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No doubt that model-based design is one of the methods that brings the control, communications, signal processing and dynamic systems to a great level. Designing for example model predictive or even nonlinear control systems are more feasible and less error-prone using this approach.

Model-based design methodology, especially in the starting stages, is used in many elds such as automotive, aircraft, robotics and others. In the other industries for example the automation industry, they tend to neglect this phase and hard-code the software program in the PLC and connect it to a simulation platform to evaluate system performance. In this article, we are briefly discussing the improvement and the value of starting the design process with the model-based design approach and how that can impact the automation industry.

In the model-based design scheme, knowing the mathematical representation, it is easier for a developer to design the model of the plant. Based on that, one can synthesize a suitable controller for that plant using graphical-interface-user blocks that represent simple arithmetic, logic and other simple operations or even more complicated operations such as PID and model predictive control blocks that handle more complicated operations, in the absence of the actual hardware. This will save a huge amount of time for a developer if he would like to code the whole system. As a result it is much easier to debug and improve the control algorithms quality. What is more interesting, even without knowing the mathematical representation of the plant, you can model the plant by depicting electrical or mechanical circuits and connected to scopes or displays blocks to observe their outputs. Veri fication of the design could be handled through Model-In-The-Loop(MIL) and Hardware-In-The-Loop(HIL) simulations. In the MIL you can test and validate the simulated controller and plant in the early phases without physical components. Once the model is tested in MIL, you can output HDL code, C code, IEC61131-1 Structured Text (using PLC coder) and reports. In the HIL method, HIL simulators will be used to act as a real plant and will communicate with controllers through sensors and actuators. In which testing is more realistic and then you are ready to go to test the prototype.

There are many advantages of using the model-based design approach. For example, most of the veri cation and validation could be done earlier before the hardware exists, as well as, adding new features will take lesser time and the development schedule will be shortened. Moreover, some model-based design platforms provide code generation feature that is optimizing the code in which more memory space and high execution speed are provided. All in all, one can see the benefits of considering a model-based design approach in the development process and how that will increase the quality of the testing of the system and decrease the errors that could be expensive in the real application.

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Introducing Transformers

The idea of training language models on large datasets and then using these pre-trained
models to enhance performance on smaller, similar datasets has been a crucial breakthrough
for progress in many NLP challenges. However, pre-training for a specific task and embedding
long-term sequential dependencies have been huge constraints to training more generalised
language models. Transformer models are unsupervised models capable of training on
unlabelled, unstructured text to perform a large array of downstream NLP tasks, including
question-and-answer for dialogue systems, named entity recognition (NER) and sequencelevel
tasks such as text generation. The typical Transformer architecture is illustrated below in
Figure 1:

Figure 1: Transformer Blocks [4]

As shown in Figure 1, the Transformer architecture consists of a block of encoders (left) and a
block of decoders (right). Instead of using a hidden state between layers (as in recurrent neural network architectures), the encodings themselves are passed between each encoder, and the
final encoder output is then passed to the first decoder in the decoder block. Each
encoder/decoder in the Transformer contains a self-attention layer, which aims to determine
which part of the sequence is most important when processing a particular word, e.g. in the
sentence “James enjoys the beach because he likes to swim”, the self-attention layer should
learn to link the word “he” to “James” as the most important for its embedding. Additionally,
each decoder contains an “Encoder-Decoder Attention” layer, which refers to the relative
importance of each encoder when the decoder predicts the output.


The Bidirectional Encoder Representation from Transformers, or BERT for short, is one of the
most influential Transformer-based models. It has earned its reputation from beating multiple
benchmark performances in various NLP tasks with its bi-directional attention mechanisms.
This means that BERT considers not only the previous context but also looks ahead when
learning embeddings. The BERT model focuses on building a language model and thus on the
encoder block of the Transformer. Figure 2 below shows the composition of BERT embeddings
as consisting of the word token embeddings, the segment embedding (for longer sequences)
and a positional embedding that keeps track of the input order:

Figure 2: BERT embeddings illustrated [1]

Fine-tuning BERT

To build our search engine, we first acknowledge that 72 data points is insufficient to fine-tune
the BERT model for our specific task. Instead, we make use of a benchmark dataset for
sentence similarity, STS-B, consisting of 8,000 pairs of semantically similar sentences from
news articles, captions and forums [3]. Since BERT is not specifically designed for sentence
embeddings, we use a modified version of BERT for sentence encoding (proposed by Reimers
and Gurevych [2]), which adds a pooling layer to the standard architecture and is trained with a
regression objective based on a siamese network, i.e. each sentence represents its own
network and their outputs are combined and then evaluated (see Figure 3). The regression
objective function here is the cosine similarity measure between these sentence embeddings,
which is used as a loss function for the fine-tuning task. From the bottom to the top, we see
that each sentence is first encoded using the standard BERT architecture, and thereafter our
pooling layer is applied to output another vector which is then used to compute the cosine similarity measure. As described in [2], we compute this similarity measure for each query and
the 72 docstrings that we obtain from the Sympathy modules and return the top 5 nodes
according to this measure.

Figure 3: Siamese BERT network for sentence similarity illustrated [2]

The Result

We have been able to build a working prototype of the semantic search engine for the 72
nodes currently available on Sympathy for Data, which we hope to integrate as a fully-fledged
plugin in the future. Our search engine performs impressively given that it has only been
trained on around 8,000 pairs of semantically similar sentences (i.e. 16,000 sentences). Below
is an illustrative example of how this works in practice.


[1] Devlin, J., Chang, M., Lee, K. and Toutanova, K. (2019). BERT: Pre-training of Deep
Bidirectional Transformers for Language Understanding. [online] Available at: [Accessed 24 Sep. 2019].
[2] Reimers, N. and Gurevych, I. (2019). Sentence-BERT: Sentence Embeddings using
Siamese BERT-Networks. [online] Available at:
[Accessed 24 Sep. 2019].
[3] Daniel Cer, Mona Diab, Eneko Agirre, Iñigo Lopez-Gazpio, and Lucia Specia (2017)
SemEval-2017 Task 1: Semantic Textual Similarity Multilingual and Cross-lingual Focused
Evaluation Proceedings of the 10th International Workshop on Semantic Evaluation (SemEval
[4] Models, H. (2019). Understanding Transformers in NLP: State-of-the-Art Models. [online]
Analytics Vidhya. Available at:
nlp-state-of-the-art-models/ [Accessed 24 Sep. 2019].

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Electricity from heat

Well, no big news there. But how about using existing waste heat instead of burning oil or splitting atoms? Instead of superheating steam just settling for 70-120C source temperatures?
The technology is surprisingly simple, but clever. Here is some text and an image from the Climeon homepage (

The heat, from geothermal sources, industrial waste heat or power production, is fed to the Climeon unit. Inside the Climeon unit a heat exchanger transfers the heat to an internal fluid, which vaporizes due to its lower boiling point. The vapors are then expanded over a turbine to run a generator and produce electricity.

Fundamentally the same electricity generation scheme as a nuclear power plant, but no nuclear stuff.
The energy efficiency of, for instance, a nuclear plant design might be considered poor considering the amount of heat that is wasted (just cooled off for no gain). Plants that combine electricity generation and district heating are more efficient from that point of view, but perhaps transporting heat to remote districts using nuclear coolant is not a great idea.
In this case, the concept is to use heat that is already there and unused, so efficiency can instead be measured solely as the amount of electricity generated per unit of heat energy. If the source is geothermal it’s basically electricity for free, once you make your initial investment and maintenance allocations.

I think the concept is great and hope they do well.

Batteries, when they are no longer suitable for their initial purpose?

There seem to be four basic answers to this question

  1. We made our money while they worked, now we need to get rid of them at as low cost as possible
  2. We are hoping to recycle them efficiently and make use of that
  3. We are hoping someone else wants them and hopefully make use of that
  4. O boy, where did all these batteries come from?

The first answer is understandable, but not convincing from an environmental or “big picture” point of view. Established recycling technology for Lithium-Ion batteries has a couple of glaring drawbacks, mainly that it doesn’t work that well and that it is based on melting (which costs a lot of energy).

The second answer is hopeful and often based on the idea that recycling will improve. Research is underway, most promising is research based on technologies that have existed in the mining industry for over 100 years. The idea in mining is to crush the material and mix it up with fluid containing molecules that attach to the element one wishes to extract. The newly formed molecules float up to the surface of the fluid and can be skimmed off (or assume whatever property might make it easy to separate them from the fluid). Then a further stage filters out the desired element. The research is looking to do this similarly in steps, separating all the desired elements along the way.

The third answer is also hopeful. As we have discussed in previous posts, the idea of a functioning business with second and possibly third life applications for used batteries is quite dependent on buyers and sellers knowing the condition of the batteries. We are hoping to do something of our own in this area, as you know.

Unfortunately, the fourth answer does exist. I am not going to point any fingers and just leave it there.

Unless someone comes up with a better battery technology soon, we are looking at an ever-increasing need for answers 2 and 3 to win out.
Authorities are also unlikely to accept answers 1 or 4 in the long run, IMO (global perspective, visualize massive toxic junkyards in some third world country). The pressure is more likely to increase than decrease on manufacturers, and it will be interesting to see where in the value chain responsibilities land. Passing the buck will probably not be that easy without some serious documentation to show where the batteries went and who is responsible for them.

Pet project

To wind this up I am going to talk a bit about a pet project. We have been asked to demonstrate something on the theme “technology is fun” for an event (Netgroup anniversary) taking place at the Göteborg opera house.
I am going to attempt to build a plasma arc speaker. They have always caught my eye (you can look them up or watch some videos on Youtube), so even if it has already been done, I think it is a perfect fit considering the venue.

First, I would like to point out that this is a high-voltage design, so building it at home with a simple on/off switch is not a great idea if you have small (or overly curious) children running around. It can cause serious heart problems or kill you, and it produces ozone which can be lethal at concentrations of more than 50ppm. Great fun, right?

Anyway, the idea I am using is something like this

For the power source, I will use a standard 700W PC power supply, using the 12V output. This will go to the flyback transformer and switching MOSFETs.

The audio source will probably be an obsolete MP3 player. The signal will go to a 555, which will then control the switching MOSFETs (I’ll use 3 parallel STP40NF10L).

The flyback transformer has the property of being able to produce high voltages, in the X kV range. Also, instead of being fed by a DC source it is typically fed by a switched source in the XY kHz range.

My idea is to produce the arc between two stainless steel screws of some respectable dimension.

So, kV and kHz? This means we get a modulated plasma arc that can play the higher frequencies of music well. It should actually be able to do it very well, since there are no moving parts, unlike speaker membranes and similar. It won’t be very loud since I have no plans to ionize western Sweden or kill the guests at the event, but it will be fun to see if I can make it work.

If anyone feels a huge urge to fiddle around with it together with me, I am looking for someone who can prevent me from electrocuting myself and maybe has some ideas for an ozone trap.

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Today’s modern vehicles feature a large set of advanced driver-assistance systems (ADAS), such as electronic stability control, lane departure warning systems, anti-lock brakes, and several others. These systems are dependent on multiple inputs to model the current state of the vehicle as well as the environment, and one can argue that the vehicle’s interaction with the road is the most important input.

The tire-road friction is essential to the stability of the vehicle and have been found to be the most important factor in avoiding crashes. About a quarter of all crashes occur due to weather-related issues, and accidents are twice as likely to happen on wet asphalt compared to dry asphalt. There is however no way to accurately measure the available friction, so some type of estimation algorithm needs to be developed.


All of the systems undergo extensive testing and are required to be evaluated for a large number of test scenarios. However, this introduce two major issues.

First, real-world data can only be used to analyse what has already happened, thus there is no certainty about what would happen in an untested reality and there is an increased risk for unforeseen conditions and edge cases. It simply takes too much time to test enough driving cases.

Second, testing for a large set of scenarios is impractical as the actual value needs to be known in order to evaluate the system, which the value often is for the testing sites. For an environment where the actual friction is an estimate, i.e. a public road, the testing is prone to errors and limits the available testing sites with valid verification since otherwise the estimations are compared to other estimations. If the approach is to train a machine learning algorithm there is no reference value of a correct answer.


To overcome these issues, simulation has been proposed as a solution. By using a digitally controlled environment, the true value of the tire-road friction is known. Furthermore, simulation allows for controllability, reproducibility, and standardization as measurement errors and uncertainties can be both eliminated and introduced at will. 

Simulation of high friction driving

Combine is currently doing a master thesis together with a major Swedish automotive company where we are investigating the possibility to digitalize the testing process. By using the generated simulation data, we will train a machine learning algorithm to estimate the tire-road friction. The master thesis is planned to be finalized by the end of the year, so stay tuned about the results. 

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Who are you?

My name is Jannes Germishuys, and I am all the way from Cape Town, South Africa. I recently completed my master’s in data science here in Gothenburg and joined Combine straight after graduation. Before my segue into data science, I actually majored in actuarial science, more commonly known as insurance mathematics, and after my studies I worked at a data science startup for 2 years.

What brings you to Sweden?

One of my main reasons for choosing Sweden was that during my visits here, I was always amazed by the openness of people to innovation and technological progress. I realized that I wanted to deepen my knowledge and experience in such an environment and found a master’s programme that perfectly matched my interests. I also wanted to broaden my horizons by experiencing a different culture, and the diversity of Sweden’s academic and working environments made me feel welcomed as an international student.

Why did you end up choosing Combine?

My primary goal when I started job-hunting was to find a great team of people with a shared sense of drive and purpose. Within a few minutes of meeting Benedikt (group manager for Data Science Solutions Gothenburg) and the rest of the team, I immediately felt that it would be a great cultural fit. I was also drawn to the ‘Enter the next level’ philosophy, which means that the technical problems Combine takes on are not only relevant but also interesting and important for progress in data science.

Which areas of Data Science interest you the most and why?

I have been fortunate enough to be involved in a diverse array of projects, from building speech-to-text engines using natural language processing to modelling water distribution networks using probabilistic graphs. This means that I usually look for the interesting problems rather than the ones that match a particular part of the data science toolkit. However, during my years of work and study, I worked deeply in natural language processing and also developed a strong research interest, as I helped to develop the initial framework for Swedish fake news detection with the Research Institutes of Sweden (RISE) for my master’s thesis project.

Can you tell us an interesting fact that not many people know about you?

Sure. I think people may notice a slight twang in my accent, and that’s because I went to high school in the island nation of Mauritius in the Indian Ocean, where I learned French and became a certified open water diver.

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Prediction of lithium-ion batteries complete lifetime

Combine is a co-founder of the company AiTree Technology AB. The vision is to provide a data-driven machine learning solution with the purpose to predict lithium-ion batteries (complete) lifetime from 1st life to end of life. The interest for our solution is immense, where we see both large, medium and small companies looking for a way to handle their batteries in a more efficient way.
Stay tuned for more information!

The IP of the tool “Sympathy for Data”

In April Combine acquired the Intellectual Property of the data science tool “Sympathy for Data”.
Our intention is to continue to license Sympathy as an open-source tool, where add-on products such as cloud services, cluster support, etc will be included in an enterprise license. The focus in now to develop functionality such as streaming support, cluster support, cloud services to further strengthen our ability to deliver kick-ass solutions to our customers.


I am glad to announce that we are moving ahead with the establishment of an office in Stockholm.
We have now signed the contract for the office at Dalagatan 7, close to the central station.
We have also signed our first two engineers in Stockholm. More information about this will follow after the summer.

Hardware In the Loop

Combine will together with a new partner develop and sell an off-the-shelf HIL solution.
All partners have the know-how and a strong network from previous work with vehicles, controls systems, and HIL solutions.
We aim to provide our customers with a more efficient, easily calibratable and plug-and-play solution that is built on open standards.

Ocean Data Factory

We are excited to announce that Combine will participate as AI experts in the collaborative work of building an Ocean Data Factory (ODF)!
ODF, which is a part of Vinnova’s investments to speed up development within AI, will be an arena to build competence and nurture innovation.
Data collected from the ocean poses challenges such as numerous data sources with varying characteristics and time scales, communication difficulties and harsh environment for the sensors which can lead to poor data quality. Overcoming these challenges using efficient AI will be vital for the future of the blue economy and sustainable ecosystems.

To summarize

The start of this year has been exciting with new initiatives that strengthen our position both as a specialist supplier but also as an innovative product development company. I believe that our investments will be fully up and running during this year, leading to more interesting opportunities in the future.

Now, I’m heading to Italy for some relaxation and vineyards.
Have a nice summer.

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One of the things that has been always drawing my attention is the automated
vehicular control strategies and how they could reshape the transport sector
dramatically. One of the methods that many automotive manufacturers have
been recently developing is what is called platooning. A platoon is a convoy of
trucks that maintains fixed inter-vehicular distances, as shown in the Figure 1,
and usually applied on highways.

Figure 1: Trucks Platoon

The advantages go beyond the driver’s convenience and comfort. Having a lead
truck with a large frontal-area would reduce the air drag force acting on the
succeeding vehicles. Therefore, the required torque to drive the trucks at cer-
tain speed will be decreased which lead to less fuel consumption. That means,
of course, less CO2 emissions and lower financial burdens.
However, in a single-vehicle level, there is another approach that has been inves-
tigated for a better fuel economy. This approach utilizes the future topography
information in order to optimize the speed and the gear for a vehicle travelling
in a hilly terrain by exploiting the vehicles’ potential and kinetic energies stor-
ages. In this approach the velocity will vary along the road depending on the
road gradient. The look-ahead strategy could be seen as a contradiction to the
platooning approach in which vehicles maintain almost the same speed along
the road.


A combination between these approaches could be implemented using the model
predictive control (MPC) scheme. Since there are many process constraints,
such as inter-vehicular distances, engine maximum torque, road velocity limits,
etc. MPC is a perfect candidate to handle these constraints especially that in
many cases the system will be operating close to the limits. The control design
could be handled in two approaches, the centralized control design and the
decoupled control design. In the centralized controller, as shown in the Figure
2, all the vehicles’ private data such as mass, engine specs, etc. in addition to
their states such as velocity and time headway are sent to the central predictive
controller via vehicle to vehicle communication, could be in one of the trucks
probably the lead vehicle or even in a cloud. One of the methods used for optimal
control is the convex quadratic programming problem (CQPP) in which every
local minimum is a global minimum. The problem is as follows

$$ min\,z = f_0(x) \\
f_i(x) \leq 0 \\
Ax = b $$

Where f0,f1,f2, …, fm, is the objective function, and the inequality constraints
are convex functions. However, the equality constraints are affine functions.
In the platoon case, some convexification is needed in order to get CQPP. Hense,
the problem is solved and the optimal speed and time headway references are
sent back to the vehicles’ local controllers. This approach optimizes the fuel
consumption for the whole platoon rather than individual vehicles in which the
group interest comes first. One of the drawbacks of this approach is that in order
to solve the problem you need to handle huge matrices since all the vehicles info
is handled at once. In other words, this approach is rather computationally

Figure 2: Centralized adaptive cruise control

The decoupled architecture, as depicted in the Figure 3, could be a solution for
the computation capacity issues. Instead of handling the quadratic program-
ming (QP) problem for the whole platoon, each vehicle considers itself, which is
why called greedy. The problem starts to be solved from the leading vehicle and
goes backwards. Each vehicle solves the QP, considering the gaps in front of the
vehicle and the road topography, and sends states to the succeeding vehicles.
The pros of this approach are that trucks need not to share their private data
and the matrices sizes are much smaller. So the computation time is less than in
the greedy control strategy but the solution is not as optimal as the centralized

Figure 3: Greedy approach


As it is mentioned above, formulating a convex quadratic programing problem
is used to get the fuel-saving velocities. Since the vehicle dynamics are quite
nonlinear, linear approximations are needed, therefore, finding an appropriate
velocity reference is essential, assuming that the vehicle will be driven close
to the reference. Finding such reference should consider many factors such as
maximum traction force along the road, road limits and the cruise speed set by
the driver. One of the other challenges is gear optimization which could be solved
using dynamic programming. The complexity of dynamic programing problem
increases exponentially with the rise of the vehicles number, as a result, the
problem become computationally demanding, therefore, it is not very reliable
for the real-time implementation.

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The simplest diagnostic example would basically consist of two sensors y and z, which are measuring the same unknown quantity x. When considering that the sensor-values could include errors, f1 and f2, the resulting system become:

y = x + f1                           (eq. 1)
z = x + f2                           (eq. 2)

As x is the only unknown variable, this system of equations is overdetermined.
This enables the construction of a residual, that is a connection between known quantities that are equal to zero in a fault free scenario. Residuals are usually denoted with r, which in this case results in the following residual:

r = z – y = f2 – f1

The residual r has the possibility of detecting the physical faults f1 and f2, but there is no way to determine which of the faults that has caused r to deviate from zero. The ability to pinpoint which fault has caused the deviation is known as the isolability of the system. By adding a third equation to the system, full isolability is achieved.

u = x + f3                           (eq. 3)

r = z- y = f2 –f1
r1 = y – u = f1 – f3
r2 = z – u = f2 – f3

It is however possible to create residuals through which all 3 faults are detectable by combining all three equations, e.g.

r3 = z – 0.5y -0.5u.

This residual does not contribute any additional information compared to the information already given by r, r1 and r2, which follows from which equations that were used to create each residual.

{E1, E2} resulting in r                   (set 1)
{E1, E3] resulting in r1                 (set 2)
{E2, E3} resulting in r2                 (set 3)
{E1, E2, E3} resulting in r3           (set 4)

What differs the top 3 sets from the bottom one is that the top three are what is called Minimal Structurally Overdetermined sets of equations, also known as MSOs. The minimal part corresponds to an MSO not being a subset to any other overdetermined set of equations. Set 2 is a subset of set 4 for instance, but not vice versa. The structural nature part of MSOs enables analysis of very complex systems as it only takes the existence of unknown variables and faults into account and not in what way these are included into the equation. For example, equation 1 would structurally be summarized as x and f1 exist. For a system of equations, this can be plotted by using a matrix, where each row corresponds to an equation, and each column represents existence or non-existence of faults or unknown variables. This is called the Dulmage-Mendelsohn decomposition.

For additional information regarding computing MSOs, see Fault Diagnosis Toolbox on github. One interesting application of residuals is model validation. This application is possible due to the fact that if a model is correct, the residual value is likely to be low and vice versa.  If a model has a low accuracy, it is often of interest to pinpoint the low accuracy to a particular subpart of the model, if it is possible. This can be achieved by letting the faults {f1, f2, f3} represent model equation errors {fe1, fe2, fe3} and then generate residuals based on MSOs.

By using as few equations as possible in each residual, maximum isolability regarding model inaccuracy can be achieved. One method used to convert residual-values to one metric (in order to compare the validity of different model equations) is to compute the mean-values for all residuals sensitive to a specific fault fex, and then multiply these means together to a single value R_fex. The absolute value of R_fex doesn’t provide much information, but by comparing R_fex to values generated through residuals that are sensitive to other faults (fey, fez,..) an indication of model accuracy is achieved.
R_fe1 > R_fe2 -> equation 1 is likely of lower accuracy then equation 2.

For further information and examples on bigger models see (Karin Lockowandt, 2017, p.30).

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ODF will be an arena to build competence and nurture innovation. It is open to all who believe that crunching data from the ocean is first of all fun, secondly, holds the answers to a sustainable blue economy and, thirdly, gets really productive when different competencies work together! Data collected from the ocean poses challenges such as numerous data sources with varying characteristics and time scales, communication difficulties and harsh environment for the sensors which can lead to poor data quality. Overcoming these challenges using efficient AI will be vital for the future of the blue economy and sustainable ecosystems.

ODF will be headed by Professor Robin Teigland from Chalmers University of Technology. SCOOT (Swedish Centre for Ocean Observing Technology) takes on the coordinating role. Stay tuned for more information in the future.

ODF is part of Vinnova’s investment to speed up development within AI.

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The issue of deep learning (DL) is a hot topic in modern society and is one of the most rapidly growing technical fields today. One of many subjects that could benefit from deep learning is control theory. Its nonlinearities enable implementation of a wider range of functions and adaptability to more complex systems. There has been significant progress in generating control policies in simulated environments using reinforcement learning. Algorithms are capable of solving complex physical control problems in continuous action spaces in a robust way. Even though the tasks are claimed to have real-world complexity it is hard to find an example of such high-level algorithms in an actual application. Moreover, we have found that in most applications in which these algorithms have been implemented, they have been trained on the hardware itself. This does not only enforce high demands on the hardware of the system but might be time-consuming or even practically infeasible for some systems. In these cases, a more efficient solution would be to train on a simulated system and transfer the algorithm to the real world. 

Furthermore, one might wonder if a traditional control method would perform better or worse on the same system. In order to recognize how well the deep learning algorithm is actually performing, it would be interesting to compare it to another method on a similar control level. 

The main purpose of this project was to provide an example of a fair comparison between a traditional control method and an algorithm based on DL, both run on a benchmark control problem. It should also demonstrate how algorithms developed in simulation can be transferred to a real physical system. 



Due to its unstable equilibrium point, the inverted pendulum setup is a commonly used benchmark in control theory. There can be found many variations of this system, all based on the same principal dynamics. An example of this is a unicycle which principal dynamics can be viewed as an inverted pendulum in two dimensions. Thus, as a platform to conduct our experiments, we constructed a unicycle. 

Figure 1: CAD model of the unicycle

Figure 1: CAD model of the unicycle



Our main focus for the design was to keep it as lightweight and simple as possible. To emphasise the low hardware requirements, we chose the low-cost ESP32 microcontroller to act as the brain of our system. On it, we implemented all sensor fusion and communication to surrounding electronics necessary to easily test the two control algorithms on hardware. We dedicated one core specifically for the two control algorithms and added a button to switch between the two algorithms with a simple press. 

To be used in simulation and control synthesis, we derived a nonlinear continuous-time mathematical model using Lagrangian dynamics. The unicycle is modelled as 3 parts, the wheel, the body and the reaction disk, including the inertia from all components in the hardware. It has 4 degrees of freedom; the spin of the wheel, the movement of the system, the pitch of the system and the rotation of the disk. The external forces on the system come from the disk and wheel motors. 


Controller Synthesis 

The infinite horizon linear quadratic regulator (LQR) is a model-based control problem which results in a state feedback controller. The feedback gain is determined offline by from an arbitrary initial state minimizing a weighted sequence of states and inputs over a time horizon that tends towards infinity. The LQR problem is one of the most commonly solved optimal control problems. As a mathematical model of the system is available and due to its characteristics, we implemented an LQR controller for this project. 

For our deep learning control of the unicycle, we chose proximal policy optimization (PPO). The method is built on a policy-based reinforcement learning which offers practical ways of dealing with continuous spaces and an infinite number of actions. The PPO has shown superiority in complex control tasks compared to other policy-based algorithms and is considered to be the state-of-the-art method for reinforced learning in continuous spaces. 

To make a long story short we trained the algorithm for the system by writing up the mathematical model of the unicycle in Python as an environment for the agent to train in. The actions the agent can take are the inputs to the two motors. After taking an action it moves to a new state and receives a reward. After some millions of iterations of taking actions and receiving rewards the agent eventually learns how to behave in this environment an creates a policy to stabilize the unicycle. 



Both methods successfully managed to stabilize the system. The LQR outperformed the PPO in most perspectives in which the hardware did not limit the control. As an example, in practice, the LQR managed to stabilize from a maximal pitch deviation of 28 degrees compared to the PPO method which managed 20 degrees. We observed this sub optimal behaviour of the PPO in several situations. Another example can be seen when applying an external impulse to the system. 

Figure 2

As can be seen, the LQR handles the impulse in a somewhat expected way while the PPO goes its own ways. 

This unexpected behaviour is not desirable for this system but we think it might be seen as beneficial for other systems. For example, systems with unspecified or even unknown optimal behaviour. However, for systems with a specified known optimal or expected behaviour, we would recommend the good old LQR, if applicable. 

Even when exposed to model errors, the PPO did not show any sign of unreliability compared to the LQR in states it had encountered during training. However, when introduced to unknown states, the performance of the PPO is impacted. By keeping the limits of the training environment general enough this should not be an issue. However, when dealing with systems with large or even unknown state limits, LQR is probably a safer option. 

We believe our project has shown a good and fair comparison between these two methods on the same system as well as has given a good and informative example of how a DL algorithm trained in simulation can be transferred to a real physical system. The unicycle is of course only an example of such a system, but we feel like we encountered a lot of interesting features that can be generalized and used to benefit other projects. If you have doubts, please read our report! 

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