Home Articles Calculating Error: What do a brain and a ship have in common?

Calculating Error: What do a brain and a ship have in common?

A visual representation of: Calculating Error

Calculating Error: What do a brain and a ship have in common?

Humans have always sought to make life easier for ourselves – it’s almost what defines us as a species.

Part of this is to alleviate ourselves from the mundane tasks of life, from making a pot-stand so it does not have to be held over a fire, to having an automatic out of office reply on your email. As systems became more complex during the industrial revolution there was increased interest in the automatic control of such systems, one of which being the automatic steering of ships.

The steering of a ship could be controlled by aiming for a location, such as a port, and setting your compass bearing to that port: keep following the bearing and you reach the port, right? One problem with steering large ships is that they can be subject to large wind forces that cause the ship to drift over time, if the steering mechanism only uses a directional bearing it will take a longer route to reach its destination that it could have done. Furthermore, they have a lot of inertia: it takes quite a bit of effort to get them to change direction or slow down.

Proportional Derivative and Integral errors

Any real-world system has some error to account and correct for and these errors can be classified mathematically in different ways. In 1911 Elmer Sperry designed a system that used calculus to better control ship steering, it had:

  • Proportional error – How far off is my current direction with the direction I want to be in?
  • Derivative error – How quickly is the rate of error changing?
  • Integral error – What is the sum-total error over a given amount of time?

The proportional error is pretty self-explanatory: there is always some error from a true bearing and that must be constantly corrected for. The integral error helps when a ship experiences strong winds because even if the proportional error is zero (it won’t be), wind will still push the ship off-course. The derivative error is helpful because it would be easy to overcompensate for the first two errors and make the ship overshoot the desired bearing and now it is still off-course (but on the opposite side of the true bearing). Sperry’s original design used a gyroscope and was adopted by the US Navy and utilised in WW1.

Controlling Movement

Moving away from ships and onto biological nervous systems. The nerves for directly controlling movement reside in the spinal cord, however when you decide to catch a ball there is some process that happens in the brain that must decide the action to take place and pass this information to the spinal cord: the spinal cord itself is unable to make such conscious decisions. One particular pathway (known as the hyperdirect pathway) has been identified as being important when different species, including humans, encounter a physical go/stop situation: think of running for a base in rounders or baseball.

Researchers from MIT reported some interesting findings in Cell Reports, July 2022 [1]. The researchers set up an experiment whereby mice navigated a virtual reality corridor via a self-powered treadmill and upon stopping at a precise landmark location for a set amount of time they received a reward. The landmark distance was randomised to prevent learning via timing, and instead the mouse must rely on what it sees visually.

MIT experiment

The researchers determined that mouse brains required some error correction to successfully stop at the landmark, in time, and collect their reward. This presented a dilemma:

  • If the mouse does not factor in how far away it is from the landmark, it will not increase its speed to get there quick enough: it needs to keep providing a stimulus for its legs to keep running.
  • If the mouse is running at full tilt it must compensate to time its braking before it overshoots the landmark and misses its reward. It must inhibit leg movement to stop.
MIT experiment 02
MIT experiment 02

What they discovered was that the mouse’s brain compares its internal movement plan with the current moving state. And when these two states become significantly different, an “error” signal is produced that is interpreted as a stop signal. Again, the same dilemma is presented:

  • If the mouse just reacts to receiving a single error signal, it will begin stopping too soon and fall short of the landmark.
  • The mouse needs to sum-total the error signal over time – otherwise known as integration in mathematics – to ensure that it really is time to begin stopping. However, the visual system of the mouse is too slow to integrate the error signal quickly enough and reliably stop before at the landmark: it would overshoot and miss its reward.

What the researchers discovered is that the mouse compares the difference between the stimulatory (aka run/go) and the inhibitory (aka error/stop) signals at any given point in time, this is analogous to taking a derivative in mathematics. This allows the mouse stop soon enough to hit the landmark without overshooting. The mouse brain is using calculus, both derivatives and integrals to create an optimal movement: a movement that could not be as well executed without doing so.

 

The PID (Proportional, Integral, Derivative) controller

Back to ships, in 1922 a Russian-American engineer Nicolas Minorsky generalised the mathematics behind Sperry’s navigation system and what emerged was the modern PID controller – an indispensable device in modern control systems, typically implemented on a small microchip.

Modern electronic PID controllers are found in devices that require some feedback to know if they are doing the right thing. For example, temperature control of an oven, cruise control of a car, reagent mixing in a chemical plant, climate control in a building… etc.

There is an irony in how Minorsky came to develop this area of control theory, he noticed that the helmsman of naval ships provided corrective adjustments to the ships’ direction based upon:

  • Current error – “I am 4°off-course, therefore correct by 4°”
  • Previous error – “How far was I off-course over the last 10 seconds?”
  • Rate of error – “How quickly am I approaching the direction I want?”

It appears, without much conscious thought, the helmsman was using calculus to optimally navigate the ship all along, just like our mouse trying to get its reward.

Engineering seeks to reduce complex systems into constituent parts to make them manageably understandable and gain deeper insight into the system as a whole, but human brains are the most complex systems we have encountered in the universe and if we could reduce it all to basic calculus, they would not still present so much mystery today. For all that engineering has solved it still doesn’t explain the conscious experience, but it is interesting to know that biology has also alleviated itself of some of the mundane tasks in life, in the same way that humans have done so with machines (PID controllers included).

[1] Dynamic control of visually guided locomotion through corticosubthalamic projections: Cell Reports
And thanks to The Brain Uses Calculus to Control Fast Movements | Quanta Magazine for highlighting this research.

 

Contact Plextek

Contact Us

Got a question?

If you have got a question, or even just an idea, get in touch


Technology Platforms

Plextek's 'white-label' technology platforms allow you to accelerate product development, streamline efficiencies, and access our extensive R&D expertise to suit your project needs.

  • 01 Configurable mmWave Radar Module

    Plextek’s PLX-T60 platform enables rapid development and deployment of custom mmWave radar solutions at scale and pace

    Configurable mmWave Radar Module
  • 02 Configurable IoT Framework

    Plextek’s IoT framework enables rapid development and deployment of custom IoT solutions, particularly those requiring extended operation on battery power

    Configurable IoT Framework
  • 03 Ubiquitous Radar

    Plextek's Ubiquitous Radar will detect returns from many directions simultaneously and accurately, differentiating between drones and birds, and even determining the size and type of drone

    Ubiquitous Radar
Evolving silicon choices in the AI age
Evolving silicon choices in the AI age

How do you choose? We explore the complexities and evolution of processing silicon choices in the AI era, from CPUs and GPUs to the rise of TPUs and NPUs for efficient artificial intelligence model implementation.

A visual representation of: SSL The Revolution Will Not Be Supervised
SSL: The Revolution Will Not Be Supervised

Exploring the cutting-edge possibilities of Self-Supervised Learning (SSL) in machine learning architectures, revealing new potential for automatic feature learning without labelled datasets in niche and under-represented domains.

A visual representation of: A Programmer's Introduction to Processing Imaging Radar Data
A Programmer’s Introduction to Processing Imaging Radar Data

A practical guide for programmers on processing imaging radar data, featuring example Python code and a detailed exploration of a millimetre-wave radar's data processing pipeline.

A visual representation of: Using artificial intelligence to explore the biological world
Using Artificial Intelligence to Explore the Biological World

Harnessing AI's capabilities to decode protein folding, catalysing a leap in biological research and therapeutic innovation.

A visual representation of: Artificial Intelligence in the Big and Scary Real World
Artificial Intelligence in the Big and Scary Real World

Analysing the application of Artificial Intelligence in real-world scenarios, addressing its transformative potential and the ethical framework required for its deployment.

A visual representation of: AI Gesture Control
AI Gesture Control

Exploring the possibilities of AI gesture control for household appliances and more, using privacy-preserving radar technology, underscoring innovation in smart home interactions.

A visual representation of: Human Problem Solving in the AI era
Human Problem Solving in the AI-era

Exploring the symbiosis of human expertise and AI, the team navigated the AI era, enhancing problem-solving capabilities across various sectors without compromising the human touch.

A visual representation of: Repurposing Innovation Bullet Proof Your Wine
Repurposing Innovation: Bullet Proof Your Wine

Repurposing military-grade technology to safeguard fine wines, ensuring their pristine condition from bottling to cellar.

A visual representation of: Webcams and Eye Contact in the Post-Covid Office
Webcams and Eye Contact in the Post-Covid Office

Exploring the challenges and technological solutions to achieving effective eye contact through webcams in virtual meetings, enhancing remote communication in the post-COVID workplace.

A visual representation of: Of mice and ships
Calculating Error: What do a brain and a ship have in common?

Analysing the commonalities between brain function and ship steering through error correction methods, highlighting the indispensable role of calculus in both biological and engineered control systems.


Related Technical Papers

View All
an image of our technical paper
mmWave Imaging Radar

Camera systems are in widespread use as sensors that provide information about the surrounding environment. But this can struggle with image interpretation in complex scenarios. In contrast, mmWave radar technology offers a more straightforward view of the geometry and motion of objects, making it valuable for applications like autonomous vehicles, where radar aids in mapping surroundings and detecting obstacles. Radar’s ability to provide direct 3D location data and motion detection through Doppler effects is advantageous, though traditionally expensive and bulky. Advances in SiGe device integration are producing more compact and cost-effective radar solutions. Plextek aims to develop mm-wave radar prototypes that balance cost, size, weight, power, and real-time data processing for diverse applications, including autonomous vehicles, human-computer interfaces, transport systems, and building security.

an image of our technical paper
Low Cost Millimeter Wave Radio frequency Sensors

This paper presents a range of novel low-cost millimeter-wave radio-frequency sensors that have been developed using the latest advances in commercially available electronic chip-sets. The recent emergence of low-cost, single chip silicon germanium transceiver modules combined with license exempt usage bands is creating a new area in which sensors can be developed. Three example systems using this technology are discussed, including: gas spectroscopy at stand off distances, non-invasive dielectric material characterization and high performance micro radar.

an image of our technical paper
Metamaterial-Based Ku-Band Flat-Panel High-Grain

This technical paper by Dr. Rabbani and his team presents research on metamaterial-based, high-gain, flat-panel antennas for Ku-band satellite communications. The study focuses on leveraging the unique electromagnetic properties of metamaterials to enhance the performance of flat-panel antenna designs, aiming for compact structures with high gain and efficiency. The research outlines the design methodology involving multi-layer metasurfaces and leaky-wave antennas to achieve a compact antenna system with a realised gain greater than +20 dBi and an operational bandwidth of 200 MHz. Simulations results confirm the antenna's high efficiency and performance within the specified Ku-band frequency range. Significant findings include the antenna's potential for application in low-cost satellite communication systems and its capabilities for THz spectrum operations through design modifications. The paper provides a detailed technical roadmap of the design process, supported by diagrams, simulation results, and references to prior work in the field. This paper contributes to the advancement of antenna technology and metamaterial applications in satellite communications, offering valuable insights for researchers and professionals in telecommunications.

an image of our technical paper
On the Radiation Resistance of Folded Antennas

This technical paper highlights the ambiguity in the antenna technical literature regarding the radiation resistance of folded antennas, such as the half-wave folded dipole (or quarter-wave folded monopole), electrically small self-resonant folded antennas and multiple-tuned antennas. The feed-point impedance of a folded antenna is increased over that of a single-element antenna but does this increase equate to an increase in the antenna’s radiation resistance or does the radiation resistance remain effectively the same and the increase in feed-point impedance is due to transformer action? Through theoretical analysis and numerical simulations, this study shows that the radiation resistance of a folded antenna is effectively the same as its single-element counterpart. This technical paper serves as an important point of clarification in the field of folded antennas. It also showcases Plextek's expertise in antenna theory and technologies. Practitioners in the antenna design field will find valuable information in this paper, contributing to a deeper understanding of folded antennas.

an image of our technical paper
Frequency-Scanning Substrate-Integrated-Waveguide Meanderline Antenna for Radar Applications at 60GHz

This paper describes the design and characterization of a frequency-scanning meanderline antenna for operation at 60 GHz. The design incorporates SIW techniques and slot radiating elements. The amplitude profile across the antenna aperture has been weighted to reduce sidelobe levels, which makes the design attractive for radar applications. Measured performance agrees with simulations, and the achieved beam profile and sidelobe levels are better than previously documented frequency-scanning designs at V and W bands.

an image of our technical paper
A Ku-Band, Low Sidelobe Waveguide Array Employing Radiating T Junctions

The design of a 16-element waveguide array employing radiating T-junctions that operates in the Ku band is described. Amplitude weighting results in low elevation sidelobe levels, while impedance matching provides a satisfactory VSWR, that are both achieved over a wide bandwidth (15.7-17.2 GHz). Simulation and measurement results, that agree very well, are presented. The design forms part of a 16 x 40 element waveguide array that achieves high gain and narrow beamwidths for use in an electronic-scanning radar system.

an image of our technical paper
Sensing Auditory Evoked Potentials with Non-Invasive Electrodes and Low-Cost Headphones

This paper presents a sensor for measuring auditory brainstem responses to help diagnose hearing problems away from specialist clinical settings using non-invasive electrodes and commercially available headphones. The challenge of reliably measuring low level electronic signals in the presence of significant noise is addressed via a precision analog processing circuit which includes a novel impedance measurement approach to verify good electrode contact. Results are presented showing that the new sensor was able to reliably sense auditory brainstem responses using noninvasive electrodes, even at lower stimuli levels.

an image of our technical paper
Long Range Retro-Reflector

Passive retro-reflectors that modulate a scattered RF signal but do not transmit in their own right are well known. They are widely used in RFID tags, and keyless entry systems with a number of standardised solutions defined within the industry. The main advantage of these systems is that the mobile unit (the tag) can either avoid completely the use of a battery by powering itself from the incident RF ‘interrogating’ signal or only require a very small battery with a long life. This enables a ‘disposable’ tag to be engineered at very low cost, size and weight. However, there are many potential applications that require a somewhat longer transmission range than can sensibly be achieved with this method. The conventional paradigm requires a higher power ‘interrogating’ signal in order to increase range and there are obvious limits to how far this can be taken. The combination of regulatory restrictions and the steep range vs power slope that results from the fundamental mode of operation generally restrict the range to a few metres at most. Plextek have been taking a fresh look at the possible ways of circumventing this obstacle to produce a long range device that is nevertheless RF passive (does not transmit but only scatters). This paper describes in outline some ideas in this space, some initial experiments that have been done and some potential applications of the techniques.

an image of our technical paper
An Optical Room Occupancy Sensor

An automated sensor system that determines whether rooms within a building are occupied by a person or people has many applications. These divide broadly into the following classes: Security: Whole-site surveillance from control node, cases where a room should not be occupied, intruder detection and asset tracking. Safety: Identification of lone workers during non-core hours and remote supervision of isolated working environments. Confirmation of building evacuation. Management of high risk processes. Facilities Management: Environmental controls (lighting/heating) to meeting room booking aid. Sensors that seem to solve this problem are plentiful and it is only when they are considered in detail that their deficiencies become apparent. This short paper makes this case and introduces a new type of sensor based on an optical method.

an image of our technical paper
An Introduction to Yocto

Yocto is a comprehensive project designed to address the complexity of building custom Linux distributions for embedded systems. Unlike conventional Linux distributions (distros) created for standard PC architectures, Yocto caters to the diverse and often incompatible hardware in the embedded world. By providing a sophisticated build system based on layered scripts called "recipes," Yocto streamlines the process of creating, maintaining, and updating embedded distros. Each package within a distro has its own recipe, maintained by the package developers, ensuring that updates and customizations are manageable and consistent. This structure allows developers to define precise sets of packages for their embedded systems, facilitates updates through package managers, and supports a wide range of hardware platforms. With support from major chip and board manufacturers, Yocto is becoming the go-to toolset for embedded Linux development, offering unparalleled flexibility and control for developers aiming to create finely tuned, market-ready products.

an image of our technical paper
GPU Computing

Power limits restrict CPU speeds, but GPUs offer a solution for faster computing. Initially designed for graphics, GPUs now handle general computing, thanks to advancements by NVIDIA, AMD, and Intel. With hundreds of cores, GPUs significantly outperform CPUs in parallel processing tasks. Modern supercomputers, like Titan, utilize thousands of GPU cores for immense speed. NVIDIA’s CUDA platform simplifies GPU programming, making it accessible for parallel tasks. While GPUs excel in parallelizable problems, they can be limited by data transfer rates and algorithm design. NVIDIA’s Tesla GPUs provide high performance in both single and double precision calculations. Additionally, embedded GPUs like the NVIDIA Jetson TX2 deliver powerful, low-power computing for specialized applications. Overall, GPUs offer superior speed and efficiency for parallel tasks compared to CPUs.