# Category: Research

Earlier this month, ICRA 2022 was in held in Philadelphia and in person this time! Unfortunately we were unable to attend ourselves but quite happy that there were still virtual attendance options available. So I followed quite some presentations and read through papers, trying to find out the latest in Aerial and Swarm robotics and if anybody was able to use the Crazyflie to good use for their research. I even had the opportunity to attend the Exhibition floor with a telepresence robot, which was a lot of fun!

We have covered IROS 2021 end of last year, and we even have started to publish Crazyflie related publications on social media to keep ourselves and the community up to date with any Crazyflie research work. So here we will list the ICRA 2022 papers we have found and write some observations.

## Crazy Platforms

What I really noticed this year is that the Crazyflie has been used in more unconventional configurations and new platforms! IROS 2021 ready amazed us by a solar-powered Crazyflie and the 4 times Crazyflie combined quadcopter (which continued this conference by UCLA in (2). But we haven’t seen yet that a Crazyflie can jump! The PogoDrone by the Swarmslab of Lehigh university turned the Crazyflie into an autonomous jumping pogo stick (5)! Moreover, wheels were added by the Institute For Systems and Robotics (TU Lisbon) for increasing the flight/autonomy durability (7).

We also noticed 3 ICRA 2022 papers with Bolt-powered platforms, which is a huge increase compared to IROS 2021 which only had 1 Bolt entry. The MAVlab of the TU Delft compared the Crazyflie against a Bolt-powered Flapper-drone for flying against wind (see the presentation of Flapperdrone in our last MiniBam). Moreover, remember that saw the Science Robotics paper using a Crazyflie board for a dual wing rotating platform. The Engineering product development of SUTD took a similar design to the next level, building a single controllable rotating wing with a Bolt platform (3). Two of these can even work together cooperatively and fly stability, so it is no wonder that they won the ICRA 2022 Outstanding Dynamics and Control Paper Award.

## List of ICRA 2022 Papers featuring the Crazyflie and Bolt

Here is a list of all the Crazyflie/Bolt papers featured in ICRA 2022 but let us know if we are missing any (⚡: Bolt, 🐝: Crazyflie). Mind that only Robotic and Automation Letter entries have been officially published on IEEE Xplore already, so from the proceeding papers I tried to share the ArXiv paper if available.

1. ⚡ ‘Passive Wall Tracking for a Rotorcraft with Tilted and Ducted Propellers using Proximity Effects’ Ding et al. from City University of Hong Kong & Massachusetts Institute of Technology
2. 🐝 ‘A Fast and Efficient Attitude Control Algorithm of a Tilt-Rotor Aerial Platform Using Inputs Redundancies’ Su et al. from UCLA
3. ⚡x2 ‘Cooperative Modular Single Actuator Monocopters Capable of Controlled Passive Separation’, Cai et al. from Singapore University of Technology & Design
• ICRA 2022 Outstanding Dynamics and Control Paper Winner!
4. 🐝’Optimal Inverted Landing in a Small Aerial Robot with Varied Approach Velocities and Landing Gear Designs’ Habas et al. from Penn State
5. 🐝 ‘PogoDrone: Design, Model, and Control of a Jumping Quadrotor’, Zhu et al from Lehigh U.
6. 🐝 ‘Clustering and Informative Path Planning for 3D Gas Distribution Mapping: Algorithms and Performance Evaluation’, Ercolani et al from EPFL
7. 🐝 ‘A Bimodal Rolling-Flying Robot for Micro Level Inspection of Flat and Inclined Surfaces’ , Pimentel et al from Instituto Superior Tecnico
8. 🐝x 2 ‘Collision Avoidance for Multiple Quadrotors Using Elastic Safety Clearance Based Model Predictive Control’, Jin et al. from USTC & Sina
9. 🐝 + ⚡🦋 ‘An Experimental Study of Wind Resistance and Power Consumption in MAVs with a Low-Speed Multi-Fan Wind System’, Olejnik et al. from TU Delft
10. 🐝x 6 ‘Formation-containment tracking and scaling for multiple quadcopters with an application to choke-point navigation’, Su et al. from The University of Manchester.

Update

11. 🐝x 6 ‘Nearest-Neighbor-Based Collision Avoidance for Quadrotors Via Reinforcement Learning’, Ourari et al. from TU Darmstadt
ArXiv

## Other Announcements: Bolt 1.1 and Dev meeting

Bolt 1.1

The Bolt is now back in stock and with two small updates making it the Bolt 1.1. Here are the changes listed:

1. The board thickness has been reduced from 1.6mm to 1.0mm to save some weight, roughly 2 grams. This is handy for the slimmest and most lightweight designs.
2. Motor signal output M4 has been moved from PB9 to PB10 to be able to support the DSHOT motor signal protocol in the future.

Other then that it is fully backwards compatible but make sure to use a recent enough firmware (2022.03) that has the Bolt 1.1 device support added.

Time and Date for Dev Meeting

In this blogpost we noted that we wanted to organize our first Developer meeting before the summer break. From this poll we saw that most of you that want to attend are currently located in Asia and Australia, so that is why this time we want to organize the meeting at:

13:00 CEST (Sweden time) on Wednesday 22th of June.

The topic will be about our new support platform and support handling in general, so I’m hoping for some fruitful discussions about that. Keep an eye on this discussion thread for any details for joining.

If anybody noticed a delay of my response on emails, forum or Github, that might be due to the fact that I was on the road for Bitcraze for the last few weeks! I was invited to give a guest lecture for a course at EPFL, and of recent they have a CO2 reducing policy regarding travel. At Bitcraze we also aim for reducing our environmental impact, so hence the idea came forth to travel to Switzerland and visit our close collaborators that are nearby(ish)… all by train! Internally we dubbed this to be The Grand Tour.

## The Itinerary

We kept the itinerary mostly within Switzerland and Germany, although I did pass the Netherlands a few days just to visit family. The full itinerary by train was:

Utrecht (NL) -> Lausanne (SW) -> Zürich (SW) -> Munich (GE) -> Berlin (GE) -> Malmö (SE)

The longest train ride was from Utrecht to Lausanne (9 hours), but all the others were well under 4 hours which was pretty comfortable. The nice thing about being in the train is that it quite easy to work on your laptop (although the wireless network + onboard WiFi was still patchy). Luckily I was able to actually phone in for Bitcraze’s morning meetings so that I wouldn’t miss a thing.

Here are some pictures of the in-between travels, with the views, trains and food. It was all awesome, but if I do have to make a confession… the train rides through Switzerland was the most beautiful of all!

## The People

The first two days in Lausanne went quite smoothly. Dario Floreano of the Laboratory of Intelligent Systems (LIS) invited us to give a Crazyflie 101 lecture to the students of the Aerial Robotics course, for which we are very grateful for the opportunity. It was great to do the talk in person this time and visit the EPFL campus, since the last two years I’ve given the same lecture from my own kitchen. I was able to see the students trying to start up the course themselves, and actually got to experience how they would install the Crazyflie framework. Next to my lecture, I was given a very nice tour through the offices, laboratories and work-spaces, where I had the possibility see all the nature inspired drone designs of the LIS-lab. In the meantime I also squeezed in a quick but fun visit with Cyberbotics, the creator of Webots, to discuss our latest efforts for a crazyflie simulator.

After a beautiful train ride towards Zurich, I first met up with the people of the Automatic Control lab (ACL), who made a video about how they handled education with the Crazyflie during the harsher COVID times. Now I got a chance to see the flight room where students are able control their Crazyflie down to the rate attitude controller. Moreover, I was treated to a full workshop, hosted by ETH Zürich’s Integrated Systems Lab (IIS) and Center of Project Based learning (PBL), joined by researchers from ETHZ, University of Bologna and IDSIA (Lugano) working on the PULP platform and/or nano-drones. The workshop consisted of them and us showcasing our current work, future plans and they showed me very impressive demos with both the AIdeck and their own prototypes decks! Complete that with a lunch with one of the best views any campus has to offer, coffee break talks, and you have a very inspiring day.

The third part of the trip took place in Germany! My first stop was near Munich, namely Hochschule Augsburg, where I visited the Cooperative Control Lab lead by Klaus Kefferpütz where we had great discussions about collaborative swarms and state estimators. They showed their lab with demos, and we spoke about positioning systems and how to improve their development experience. They are currently integrating the Bolt with a Raspberry Pi with the latest functionalities we implemented into our firmware, which we can imagine is a very wanted feature by the community! I also had a brief visit at TU Munich as well to visit my friend Sophie Armanini from the eAviation and Sustainable Flight Group, and to my surprise I got to fly with a Crazyflie Bolt fueled Flapper drone!

As my final stop, I visited Wolfgang Hönig from the Intelligent Multi-Robot Coordination Lab (IMRC) at TU Berlin. Here we discussed all about Crazyswarm, simulations and firmware python bindings among many things. Also, we had a successful hackathon where we managed to generate python bindings of the Mellinger & PID controller and the motor mixing. On top of that, we managed to fly with the PID binding in the Webots simulator, which has been on the wish list for a little while now. It was great working together again in person after 1.5 years!

## The Insights

It was great to see all the different ways that our products are used and what matters to the community members were dealing with. I’ve visited labs that tweak the attitude rate controllers, trying to improve the quality of the state estimators, or experiment with the actual mechanics. However, it was clear to see that quite some were controlling the Crazyflies on a higher level of autonomy, either off-board or onboard. This is all spread out over education and research alike, so there is a very wide range of people that are working with the Crazyflie.

There is of course also a huge variety in their approach. Some used our internally development framework with the Cflib and cfclient, and I’ve generated quite some new Github tickets in those respective repositories based on the discussions I had. However, it was interesting to see that many have made their own clients to tailor more to their research and education objectives. Moreover, about half of the users I met used ROS to interact with the Crazyflies. Is it perhaps a sign that we should start to rethink the communication infrastructure and how it all fits together?

There was also quite the difference on how close these users were on our latest changes. It ranged from working on a branch forked 4 years ago to being on the very edge of the commits, which each have their pros and cons. Working on a stable branch that has been proven worthy might be beneficial with education classes, but also makes people miss out on new features like the new lighthouse integration. However, it is not all fine and dandy on the edge of development either, as I have heard of many having issues with the new kbuild intergration, installing the cfclient or our latest efforts of getting the AIdeck out of early access. That is something that these pioneers has to deal every time they merge the new master, so we need to find better ways to make it easier for them as well.

And last but not least, it seems that the simulation we have been working on has generated quite the buzz, as most of whom I spoke to were quite interested in it, or has used a different simulation for their purpose. It was clear that there is not yet a standard simulator for aerial robotics that can fulfill everybody’s requirements in terms of swarming, (vision-based) autonomy or control. Perhaps that is a good reason to promote the simulation work from Fun-Fridays to a regular day project and have some interesting future discussions with the community how to shape this to most of our needs.

## The Conclusion

All and all, those were very inspiring 2 weeks of travel for me. Even though physically I was a bit exhausted afterwards, mentally it was very motivating and inspiring! After two of the worst years of the pandemic it was great to talk to people in person and I really feel stronger connections with those I visited than the remote video calls we have done before. It is so important to stay in touch with the community in person, after so long time of absence, as we get a better sense of what the needs are and how people are using the Crazyflie and its ecosystem. The Grand Tour was according to us a great success, and who knows…. perhaps we will do an 2023 edition as well :)

Today we will have a guest blogpost by Dominik Natter, working in the Robotics & Control group at SINTEF in Trondheim, Norway. Enjoy!!

In this blogpost we will teach you how to fly the Crazyflie beyond edges without crashing, using only on-board sensors. Come join in!

## Introduction

UAVs have seen tremendous progress in the last decades and have since moved from research labs to various real-world environments. Small UAVs (so-called micro air vehicles, MAVs) like the Crazyflie open up even more possibilities. For example, their size allows them to traverse narrow passages or fly in cluttered environments (as recently showcased in this blog post). However, in order to achieve these complex tasks the community must further improve the cognitive ability of these MAVs in order to avoid crashes.

One task on this list and today’s topic is the possibility to fly at constant altitude irrespective of the terrain. This feature has been discussed in the community already two years ago. To understand the problem, let’s look at the currently implemented solution: With the Flow deck mounted the Crazyflie uses a 1D lidar sensor to estimate its vertical position. This vertical position (more or less) equals the current sensor reading. On flat floors this solution works very well. However, if the Crazyflie shall traverse through a narrow window or fly above irregular terrain its altitude will change based on the sensor readings. This can lead to unstable flights, as in the following video, or even crashes!

You might wonder: why not use any of the other great tools from the Bitcraze universe? Indeed, the Lighthouse positioning system and the Loco positioning system work well for absolute positioning (as we have seen earlier, e.g., in this blog post). However, the required setups are often not available in difficult environments. Alternatively, the barometer could be used to achieve a solution based solely on on-board sensors. In fact, Bitcraze has proposed an altitude hold functionality a few years ago. This is a cool feature, but its positioning accuracy of “roughly ±15cm” is not fully satisfying. Finally, relying on the on-board IMU alone will inevitably lead to drifting over time.

Thus, we propose a solution based on the Flow deck and the Multiranger deck. This approach, only based on on-board sensors, allows to fly at constant altitude with obstacles above, below, or even both above and below the Crazyflie. Kristoffer Skare developed this solution when he worked with us as an intern in 2021.

## Technical Description

As a first step, the upward-facing lidar of the Multiranger deck is incorporated in the same way the downward-facing lidar of the Flow deck is used in the firmware. This additional measurement can then be used in the extended Kalman filter (EKF) to improve the state estimation. Currently, the EKF estimates and outputs 1 value for the altitude. For our purpose two more states are added to the EKF: one state is defined as the height of the object under the Crazyflie compared to the height where the altitude state is defined as 0. Similarly, the other state is defined as the height of the object above the Crazyflie compared to the same reference height. The Crazyflie keeps therefore track of the environment in order to keep its own altitude constant. To achieve this, an edge detection was implemented: The errors between the predicted and measured distance are tracked in both the upward or downward range measurement. If either of these errors is too large the algorithm assumes that the floor or roof has changed (while the original EKF would think the drone’s position has changed, triggering a change in thrust). Thus, the corresponding state gets updated. For more details on the technical implementation and the code itself, check out our pull request.

## Results

To analyze our approach we have used a Qualisys motion capture system. We have conducted many different tests: flying over different obstacles, flying at different velocities, flying at different altitudes, or even flying under different lighting conditions. Exemplarily, in this post we will have a look at a baseline example, a good estimate, and a bad estimate. In each picture you can see the altitude (in meters) over time (in seconds) for different flight speeds (in centimeters per second). You will see three lines: The motion capture ground truth (blue), the altitude estimated by our code (orange), and the new state keeping track of the floor height (green). For each plot, the Crazyflie takes off, flies in positive x direction, and lands.

In the baseline experiment, it flies over a flat floor. Clearly, the altitude estimates follow the ground truth values well, and the floor is correctly estimated to be flat.

In the next example, we have added a box with an approximate height of 0.225 m and made the Crazyflie fly over it. Despite the obstacle the altitude estimates follow the ground truth values well. Note how the floor estimates indicates the shape of the box.

Because the algorithm is based on an edge detection, we had a hunch that smoothly changing obstacles will pose a problem. Indeed, the estimates can be messy as we see in the next example. Here, the Crazyflie flies over an orthogonal triangle, with the short leg at 0.23 m pointing upwards and the long leg with 0.65 m pointing in flight direction (thus forming a slope). For different flight speeds different the estimates turn out quite differently.

If you don’t like looking at plots, check out this video with some cool shots instead!

## Conclusion

To summarize, we propose a solution for constant altitude flight with Crazyflies, using the Flow deck and the Multiranger deck. We have tested it successfully under various circumstances. Still, we see some potential for improvement, e.g. when dealing with slopes. In addition, the current implementation is quite a change to the original EKF, which poses a problem for integration.

Thus, a way forward can be an out-of-tree build to ease the use of the solution for the community. At SINTEF we certainly plan to deploy this code in all of our tests in 2022, which will hopefully allow us to gather more experience and thus find further ways to improve or tune the system.

We want to emphasize that this is not a perfect solution. That means a) you should use it with care and b) you are very much welcomed to contribute. E.g. feel free to chime in in the pull request, test the code in your environments, propose improvements, or implement an out-of-tree build! :) Maybe you can even come up with an alternative approach for constant altitude flights?

If you want to check out more of our work, visit our website. Also, keep reading this amazing blog from Bitcraze as we try to be back some day (if Bitcraze wants us hehe)!

This week we have a guest blog post from Enrica Soria from the Laboratory of Intelligent Systems Faculty of Ecole Polytechnique Fédérale de Lausanne (EPFL) . Enjoy!

From Star Wars to Black Mirror, sci-fi movies predict a future where thousands of drones will fill our sky. Curving sharply around trees or soaring over buildings, they fly just like a flock of starlings. To turn this vision into a reality, real drone swarms need to increase their autonomy and operate in a decentralized fashion. In a decentralized swarm, each robot makes its own decision based only on local information. Decentralization not only allows the swarm to be more robust to the failure of single individuals, but also removes the dependency from a single computing unit, thus making the swarm more scalable in terms of size.

We at LIS (EPFL) have shown that predictive controllers can improve the safety of aerial swarms by predicting and optimizing the agents’ future behavior in an iterative process. However, the centralized nature of this method allowed us to only control five drones and prevented us from scaling up to a large number of drones. For this reason, we have worked on a novel decentralized and scalable swarm controller that allows the safe and cohesive flight of aerial swarms in cluttered environments. In our latest article, published in IEEE Robotics and Automation Letters (RA-L), we describe how we designed the controller, show its scalability in size, and demonstrate its robustness to noise. We studied the swarms’ performance and compared how it changes in two different environments: a forest and funnel-like environment.

The Crazyflie 2.1 was the perfect platform for our experiments. They are lightweight, modular, and tough. This quadcopter can survive big hits when things don’t go as planned… and, if you work on swarms, things can go wrong!

With our algorithm, sixteen robots were able to fly through an artificial forest that we set up in our indoor motion capture arena. In our previous work, we installed four markers on each quadcopter and used the rigid body tracking from Motive (the Optitrack software). The large volume of our experimental room required the usage of big markers for long-distance detection, which added considerable weight to the drone. Hence, in our new work, we use a single marker per drone. Tracking is supported by the ‘crazyswarm’ package and communication with the entire swarm only requires two radio links. However, despite our model being decentralized, in our implementation robots relay the information to an external brain, which does the computations for them. In the future, all the necessary code will be embedded onboard, removing the dependency on external infrastructure.

This work is a step forward towards the fully autonomous deployment of drone swarms in our cities. By enabling safe navigation in cluttered environments, drone fleets will be able to integrate with conventional air traffic, search for missing people, inspect dangerous areas, transport injured people to hospitals quicker, and deliver important packages right to our doors.

For further details, check out our article here!

Last week it was time for the International Conference on Intelligent Robots and Systems (IROS), which is one of the biggest yearly robotics conferences! In previous editions (see 2018 blog post, 2019 event page), we joined IROS’ exhibition and showed an autonomous demos for everybody to enjoy during the coffee breaks. Then… as everybody knows… the Covid-19 pandamic hit and we had to cancel our plans to go to the 2020’s Las Vegas edition. This year’s IROS was supposed to be held in Prague, but was very early announced that this was going to be an online edition.

Eventhough we considered joining IROS’s online exhibition, after our decision to organize the Bitcraze Awesome Meetup (BAM) days as a celebration to our 10 year anniversary (see this blo gpost), we wouldn’t have enough time to prepare for both. However, we still signed up for the conference itself, so we could see how and where the Crazyflie is used in the robotics community! So this blog post will give a list and small overview of the Crazyflie-fueled research with some highlights.

## Crazyflie as a Demonstration Tool in Research

A common use-case that we saw is to use the Crazyflie as a research demonstration tool. In the case of designing algorithms for quadcopters, many of the researchers we heard from or talked to told us that there is significant added value to demonstrate their ideas on a real platform. Then it can be truly evaluated with real environmental issues and platform dynamics. For this, the majority of the papers have used the ROS package developed for the CrazySwarm project but some researchers has gone as far as implementing it fully on the Crazyflie’s MCU [6, 8]!

We also noticed the large spread of the Crazyflie-featured papers throughout the sessions of the conference. A bunch of the papers could obviously be found in Aerial System sub-sessions as in ‘Perception and Autonomy’ [1], ‘Applications’ [3], ‘Mechanics and Control’ [4 , 5], but many were spread out in areas like Reinforcement Learning [2], Localization [6] and Collision avoidance [7]. There were also some papers to be found in the Swarm Robotics session [8, 9], as well as in Distributed Robot Systems [10].

Note that there is usually quite some overlap between the different sessions, but it is still very exciting to see that the Crazyflie being used in so many fields!

## Highlights and the Community

We saw lots of awesome applications but there are a few that we really like to highlight! There was a presentation of an actual solar-powered Crazyflie [2] which can literally fly forever. This research was done by the same group at the University of Washington that also was featured in a blog post last year, and who is responsible for the Smellicopter. Also, our jaw literally dropped at the sight of the 4 Crazyflie-fueled mega-copter by the University of California, Los Angeles [4, 5]. Last but not least, the fully onboard autonomous gas-seeking swarm, Sniffybug [8], from the MAVLab (TU Delft), never stops to amaze us. They wrote a blog post about their work on our website this summer!

We are hoping for more interesting blog posts related to the papers in the list below in the future. We also would like to invite all the researchers, who have been working with the Crazyflie, to join us for discussions at the Community Q&A at the BAMdays. Most of the amazing aspects of the Crazyflie in terms of autonomy, localization and swarming have all been contributions of the research community in the past. So join the discussion to continue that path in order to bring the Crazyflie to a new level!

## List of IROS 2021 Papers featuring the Crazyflie

Here is a list of all the Crazyflie-related papers we could find, but please let us know if we are missing any!

• [1] Target-Visible Polynomial Trajectory Generation within an MAV Team Yunwoo Lee, Jungwon Park, Boseong Jeon and H. Jin Kim
• Lab for Autonomous Robotic Research (LARR), Seoul National University
• Video
• [2] Inclined Quadrotor Landing using Deep Reinforcement Learning Jacob E. Kooi and Robert Babuska
• [3] Toward battery-free flight: Duty cycled recharging of small drones Nishant Elkunchwar, Suvesha Chandrasekaran, Vikram Iyer and Sawyer B. Fuller
• Department of Mechanical Engineering, University of Washington
• [4] An Over-Actuated Multi-Rotor Aerial Vehicle with Unconstrained Attitude Angles and High Thrust Efficiencies Pengkang Yu, Yao Su , Matthew J. Gerber, Lecheng Ruan and Tsu-Chin Tsao
• [5] Nullspace-Based Control Allocation of Overactuated UAV Platforms Yao Su, Pengkang Yu, Matthew J. Gerber, Lecheng Ruan and Tsu-Chin Tsao
• University of California, Los Angeles
• [6] A Computationally Efficient Moving Horizon Estimator for Ultra-Wideband Localization on Small Quadrotors Sven Pfeiffer, Christophe de Wagter and Guido C.H.E. de Croon
• MAVlab, Delft University of Technology
• Paper IEEExplore
• [7] A Scalable Distributed Collision Avoidance Scheme for Multi-agent UAV systems Bjorn Lindqvist, Pantelis Sopasakis and George Nikolakopoulos
• [8] Sniffy Bug: A Fully Autonomous Swarm of Gas-Seeking Nano Quadcopters in Cluttered Environments
• Bardienus P. Duisterhof Shushuai Li Javier Burgues, Vijay Janapa Reddi and Guido C.H.E. de Croon
• MAVlab, Delft University of Technology
• Video playlist
• ArXiv Preprint
• [9] micROS.BT: An Event-Driven Behavior Tree Framework for Swarm Robots Yunlong Wu, Jinghua Li, Huadong Dai, Xiaodong Yi, Yanzhen Wang and Xuejun Yang
• Artificial Intelligence Research Center, National Innovation Institute of Defense Technology, Beijing
• [10] Neural Tree Expansion for Multi-Robot Planning in Non-Cooperative Environments  Benjamin Riviere, Wolfgang Honig, Matthew Anderson and Soon-Jo Chung

Update 21-10-6

• [11] Trust your supervisor: quadrotor obstacle avoidance using controlled invariant sets Luigi Pannocchi, Tzanis Anevlavis, Paulo Tabuada
• University of California, Los Angeles
• [12] Continuous-time Gaussian Process Trajectory Generation for Multi-robot Formation via Probabilistic Inference Shuang Guo , Bo Liu , Shen Zhan , Jifeng Guo and Changhong Wang
• Harbin institute of Technology
• [13] Non-Prehensile Manipulation of Cuboid Objects Using a Catenary Robot Gustavo A. Cardona , Diego S. D’Antonio , Cristian-Ioan Vasile and David Saldana
• Lehigh University

This week we have a guest blog post from Bart Duisterhof and Prof. Guido de Croon from the MAVlab, Faculty of Aerospace Engineering from the Delft University of Technology. Enjoy!

Tiny drones are ideal candidates for fully autonomous jobs that are too dangerous or time-consuming for humans. A commonly shared dream would be to have swarms of such drones help in search-and-rescue scenarios, for instance to localize gas leaks without endangering human lives. Drones like the CrazyFlie are ideal for such tasks, since they are small enough to navigate in narrow spaces, safe, agile, and very inexpensive. However, their small footprint also makes the design of an autonomous swarm extremely challenging, both from a software and hardware perspective.

From a software perspective, it is really challenging to come up with an algorithm capable of autonomous and collaborative navigation within such tight resource constraints. State-of-the-art solutions like SLAM require too much memory and processing power. A promising line of work is to use bug algorithms [1], which can be implemented as computationally efficient finite state machines (FSMs), and can navigate around obstacles without requiring a map.

A downside of using FSMs is that the resulting behavior can be very sensitive to their hyperparameters, and therefore may not generalize outside of the tested environments. This is especially true for the problem of gas source localization (GSL), as wind conditions and obstacle configurations drastically change the problem. In this blog post, we show how we tackled the complex problem of swarm GSL in cluttered environments by using a simple bug algorithm with evolved parameters, and then tested it onboard a fully autonomous swarm of CrazyFlies. We will focus on the problems that were encountered along the way, and the design choices we made as a result. At the end of this post, we will also add a short discussion about the future of nano drones.

Why gas source localization?

Overall we are interested in finding novel ways to enable autonomy on constrained devices, like CrazyFlies. Two years ago, we showed that a swarm of CrazyFlie drones was able to explore unknown, cluttered environments and come back to the base station. Since then, we have been working on an even more complex task: using such a swarm for Gas Source Localization (GSL).

There has been a lot of research focussing on autonomous GSL in robotics, since it is an important but very hard problem. The difficulty of the task comes from the complexity of how odor can spread in an environment. In an empty room without wind, a gas will slowly diffuse from the source. This can allow a robot to find it by moving up gradient, just like small bacteria like E. Coli do. However, if the environment becomes larger with many obstacles and walls, and wind comes into play, the spreading of gas is much less regular. Large parts of the environment may have no gas or wind at all, while at the same time there may be pockets of gas away from the source. Moreover, chemical sensors for robots are much less capable than the smelling organs of animals. Available chemical sensors for robots are typically less sensitive, noisier, and much slower.

Due to these difficulties, most work in the GSL field has focused on a single robot that has to find a gas source in environments that are relatively small and without obstacles. Relatively recently, there have been studies in which groups of robots solve this task in a collaborative fashion, for example with Particle Swarm Optimization (PSO). This allows robots to find the source and escape local maxima when present. Until now this concept has been shown in simulation [2] and on large outdoor drones equipped with LiDAR and GPS [3], but never before on tiny drones in complex, GPS-denied, indoor environments.

Required Infrastructure

In our project, we introduce a new bug algorithm, Sniffy Bug, which uses PSO for gas source localization. In order to tune the FSM of Sniffy Bug, we used an artificial evolution. For time reasons, evolution typically takes place in simulation. However, early in the project, we realized that this would be a challenge, as no end-to-end gas modeling pipeline existed yet. It is important to have an easy-to-use pipeline that does not require any aerodynamics domain knowledge, such that as many researchers as possible can generate environments to test their algorithms. It would also make it easier to compare contributions and to better understand in which conditions certain algorithms work or don’t work. The GADEN ROS package [4] is a great open-source tool for modeling gas distribution when you have an environment and flow field, but for our objective, we needed a fully automated tool that could generate a great variety of random environments on-demand with just a few parameters. Below is an overview of our simulation pipeline: AutoGDM.

First, we use a procedural environment generator proposed in [5] to generate random walls and obstacles inside of the environment. An important next step is to generate a 3D flowfield by means of computational fluid dynamics (CFD). A hard requirement for us was that AutoGDM needed to be free to use, so we chose to use the open-source CFD tool OpenFOAM. It’s used for cutting-edge aerodynamics research, and also the tool suggested by the authors of GADEN. Usually, using OpenFOAM isn’t trivial, as a large number of parameters need to be selected that require field expertise, resulting in a complicated process. Next, we integrate GADEN into our pipeline, to go from environment definition (CAD files) and a flow field to a gas concentration field. Other parts that needed to be automated were the random selection of boundary conditions, which has a large impact on the actual flow field, and source placement, which has an equally large impact on the concentration field.

After we built this pipeline, we started looking for a robot simulator to couple it to. Since we weren’t planning on using a camera, our main requirement was for the simulator to be efficient (preferably in 2D) so that evolutions would take relatively little time. We decided to use Swarmulator [6], a lightweight C++ robot simulator designed for swarming and we plugged in our gas data.

Algorithm Design

Roughly speaking, we considered two categories of algorithms for controlling the drones: 1) a neural network, and 2) an FSM that included PSO, with evolved parameters. Since we used a tiny neural network for light seeking with a CrazyFlie in our previous work, we first evolved neural networks in simulation. One of the first experiments is shown below.

While it worked pretty well in simple environments with few obstacles, it seemed challenging to make this work in real life with complex obstacles and multiple agents that need to collaborate. Given the time constraints of the project, we have opted for evolving the FSM. This also facilitated crossing the reality gap, as the simulated evolution could build on basic behaviors that we developed and validated on the real platform, including obstacle avoidance with four tiny laser rangers, while communicating with and avoiding other drones. An additional advantage of PSO with respect to the reality gap is that it only needs gas concentration and no gradient of the gas concentration or wind direction (which many algorithms in literature use). On a real robot at this scale, estimating the gas concentration gradient or the direction of a light breeze is hard if not impossible.

Hardware

Our CrazyFlie needs to be able to avoid obstacles, execute velocity commands, sense gas, and estimate the other agent’s position in its own frame. For navigation, we added the flow deck and laser rangers, whereas for gas sensing we used a TGS8100 gas sensor that was used on a CrazyFlie before in previous work [7]. The sensor is lightweight and inexpensive, but accurately estimating gas concentrations can be difficult because of its size. It tends to drift and needs time to recover after a spike in concentration is observed. Another thing we noticed is that it is possible to break them, a crash can definitely destroy the sensor.

To estimate the relative position between agents, we use a Decawave Ultra-Wideband (UWB) module and communicate states, as proposed in [8]. We also use the UWB module to communicate gas information between agents and collaboratively seek the source. The complete configuration is visible below.

Evaluation in Simulation

After we optimized the parameters of our model using Swarmulator and AutoGDM, and of course trying many different versions of our algorithm, we ended up with the final Sniffy Bug algorithm. Below is a video that shows evolved Sniffy Bug evaluated in six different environments. The red dots are an agent’s personal target waypoint, whereas the yellow dot is the best-known position for the swarm.

Simulation showed that Sniffy Bug is effective at locating the gas source in randomly generated environments. The drones successfully collaborate by means of PSO.

Real Flight Testing

After observing Sniffy Bug in simulation we were optimistic, but unsure about performance in real life. First, inspired by previous works, we disperse alcohol through the air by placing liquid alcohol into a can which is then dispersed using a computer fan.

We test Sniffy Bug in our flight arena of size 10 x 10 meters with large obstacles that are shaped like walls and orange poles. The image below shows four flight tests of Sniffy Bug in cluttered environments, flying fully autonomously, i.e., without the help from any external infrastructure.

In the total of 24 runs we executed, we compared Sniffy Bug with manually selected and evolved parameters. The figure below shows that the evolved parameters are more efficient in locating the source as compared to the manual parameters.

This does not only show that our system can successfully locate a gas source in challenging environments, but it also demonstrates the usefulness of the simulation pipeline. The parameters that were learned in simulation yield a high-performance model, validating the environment generation, randomization, and gas modeling parts of our pipeline.

Conclusion and Discussion

With this work, we believe we have made an important step towards swarms of gas-seeking drones. The proposed solution is shown to work in real flight tests with obstacles, and without any external systems to help in localization or communication. We believe this methodology can be extended to larger environments or even to 3 dimensions, since PSO is a robust, multi-dimensional heuristic search method. Moreover, we hope that AutoGDM will help the community to better compare gas seeking algorithms, and to more easily learn parameters or models in simulation, and deploy them in the real world.

To improve Sniffy Bug’s performance, adding more laser rangers will definitely help. When working with only four laser rangers you realize how little information it actually provides. If one of the rangers senses a low value it is unclear if a slim pole or a massive wall is detected, adding inefficiency to the algorithm. Adding more laser rangers or using other sensor modalities like vision will help to avoid also more complex obstacles than walls and poles in a reliable manner.

Another interesting discussion can be held on the hardware required for real deployment. When working with 40 grams of maximum take-off weight, the sensors and actuators that can be selected are limited. For example, the low-power and lightweight flow deck works great but fails in low-light scenarios or with smoke. Future work exploring novel sensors for highly constrained nano robots could really help increase the Technological Readiness Level (TRL) of these systems.

Finally, this has been a really fun project to work on for us and we can’t wait to hear your thoughts on Sniffy Bug!

References

Video:

Please reach out if you have any questions or ideas, you can reach us at: b.p.duisterhof@gmail.com or g.c.h.e.decroon@tudelft.nl

This week we have a guest blog post from Dr Feng Shan at School of Computer Science and Engineering
Southeast University, China. Enjoy!

It is possible to utilize tens and thousands of Crazyflies to form a swarm to complete complicated cooperative tasks, such as searching and mapping. These Crazyflies are in short distance to each other and may move dynamically, so we study the dynamic and dense swarms. The ultra-wideband (UWB) technology is proposed to serve as the fundamental technique for both networking and localization, because UWB is so time sensitive that an accurate distance can be calculated using the transmission and receive timestamps of data packets. We have therefore designed a UWB Swarm Ranging Protocol with key features: simple yet efficient, adaptive and robust, scalable and supportive. It is implemented on Crazyflie 2.1 with onboard UWB wireless transceiver chips DW1000.

## The Basic Idea

The basic idea of the swarm ranging protocol was inspired by Double Sided-Two Way Ranging (DS-TWR), as shown below.

There are four types of message in DS-TWR, i.e., poll, response, final and report message, exchanging between the two sides, A and B. We define their transmission and receive timestamps are Tp, Rp, Tr, Rr, Tf, and Rf, respectively. We define the reply and round time duration for the two sides as follows.

Let tp be the time of flight (ToF), namely radio signal propagation time. ToF can be calculated as Eq. (2).

Then, the distance can be estimated by the ToF.

In our proposed Swarm Ranging Protocol, instead of four types of messages, we use only one type of message, which we call the ranging message.

Three sides A, B and C take turns to transmit six messages, namely A1, B1, C1, A2, B2, and C2. Each message can be received by the other two sides because of the broadcast nature of wireless communication. Then every message generates three timestamps, i.e., one transmission and two receive timestamps, as shown in Fig.3(a). We can see that each pair has two rounds of message exchange as shown in Fig.3(b). Hence, there are sufficient timestamps to calculate the ToF for each pair, that means all three pairs can be ranged with each side transmitting only two messages. This observation inspires us to design our ranging protocol.

## Protocol Design

The formal definition of the i-th ranging message that broadcasted by Crazyflie X is as follows.

Xi is the message identification, e.g., sender and sequence number; Txi-1 is the transmission timestamp of Xi-1, i.e., the last sent message; RxM is the set of receive timestamps and their message identification, e.g., RxM = {(A2, RA2), (B2, RB2)}; v is the velocity of X when it generates message Xi.

As mentioned above, six timestamps (Tp, Rp, Tr, Rr, Tf, Rf,) are needed to calculate the ToF. Therefore, for each neighbor, an additional data structure is designed to store these timestamps which we named it the ranging table, as shown in Fig.4. Each device maintains one ranging table for each known neighbor to store the timestamps required for ranging.

Let’s focus on a simple scenario where there are a number of Crazyflies, A, B, C, etc, in a short distance. Each one of them transmit a message that can be heard by all others, and they broadcast ranging messages at the same pace. As a result, between any two consecutive message transmission, a Crazyflie can hear messages from all others. The message exchange between A and Y is as follows.

The following steps show how the ranging messages are generated and the ranging tables are updated to correctly compute the distance between A and Y.

The message exchange between A and Y could be also A and B, A and C, etc, because they are equal, that’s means A could perform the ranging process above with all of it’s neighbors at the same time.

To handle dense and dynamic swarm, we improved the data structure of ranging table.

There are three new notations P, tn, ts, denoting the newest ranging period, the next (expected) delivery time and the expiration time, respectively.

For any Crazyflie, we allow it to have different ranging period for different neighbors, instead of setting a constant period for all neighbors. So, not all neighbors’ timestamps are required to be carried in every ranging message, e.g., the receive timestamp to a far apart and motionless neighbor is required less often. tn is used to measure the priority of neighbors. Also, when a neighbor is not heard for a certain duration, we set it as expired and will remove its ranging table.

If you are interested in our protocol, you can find much more details in our paper, that has just been published on IEEE International Conference on Computer Communications (INFOCOM) 2021. Please refer the links at the bottom of this article for our paper.

## Implementation

We have implemented our swarm ranging protocol for Crazyflie and it is now open-source. Note that we have also implemented the Optimized Link State Routing (OLSR) protocol, and the ranging messages are one of the OLSR messages type. So the “Timestamp Message” in the source file is the ranging message introduced in this article.

The procedure that handles the ranging messages is triggered by the hardware interruption of DW1000. During such procedure, timestamps in ranging tables are updated accordingly. Once a neighbor’s ranging table is complete, the distance is calculated and then the ranging table is rearranged.

All our codes are stored in the folder crazyflie-firmware/src/deck/drivers/src/swarming.

The following figure is a ranging performance comparison between our ranging protocol and token-ring based TWR protocol. It’s clear that our protocol handles the large number of drones smoothly.

We also conduct a collision avoidance experiment to test the real time ranging accuracy. In this experiment, 8 Crazyflie drones hover at the height 70cm in a compact area less than 3m by 3m. While a ninth Crazyflie drone is manually controlled to fly into this area. Thanks to the swarm ranging protocol, a drone detects the coming drone by ranging distance, and lower its height to avoid collision once the distance is small than a threshold, 30cm.

## Build & Run

Clone our repository

git clone --recursive https://github.com/SEU-NetSI/crazyflie-firmware.git

Go to the swarming folder.

cd crazyflie-firmware/src/deck/drivers/src/swarming

Then build the firmware.

make clean
make

Flash the cf2.bin.

cfloader flash path/to/cf2.bin stm32-fw

Open the client, connect to one of the drones and add log variables. (We use radio channel as the address of the drone) Our swarm ranging protocol allows the drones to ranging with multiple targets at the same time. The following shows that our swarm ranging protocol works very efficiently.

## Summary

We designed a ranging protocol specially for dense and dynamic swarms. Only a single type of message is used in our protocol which is broadcasted periodically. Timestamps are carried by this message so that the distance can be calculated. Also, we implemented our proposed ranging protocol on Crazyflie drones. Experiment shows that our protocol works very efficiently.

Our research group websitehttps://seu-netsi.net

Feng Shan, Jiaxin Zeng, Zengbao Li, Junzhou Luo and Weiwei Wu, “Ultra-Wideband Swarm Ranging,” IEEE INFOCOM 2021, Virtual Conference, May 10-13, 2021.

This week we have a guest blog post from Wenda Zhao, Ph.D. candidate at the Dynamic System Lab (with Prof. Angela Schoellig), University of Toronto Institute for Aerospace Studies (UTIAS). Enjoy!

Accurate indoor localization is a crucial enabling capability for indoor robotics. Small and computationally-constrained indoor mobile robots have led researchers to pursue localization methods leveraging low-power and lightweight sensors. Ultra-wideband (UWB) technology, in particular, has been shown to provide sub-meter accurate, high-frequency, obstacle-penetrating ranging measurements that are robust to radio-frequency interference, using tiny integrated circuits. UWB chips have already been included in the latest generations of smartphones (iPhone 12, Samsung Galaxy S21, etc.) with the expectation that they will support faster data transfer and accurate indoor positioning, even in cluttered environments.

In our lab, we show that a Crazyflie nano-quadcopter can stably fly through a cardboard tunnel with only an IMU and UWB tag, from Bitcraze’s Loco Positioning System (LPS), for state estimation. However, it is challenging to achieve a reliable localization performance as we show above. Many factors can reduce the accuracy and reliability of UWB localization, for either two-way ranging (TWR) or time-difference-of-arrival (TDOA) measurements. Non-line-of-sight (NLOS) and multi-path radio propagation can lead to erroneous, spurious measurements (so-called outliers). Even line-of-sight (LOS) UWB measurements exhibit error patterns (i.e., bias), which are typically caused by the UWB antenna’s radiation characteristics. In our recent work, we present an M-estimation-based robust Kalman filter to reduce the influence of outliers and achieve robust UWB localization. We contributed an implementation of the robust Kalman filter for both TWR and TDOA (PR #707 and #745) to Bitcraze’s crazyflie-firmware open-source project.

## Methodology

The conventional Kalman filter, a primary sensor fusion mechanism, is sensitive to measurement outliers due to its minimum mean-square-error (MMSE) criterion. To achieve robust estimation, it is critical to properly handle measurement outliers. We implement a robust M-estimation method to address this problem. Instead of using a least-squares, maximum-likelihood cost function, we use a robust cost function to downweigh the influence of outlier measurements [1]. Compared to Random Sample Consensus (RANSAC) approaches, our method can handle sparse UWB measurements, which are often a challenge for RANSAC.

From the Bayesian maximum-a-posteriori perspective, the Kalman filter state estimation framework can be derived by solving the following minimization problem:

Therein, xk and yk are the system state and measurements at timestep k. Pk and Rk denote the prior covariance and measurement covariance, respectively.  The prior and posteriori estimates are denoted as xk check and xk hat and the measurement function without noise is indicated as g(xk,0). Through Cholesky factorization of Pk and Rk, the original optimization problem is equivalent to

where ex,k,i and ey,k,j are the elements of ex,k and ey,k. To reduce the influence of outliers, we incorporate a robust cost function into the Kalman filter framework as follows:

where rho() could be any robust function (G-M, SC-DCS, Huber, Cauchy, etc.[2]).

By introducing a weight function for the process and measurement uncertainties—with e as input—we can translate the optimization problem into an Iteratively Reweighted Least Squares (IRLS) problem. Then, the optimal posteriori estimate can be computed through iteratively solving the least-squares problem using the robust weights computed from the previous solution. In our implementation, we use the G-M robust cost function and the maximum iteration is set to be two for computational reasons. For further details about the robust Kalman filter, readers are referred to our ICRA/RA-L paper and the onboard firmware (mm_tdoa_robust.c and mm_distance_robust.c).

## Performance

We demonstrate the effectiveness of the robust Kalman filter on-board a Crazyflie 2.1. The Crazyflie is equipped with an IMU and an LPS UWB tag (in TDOA2 mode). With the conventional onboard extended Kalman filter, the drone is affected by measurement outliers and jumps around significantly while trying to hover. In contrast, with the robust Kalman filter, the drone shows a more reliable localization performance.

The robust Kalman filter implementations for UWB TWR and TDOA localization have been included in the crazyflie-firmware master branch as of March 2021 (2021.03 release). This functionality can be turned on by setting a parameter (robustTwr or robustTdoa) in estimator_kalman.c. We encourage LPS users to check out this new functionality.

As we mentioned above, off-the-shelf, low-cost UWB modules also exhibit distinctive and reproducible bias patterns. In our recent work, we devised experiments using the LPS UWB modules and showed that the systematic biases have a strong relationship with the pose of the tag and the anchors as they result from the UWB radio doughnut-shaped antenna pattern. A pre-trained neural network is used to approximate the systematic biases. By combining bias compensation with the robust Kalman filter, we obtain a lightweight, learning-enhanced localization framework that achieves accurate and reliable UWB indoor positioning. We show that our approach runs in real-time and in closed-loop on-board a Crazyflie nano-quadcopter yielding enhanced localization performance for autonomous trajectory tracking. The dataset for the systematic biases in UWB TDOA measurements is available on our Open-source Code & Dataset webpage. We are also currently working on a more comprehensive dataset with IMU, UWB, and optical flow measurements and again based on the Crazyflie platform. So stay tuned!

## Reference

[1] L. Chang, K. Li, and B. Hu, “Huber’s M-estimation-based process uncertainty robust filter for integrated INS/GPS,” IEEE Sensors Journal, 2015, vol. 15, no. 6, pp. 3367–3374.

[2] K. MacTavish and T. D. Barfoot, “At all costs: A comparison of robust cost functions for camera correspondence outliers,” in IEEE Conference on Computer and Robot Vision (CRV). 2015, pp. 62–69.

The authors are with the Dynamic Systems Lab, Institute for Aerospace Studies, University of Toronto, Canada, and affiliated with the Vector Institute for Artificial intelligence in Toronto.

Feel free to contact us if you have any questions or suggestions: wenda.zhao@robotics.utias.utoronto.ca.

<code>@ARTICLE{Zhao2021Learningbased,
author={W. {Zhao} and J. {Panerati} and A. P. {Schoellig}},
title={Learning-based Bias Correction for Time Difference of Arrival Ultra-wideband Localization of Resource-constrained Mobile Robots},
journal={IEEE Robotics and Automation Letters},
volume={6},
number={2},
pages={3639-3646},
year={2021},
publisher={IEEE}
doi={10.1109/LRA.2021.3064199}}
</code>

Hi!

Since the middle of January, Bitcraze has had two additional guests: us! We, Josefine & Max, are currently doing our master thesis at Bitcraze during our final semester at LTH.

Unfortunately, the pandemic means remote working which could have caused some difficulties with hardware and equipment accessibility. Fortunately, for us, our goal with the thesis is to emulate the Crazyflie 2.1 hardware in the open source software Renode. We can therefore do the work at home.

Since this is the first time either of us have tried to emulate hardware it is exciting to see if it will even be possible, especially as we do not know what limitations Renode might have. Thus far, four weeks in, there have been some hiccups and crashes but also progress and success. One example was when we got the USART up and running and it became possible to start printing debug messages and another was when the LED lights were connected and it was possible to see when they were turned on and off.

If all goes well, the emulated hardware could be used as a part of the CI pipeline to automatically hunt for bugs. Academically, it would be used to further study testing methods of control firmware.

Getting a glimpse into the workings at Bitcraze and the lovely people working here has been most interesting and we are looking forward to the time ahead. Until next time, hopefully with a working emulation, Josefine & Max.

This week we have a guest blog post from Bárbara Barros Carlos, PhD candidate at DIAG Robotics Lab. Enjoy!

Quadrotors are characterized by their underactuation, nonlinearities, bounded inputs, and, in some cases, communication time-delays. The development of their maneuvering capability poses some challenges that cover dynamics modeling, state estimation, trajectory generation, and control. The latter, in particular, must be able to exploit the system’s nonlinear dynamics to generate complex motions. However, the presence of communication time-delay is known to highly degrade control performance.

In our recent work, we present an efficient position control architecture based on real-time nonlinear model predictive control (NMPC) with time-delay compensation for quadrotors. Given the current measurement, the state is predicted over the delay time interval using an integrator and then passed to the NMPC, which takes into account the input bounds. We demonstrate the capabilities of our architecture using the Crazyflie 2.1 nano-quadrotor.

## Time-Delay Compensation

In our aerial system, because of the radio communication latency, we have delays both in receiving measurements and sending control inputs. Likewise, since we intend to use NMPC, the potentially high computational burden associated with its solution becomes an element that must also be taken into account to minimize the error in the state prediction.

To tackle this issue, we use a state predictor based on the round-trip time (RTT) associated with the sum of network latencies as a delay compensator. The prediction is computed by performing forward iterations of the system dynamic model, starting from the current measured state and over the RTT, through an explicit Runge Kutta 4th order (ERK4) integrator. Due to the independent nature of this operation, perfect delay compensation can be achieved by adjusting the integration step to be equal to the RTT. Thus, it is assumed that there is a fixed RTT, defined by τr, to be compensated.

## Nonlinear Model Predictive Control

The NMPC controller is defined as the following constrained nonlinear program (NLP):

Therein, p denotes the inertial position, q the attitude in unit quaternions, vb the linear velocity expressed in the body frame, ω the angular rate, and Ωi the rotational speed of the ith propeller. The NLP is tailored to the Crazyflie 2.1 and is implemented using the high-performance software package acados, which solves optimal control problems and implements a real-time iteration (RTI) variant of a sequential quadratic programming (SQP) scheme with Gauss-Newton Hessian approximation. The quadratic subproblems (QP) arising in the SQP scheme are solved with HPIPM, an interior-point method solver, built on top of the linear algebra library BLASFEO, finely tuned for multiple CPU architectures. We use a recently proposed Hessian condensing algorithm particularly suitable for partial condensing to further speed-up solution times.

When designing an NMPC, choosing the horizon length has profound implications for computational burden and tracking performance. For the former, the longer the horizon, the higher the computational burden. As for the latter, in principle, a long prediction horizon tends to improve the overall performance of the controller. In order to select this parameter and achieve a trade-off between performance and computational burden, we implemented the NLP in acados considering: five horizon lengths (N = {10,20,30,40,50}), input bounds on the rotational speed of the propellers (lower bound = 0, upper bound = 22 krpm), discretizing the dynamics using an ERK4 integration scheme. Likewise, we compare the condensing approach with the state-of-the-art solver qpOASES against the partial condensing approach with HPIPM, concerning the set of horizons regarded.

As qpOASES is a solver based on active-set method, it requires condensing to be computationally efficient. In line with the observations found in the literature that condensing is effective for short to medium horizon lengths, we note that qpOASES is competitive for horizons up to approximately N = 30 when compared to HPIPM. The break-even point moves higher on the scale for longer horizons, mainly due to efficient software implementations that cover: (a) Hessian condensing procedure tailored for partial condensing, (b) structure-exploiting QP solver based on novel Riccati recursion, (c) hardware-tailored linear algebra library. Therefore, we chose horizon N = 50 as it offers a reasonable trade-off between deviation from the reference trajectory and computational burden.

## Onboard Controller Considerations

How the onboard controllers (PIDs) use the setpoints of the offboard controller (NMPC) in our architecture is not entirely conventional and, thereby, deserves some considerations. First, the reference signals that the PID loops track do not fully correspond to the control inputs considered in the NMPC formulation. Instead, part of the state solution is used in conjunction with the control inputs to reconstruct the actual input commands passed as a setpoint to the Crazyflie. Second, a part of the reconstructed input commands is sent as a setpoint to the outer loop (attitude controller), and the other part is sent to the inner loop (rate controller). Furthermore, as the NMPC model does not include the PID loops, it does not truly represent the real system, even in the case of perfect knowledge of the physical parameters. As a consequence, the optimal feedback policy is distorted in the real system by the PIDs.

## Closed-loop Position Control Performance

Our control architecture hinges upon a ROS Kinetic framework and runs at 66.67 Hz. The Crazy RealTime Protocol (CRTP) is used in combination with our crazyflie_nmpc stack to stream in runtime custom packages containing the required data to reconstruct the part of the measurement vector that depends on the IMU data. Likewise, the cortex_ros bridge streams the 3D global position of the Crazyflie, which is then passed through a second-order, discrete-time Butterworth filter to estimate the linear velocities.

To validate the effectiveness of our control architecture, we ran two experiments. For each experiment, we generate a reference trajectory on a base computer and pass it to our NMPC ROS node every τs = 15 ms. When generating the trajectories, we explicitly address the feasibility issue in the design process, creating two references: one feasible and one infeasible. In addressing this issue, we prove through experiments that the performance of the proposed NMPC is not degraded even when the nano-quadrotor attempts to track an infeasible trajectory, which could, in principle, make it deviate significantly or even crash.

Overall, we observe that the most challenging setpoints to be tracked are the positions in which, given a change in the motion, the Crazyflie has to pitch/roll in the opposite direction quickly. These are the setpoints where the distortion has the greatest influence on the system, causing small overshoots in position. The average solution time of the tailored RTI scheme using acados was obtained on an Intel Core i5-8250U @ 3.4 GHz running Ubuntu and is about 7.4 ms. This result shows the efficiency of the proposed scheme.

## Outlook

In this work, we presented the design and implementation of a novel position controller based on nonlinear model predictive control for quadrotors. The control architecture incorporates a predictor as a delay compensator for granting a delay-free model in the NMPC formulation, which in turn enforces bounds on the actuators. To validate our architecture, we implemented it on the Crazyflie 2.1 nano-quadrotor. The experiments demonstrate that the efficient RTI-based scheme, exploiting the full nonlinear model, achieves a high-accuracy tracking performance and is fast enough for real-time deployment.