Introduction
My aim is to understand methodologies for collective control of a number of systems. The notion of collective control in this context refers to two things. Firstly, I hope to effect (or side-effect, even) a number of collective activities. Secondly, I wish to do this in a distributed manner wherever appropriate. These two elements in the control of the system are in some sense separable. Consider the following tabular classification:

	Single Controllee	Many Controllees
Single Controller	Many many systems fall into this category. Consider a robot watering a flower.	Consider the example of a traffic officer controlling traffic at a busy intersection.
Many Controllers	There are numerous examples, many have competitive elements. A ball in soccer could be the controlee, with each team (or player) being the controllers.	Few of these systems exist. They're usually complex, like, for example, the Air Traffic Control system.

Note, that in all cases, physical extent draws the distinction between the systems. In some cases, the communication medium can result in low bandwidth or noisy communication. Also, the distinction between communications and control systems is in some sense a grey line. It is clear that the ball is being controlled, and aircraft control falls closer to communication; vehicular control seems less obvious. I am interested in studying the ``many controlees'' cases.

Examples
I aim to find meaningful representations for systems where control can be performed based on macroscopic information, rather than requiring detailed information regarding the elements. There are numerous examples of systems that require only collective properties to control.

• Ducks / Sheep and Cows. These can be herded and directed. Computation on how to move these entities may only depend on global properties. At least in the case of ducks, it has been shown that a centroid estimate is sufficient for certain one-dimensional control tasks [1]. It is highly plausible that perimeter and density estimates are sufficient for other tasks.
• Vehicular Traffic. Perhaps the largest physically distributed system where external control plays a vital component. Vehicle flow is the ideal for scientific study as there is ample data easily obtainable. The field of traffic modelling has studied congestion and other interference effects from as early as the 1940's [2] there is a wealth of modelling techniques, and empirical findings. Compared to most of the spatial tasks we want our robots to perform, traffic is highly structured; this limits the applicability of traffic models directly to robotics work. There are some exceptions, where methodologies utilized for traffic have been used for multi-robotics analysis (see, for example [3]). Also, control of traffic usually occurs through traffic-signals, where there is a recognition that at high densities people can handle the loads more efficiently, since the light system is insufficiently adaptive. There are also, rare, instances of roads with lanes that can be used dynamically in one of two directions.
• Pedestrian Dynamics. High densities of people occur in every day life. The flow of people while moving from place to place is governed by rules. These rules are similar to the rigorous rules of the road, but are implicit. Analysis techniques are similar to the vehicular traffic case.
• Evacuation Dynamics. Like the previous case, this deals with the movement of people on foot. In emergencies the densities of people can be the highest, and the need to aid movement the most urgent. Eminent danger can result in regular ``unspoken'' rules (like the symmetry breaking that occurs) being either ineffective or rejected. A number of models for this sort of behaviour exist. Most often they qualitatively capture some observed phenomenon.

Capturing Structure
Much of the work done in the Interaction Lab has a philosophical basis in work on behaviour-based control. We consider that behavioural structure should be reflected in the representation used for control, and that this is a principled thing to do. This is perhaps best summed up in the motif, ``Think the way you act'' [4]. Strategies based on this view have been used for design of mobile robots capable of operating in the presence of uncertainty. These techniques have further shown their utility in scaling to multi-robot problems. Also, structure in human motion is used as a methodology for overcoming problems in traditional control of highly articulated humanoids. These cases use the underlying regularity is used as a mechanism for reducing the dimensionality of the control problem.

There is structure in collective motion too; I believe that there are still a number of ways that this structure can be exploited. This structure is a property of the global behaviour, which implies that it is really only observable at a macroscopic level. The process through which collective behaviour results from local interactions is not well understood (nor, do I believe that it will be for sometime).

This research is based on the observation that macroscopic properties are often sufficient for people to use in affecting systems. Thus, macroscopic models, whose purpose it is to show the collective structure, should be used for control. Next, I highlight what this claim implies:

• Microscopic detail is not necessary for course-grained control. Without defining what I mean by ``course-grained'' control, this statement is kind of vacuous. I defer a discussion of the notion of control until a later section (the one after the next).
• Systems for which we don't have detailed knowledge of the controller innards are still suitable for control with this methodology. So, the methodology could be used for crowd or traffic control.
• Controlee's can be designed simply with interesting macroscopic properties. This permits a method of construction of heterogeneous systems.
• Even for very small (nano-scale) systems, or systems where failures occur frequently, if the macroscopic behaviour is interesting, it could be loosely controlled.
• Macroscopic behaviour is often most easily analysable in the limit, i.e. for very large numbers of entities. Therefore, this methodology is scalable in certain cases.

Multi-Robot Control
Since the local-to-global problem (and its inverse-problem) are now well understood, one might well ask, how does one design any predictable multi-agent system. The answer is that it is, for a large part, still an art. Essentially, creative people build systems carefully, often using simulation and experiments to obtain insights on a implementation-by-implementation basis.

Multi-robot systems tend to alter collective behaviour by altering the local rules that produce it, and by seeing if this results in desired global properties. Control by explicitly considering macroscopic effects is not common (I don't know of any!). This is because the system needs to inherently have properties that make macroscopic effects externally controllable.

Typically, multi-robot controllers are designed with some number of parameters, and tested under certain conditions. They are infrequently designed with non-linearities such that when conditions are altered interesting things appear. Most often, focus is placed on attempting to drowning out conditions that result in this interesting behaviour. I think that this is a natural extension to a macroscopic level design, the arguments that have been put forward for minimalism at the microscopic level, see [5]. Also, this argument resembles the relationship that behaviour-based robotics has with control theory. The first recognizes that interesting behaviour occurs when there are non-linearities, and specifically those systems that have been traditionally difficult to analyse.

Another way to pose this particular view is that multi-robot systems are built to obtain a single stable behaviour. The view I assert, is that we should build systems that exhibit some number of stability points. Deliberative control can then be performed to move the system between these. This is, I believe, a fundamentally new approach to design of multi-robot systems.

It does not, however, solve the local-to-global problem, nor does it aim to. It recognises that there is potential for interesting behaviour in our robotic systems beyond that which we currently exploit.

What sort of control?
Perhaps the most unsatisfying part of this entire discussion is the imprecision with which I have used the words control, and affect, and influence. So, exactly what control would the systems I propose exhibit over the controlees?

The answer, of course, depends on the controlees. It depends on how amenable the system is to outside influences, and whether those influences are always drowned out, or spread through the system. Whether there are critical parameters which can be influenced, and how that effects the behaviour is the subject of the model.

Consider the following example graph from traffic data (not models, but actual collected data) from [2]:

This means that any mechanism that can control the density can alter the macroscopic behaviour. Notice, that in order to control a macroscopic state, we need to alter a macroscopic variable. This seems typical of a number of systems. It also indicates that perhaps most utility will come from ``Many Controllers'' when dealing with ``Many Controlees''. One approach to increasing density would be to decrease the number of lanes, or to introduce some large number of vehicles. Note, that this is in many ways very different from the Air Traffic Control system given as an example above; perhaps this is a more implicit methodology for collective control?

Much inspiration for answering questions regarding the quantity of vehicles and such is based on Statistical Thermodynamics and such. Typically, this deals with systems that are in some equilibrium state. This may not be the case in general, but so far this tools seem to offer the most promise.

There are other questions, for example, will this coarse methodology for control ever be sufficient for performing useful tasks? I believe that in a number of cases it will.

References