linear Systems


The null-space of L can be used for communication.

Communication in Terminal Endpoint Linear Control Problems


Terminal Endpoint Control with Communication

steers the system from 0 to x1

and communicates the message


Message Encoder

G(s)u yobjective+ysignal

Decoder

Receivedmessage

Control with Communication

Design considerations:• Consistent with primary control objective• Low energy• Reliability• Stealth/security


Reliable Control with Communication


Double Integrator Example

Choices of Fourier bases:

1.

2.


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 problem2. Optimal sampling for reliable decoding3. Coding for noisy environments (channels)4. Communication and vehicle motion control problems


Problems in Communication Complexity


Wong’s Problem

Alice and Bob use a control process to collaboratively compute the value f(), with Alice choosing and Bob choosing .

Alice Bob


Next Steps

Immediate future research goals:

1. For a variety of control system settings, study the problem of multiple agents having control inputs u1,u2,… 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 toward a theory of protocols for...

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