Keeping the microcontroller asleep as much as possible is a key goal for a sensor system, so it makes sense to organise the entire software process around that.

The standard Arduino software model is, well, standard: programs (“sketches”) are structured in terms of a setup() function that runs once when the system restarts and a loop() function that is run repeatedly. This suggests that the system spends its time running, which possibly isn’t all that desirable: a sensor system typically tries to stay in a low-power mode as much as possible. The easiest way to do this is to provide a programming framework that handles the sleeping, and where the active bits of the program are scheduled automatically.

There are at least two ways to do this. The simplest is a library that lets loop() sleep, either directly or indirectly. This is good for simple programs and not so good for more complicated ones, as it means that loop() encapsulates all the program’s logic in a single block. A more modern and compositional approach is to let program fragments request when they want to run somehow, and have a scheduler handle the sleeping, waking up, and execution of those fragments. That lets (for example) one fragment decide at run-time to schedule another

If we adopt this approach,we have to worry about the fact that one fragment might lock-out another. A desktop system might use threads; this is more problematic for a microcontroller, but an alternative is to force all fragments to only execute for a finite amount of time, so that the scheduler always gets control back. This might lead to a fragment not running when it asked (if other fragments were still running), but if we assume that the system spends most of its time asleep anyway, there will be plenty of catch-up time. Doing this results in an actor system where the fragments are actors that are scheduled from an actor queue.

Turning this into code, we get the SleepySketch library: a library for building Arduino sketches that spend most of their time sleeping.

There are a few wrinkles that need to be taken care of for running on a resource-constrained system. Firstly, the number of actors available is fixed at start-up (defaulting to 10), so that we can balance RAM usage.(With only 2k to play with, we need to be careful). Secondly, we use a class to manage the sleeping functionality in different ways: a BusySleeper that uses the normal delay() function (a busy loop) with no power-saving functions, a HeavySleeper that uses the watchdog timer to shut the system down as far as possible, and possibly some other intermediate strategies. Actors are provided by sub-classing the Actor class and providing a behaviour. We also allow pre- and post-behaviour actions to define families of actors, for example sensor observers. We separate the code for an actor from its scheduling.

The standard library uses singleton classes quite a lot, so for example the Serial object represents the USB connection from an Arduino to its host computer and is the target for all methods. We use the same approach and define a singleton, Sleepy

The program structure then loops something like this. If we assume that we’ve defined an actor class PingActor, then we can do the following:

void setup() {
   Serial.begin(9600);
   Sleepy.begin(new HeavySleeper());

   Sleepy.scheduleIn(new PingActor("Ping!"), 10000);
}

void loop() {
   Sleepy.loop();
}

The setup() code initialises the serial port and the sleepy sketch using a HeavySleeper, and then schedules an actor to run in 10000ms. The loop() code runs the actors while there are actors remaining to schedule. If the PingActor instance just prints its message, then there will be no further actors to execute and the program will end; alternatively the actor could schedule further actors to be run later, and the sketch will pick them up. The sketch will remain asleep for as long as possible (probably for over 9s between start-up and the first ping), allowing for some fairly significant power saving.

This is a first design, now just about working. It’s still not as easy as it could be, however, and needs some testing to make sure that the power savings do actually materialise.

The Arduino has several sleep modes that can be used to reduce power consumption. The most useful for sensor networks is probably the one that uses the watchdog timer.

Powering-down the Arduino makes a lot of sense for a sensor network: it saves battery power allowing the system to survive for longer. Deciding when to power the system down is another story, but in this post we’ll concentrate on documenting the mechanics of the process. The details are necessarily messy and low-level. (I’ve been greatly helped in writing this post by the data sheet for the Atmel ATmega328P microcontroller that’s used in the Arduino Uno, as well as by a series of blog posts by Donal Morrissey that also deal with other sleep modes for the Atmel.)

Header files and general information

#include <avr/power.h>
#include <avr/wdt.h>

These provide definitions for various functions and variables needed to control the watchdog timer and manage some of the other power functions.

Power modes

A power (or sleep) mode is a setting for the microcontroller that allows it to use less power in exchange of disabling some of its functions. Since a microcontroller is, to all intents and purposes, a small computer on a chip, it has a lot of sub-systems that may not be needed all the time. A power mode lets you shut these unneeded sub-systems down. The result saves power but reduces functionality.

Power modes are pretty coarse control mechanisms, and can shut down more than you intend. If your project is basically software-driven, with the Arduino making all the decisions, then a “deep” power-saving mode is ideal; on the other hand, if you rely on hardware-based signals at all, a “deep” sleep will probably ignore your hardware and the Arduino may never wake up.

The watchdog timer is used to manage the “power-down” mode, the deepest sleep mode with the biggest power savings.

Watchdog timer

The Arduino’s watchdog timer is a countdown timer that’s driven by its own oscillator on the microcontroller. It’s designed to run even when all the other circuitry is powered down, meaning that the microcontroller is drawing as little power as possible without actually being turned off completely.

Why “watchdog” timer? The basic function of a watchdog timer is to “bite” after a certain period, where “biting” means raising an interrupt, re-setting the system, or both. A typical use of a watchdog is to make a system more robust to software failures. Since the watchdog is handled by the microcontroller’s hardware, independent of any program being run, it will still bite even if the software gets stuck in an infinite loop (for example). Some designers set the watchdog ahead of complex operations, so that if the operation fails, the system will reset in a short amount of time and end up back in a known-good configuration. At the end of a successful operation, the program disables the watchdog (before it bites) and carries on. Of course this assumes that the operation completes before the watchdog bites, which means the programmer needs to have a good idea of how long it will take.

Setting the time-out period

It’s as well to understand how watchdog timers on microcontrollers work. Typically they have a fairly coarse resolution, counting a fixed number of timer ticks before “biting” and performing some function. In the case of the Arduino, the watchdog timer is driven by the internal oscillator running at 128KHz and counts off some multiple of ticks before biting. This value — the number of ticks counted — is referred to as the “prescalar” for the timer.

The prescalar is controlled by the values of four bits in the watchdog timer’s control register, WDTCSR. To set them up, you pick the value of prescalar you want and set the appropriate bits. If the bits contain a number ( i ), then the watchdog will bite after ( (2048 << i) / 128000 ) seconds. So ( i = 0) means the watchdog bites after 16ms; ( i = 1 ) produces  delay of 32ms; and so on up to ( i = 9 ) (the largest value allowed) means the watchdog bites after about 8s.

The word “about” is important here: the oscillator’s exact frequency depends on the supply voltage to the chip and some other factors, meaning that you should be conservative about relying on the delay time.

Writing the appropriate value of ( i ) into the control register involves representing ( i ) as a four-digit binary number and then writing these bits into four bits of the register — and unfortunately these bits aren’t consecutive. if ( i = 7 ) for example, then this is 0b0111 in binary, so we write 1 into bits WDP0, WDP1 and WDP2, and 0 into bit WDP3, and 0 into all the other bits:

WDTCSR = (1 << WDP0) | (1 << WDP1) | (1 << WDP2);

The phrases of the form (1 << WDP0) simply takes a binary digit 1 and shifts it left into bit position WDP0. The | symbols logically OR these bits together to generate the final bit mask that is assigned to the control register.

Actually there’s a little bit more to it than this, as we can’t change the watchdog’s configuration arbitrarily. Instead we have to notify the chip that it’s configuration is about to be changed, by setting two other bits in the control register and then performing the updates we want:

WDTCSR |= (1 << WDCE) | (1 << WDE);

Setting WDCE enables changes in configuration to be made in the next few processor cycles, i.e. immediately. Setting WDE resets the timer.

Finally we enable the watchdog timer interrupts by setting bit WDIE. When the watchdog timer bites, the microcontroller executes an interrupt handler, re-starts the main program, and clears WDIE. Any further interrupts, if the time is re-enabled, will then cause a system reset.

WDTCSR |= (1 << WDIE);

So the complete code the setting up the watchdog timer to bite in 2s is:

set_sleep_mode(SLEEP_MODE_PWR_DOWN);              // select the watchdog timer mode
MCUSR &= ~(1 << WDRF);                            // reset status flag
WDTCSR |= (1 << WDCE) | (1 << WDE);               // enable configuration changes
WDTCSR = (1 << WDP0) | (1 << WDP1) | (1 << WDP2); // set the prescalar = 7
WDTCSR |= (1 << WDIE);                            // enable interrupt mode
sleep_enable();                                   // enable the sleep mode ready for use
sleep_mode();                                     // trigger the sleep

/* ...time passes ... */

sleep_disable();                                  // prevent further sleeps</pre>

 Interrupt handler

What happens when the watchdog bites? It causes an interrupt that has to be handled before the program can continue. The interrupt could be used for all sorts of things, but there’s often no point in worrying about it: but it still has to be there, to prevent the microcontroller just resetting. The following code installs a dummy interrupt handler:

ISR( WDT_vect ) {
  /* dummy */
}

The WDT_vect identifies the watchdog timer’s interrupt vector.

While this might seem like a waste of time, it’s important to have an interrupt handler as the default behaviour of the watchdog timer is to reset the microcontroller, which we want to avoid. It’s also worth noting that, once enabled, the watchdog timer will keep biting, so the interrupt handler will be called repeatedly. (Put a print statement in the hander to see.) This doesn’t cause any problems.

Where does mathematics end and computer science begin?

I don’t seem to have posted to this blog recently, so let’s re-start with a big question: where is the edge of computer science? That is to say, what separates it from maths? How do mathematicians and computer scientists see problems differently, and indeed select differently what constitutes an interesting problem?

This has been on my mind recently because of some work I’ve been doing with my student Saray on adaptive complex networks. A complex network is one that has statistical regularity in the distribution of the wires, or links, between its nodes. The internet is a complex network where the links obey a power-law distribution: a small number of sites (Yahoo, Google, IBM, …) have a huge number of links to them, while the majority (this site) have almost none. Complex networks are created naturally by lots of processes, and are useful for describing a whole range of phenomena. (An accessible introduction is Albert-László Barabási. Linked: how everything is connected to everything else, and what it means for business and daily life. 2003.) An adaptive complex network is one where the way the network is wired changes with time. A good example is a meeting-with-friends network where there is a link between you and those people you meet in a particular timeframe. You might change the people you meet if you discover that one of them is ill, for example, so the the friend-meeting network would be re-wired to remove links to your sick friends. If we were to model the spread of an illness through this network, there would be two processes at work: a spreading process that made people who met sick people ill themselves (with some probability); and a re-wiring process that tried to remove links to those friends known to be sick (again perhaps with some probability). Our paper (Saray Shai and Simon Dobson. Complex adaptive coupled networks. Physical Review E 87(4). 2013.) shows how there are unsuspected subtleties in the way spreading processes work on such networks, where common simplifications can actually hide crucial features of the network’s behaviour.

The literature on network science is full of papers analysing such processes. Typically the analysis is both analytic and numerical. That is to say, a mathematical model is developed that describes the state of the network after lots of time has passed (its equilibrium behaviour); and numerical simulation is then performed by creating a large number of networks, running the spreading processes on them, and seeing whether the results obtained match the analytical model. (It was an unexpected mis-match between analytical and numerical results that led us to the main result reported in our paper.) Typically the community finds analytical results more interesting than numerical results, and with good reason: an analytic result provides both a final, closed-form solution that can be used to describe any network with particular statistical properties, without simulation; and it often also provides insight into why a given equilibrium behaviour occurs. These are the sorts of general statements that can lead to profound understanding of wide ranges of phenomena.

There’s a sting in the tail of analysis, however, which is this. In order to be able to form an analytic model, the process being run over the network has to be simple enough that the mathematics converges properly. A typical analysis might use a probabilistic re-wiring function, for example, where nodes are re-wired with a fixed probability, or one that varies only slowly. Anything more complex than this defeats analysis, and as a result one never encounters anything other than simple spreading processes in the literature.

As a computer scientist rather than a mathematician I find that unsatisfying, and I think my dissatisfaction may actually define the boundary between computing and mathematics. The boundary is the halting problem — or, more precisely, sustaining your interest in a problem once you’ve hit it.

The halting problem is one of the definitive results in computer science, and essentially says that there are some problems for which it’s impossible to predict ahead of time whether they’ll complete with a solution or simply go on forever. Put another way, there are some problems where the only way to determine what the solution is is to run a piece of code that computes it, and that may or may not deliver a solution. Put yet another way, there are problems for which the code that computes the solution is the most concise description available.

What this has to do with complex systems is the following. When a computer scientist sees a problem, they typically try to abstract it as far as possible. So on encountering a complex network, our first instinct is to build the network and then build the processes running on it as separate descriptions that can be defined independently. That is, we don’t limit what kind of functions can hang off each node to define the spreading process: we just allow any function — any piece of code — and then run the dynamics of the network with that code defining what happens at each node at each timestep. The immediate consequence of this approach is that we can’t say anything a priori about the macroscopic properties of the spreading process, because to do so would run into the fact that there isn’t anything general one can say about an arbitrary piece of code. The generality we typically seek precludes our making global statements about behaviour.

Mathematicians don’t see networks this way, because they want to make precisely the global statements that the general approach precludes — and so don’t allow arbitrary functions into the mix. Instead they use functions that aggregate cleanly, like fixed-probability infection rates, about which one can make global statements. One way to look at this is that well-behaved functions allow one to make global statements about their aggregate behaviour without having to perform any computation per se: they remain within an envelope whose global properties are known. A mathematician who used an ill-behaved function would be unable to perform analysis, and that’s precisely what they’re interested in doing, even though by doing so they exclude a range of possible network behaviours.In fact, it’s worse than that: the range of behaviours excluded is infinite, and contains a lot of networks that seem potentially very interesting, for example those whose behaviours depend on some transmitted value, or one computed from values spread by the process.

So a mathematician’s (at least as represented in most of the complex systems literature) interest in a problem is lost at precisely the point that a computer scientist’s interest kicks in: where the question is about behaviour of arbitrary computations. The question this leads to is, what model do real-world networks follow more closely? Are they composed of simple, well-behaved spreading processes? Or do they more resemble arbitrary functions hanging off a network of relationships, whose properties can only be discovered numerically? And what effect does the avoidance of arbitrary computation have on the choice of problems to which scientists apply themselves? Perhaps the way forward here is to try to find the boundary of the complexity of functions that remain analytic when used as part of a network dynamics, to get the best of both worlds: global statements about large categories of networks, without needing numerical simulation of individual cases.

Such a classification would have useful consequences for general computer science as well. A lot of the problems in systems design come from the arbitrariness of code and its interactions, and from the fact that we’re uncomfortable restricting that generality a priori because we don’t know what the consequences will be for the re-usability and extensibility of the systems being designed. A more nuanced understanding of behavioural envelopes might help.

Any sensor network has to represent sampled data somehow. What would be the most friendly format for so doing?

Re-usable software has to take an extensible view of how to represent data, since the exact data that will be represented may change over time. There are several approaches that are often taken, ranging from abstract classes and interfaces (for code-based solutions) to formats such as XML for data-based approaches.

Neither of these is ideal for a sensor network, for a number of reasons.

A typical sensor network architecture will use different languages one the sensors and the base station, with the former prioritising efficiency and compactness and the latter emphasising connectivity to the internet and interfacing with standard tools. Typically we find C or C++ on the sensors and Java, JavaScript, Processing, or some other language on the base station. (Sometimes C or C++ too, although that’s increasingly rare for new applications.) It’s therefore tricky to use a language-based approach to defining data, as two different versions of the same structure would have to be defined and — more importantly — kept synchronised across changes.

That suggests a data-based approach, but these tend to fall foul of the need for a compact and efficient encoding sensor-side. Storing, generating, and manipulating XML or RDF, for example, would typically be too complex and too memory-intensive for a sensor. These formats also aren’t really suitable for in-memory processing — unsurprisingly, as they were designed as transfer encodings, not primary data representations. Even though they might be attractive, not least for their friendliness to web interactions and the Semantic Web, they aren’t really usable directly.

There are some compromise positions, however. JSON is a data notation derived initially from JavaScript (and usable directly within it) but which is sufficiently neutral to be used as an exchange format in several web-based systems. JSON essentially lets a user form objects with named fields, whose values can be strings, numbers, arrays, or other objects. (Note that this doesn’t include code-valued fields, which is how JSON stays language-neutral: it can’t encode computations, closures, or other programmatic features.)

JSON’s simplicity and commonality have raised the possibility of using it as a universal transport encoding: simpler than XML, but capable of integration with RDF, ontologies, and the Semantic Web if desired. There are several initiatives in this direction: one I came across recently is JSON-LD (JSON for Linked Data) that seeks to integrate JSON records directly into the linked open data world.

This raises the possibility of using JSON to define the format of sensor data samples, sample collections (datasets), and the like, and linking those descriptions directly to ontological descriptions of their contents and meaning. There are some problems with this, of course. Foremost, JSON isn’t very compact, and so would require more storage and wireless bandwidth than a binary format. However, one approach might be to define samples etc in JSON format and then either use them directly (server-side) or compile them to something more static but more efficient for use sensor-side and for exchange. This would retain the openness but without losing performance.