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This is incredible.

I've wanted to thank the author for a while for his past articles [1][2] which have been a wonderful source of information when working on my sonar systems [3]. This article again explains really well a complicated topic. Please, keep up the great work!

[1]: https://hforsten.com/radar-phase-measurements.html

[2]: https://hforsten.com/6-ghz-frequency-modulated-radar.html

[3]: https://twitter.com/alextoussss/status/1756371553460121766


I tried to use SymPy for a similar problem: computing the Jacobian of a complicated integral using quaternion rotations.

Problem was that the symbolic results were way too complicated and the simplify function didn't help much. So, I got back to manual differentiation.


  Role: Six-month intern/fixed term job March-September 2024
  Location: Anywhere in the world (on-site), willing to relocate
  Skills: 

    * Digital signal processing, machine learning, computer vision, control theory, electronics, electrical engineering
    * C/C++/Assembly, Python, Go, Javascript, Django, React, Docker, OpenGL, OpenCV ...
    * High-speed pcb design, FPGA programming,
Hey! I’m Alex Toussaint, an engineering student at CentraleSupélec (France). I’m currently working on drone navigation algorithms, and I’m looking for a full-time second six month internship abroad in robotics/computer science.

I’ve been passionate about technology and robotics for as long as I can remember! Here are a few things I worked on:

- Co-founded, built and sold a no-code crypto trading bot editor startup when I was in high-school (kaktana.com)

- Built an ultrasonic 3d scanner that works in the air capable of scanning in 3D a 140deg*140deg*8meters volume at 60fps[1] [2]

- Built my own high-performance quadcopter flight controller pcb and code from scratch.

See my GitHub [3] and resume [4][5] above for more! I’m looking for a fast-paced environment and don’t mind working on very hard technical projects.

[1]: https://news.ycombinator.com/item?id=27090795

[2]: https://www.alextoussaint.com/2021-04-28_How-I-built-an-ultr...

[3]: https://github.com/alextousss

[4]: https://alextoussaint.com

[5]: https://alextoussaint.com/resumev2.pdf


One method that solves 99% of your control problems is the Ziegler-Nichols method [1]. It's a shame it's not taught more often.

No need to model your system, just increase the P gain until the system oscillates naturally. Measure the oscillation period, and then refer to the tables at [1] to choose the P, I, D gains depending on how you like your system response to look like.

[1]: https://en.wikipedia.org/wiki/Ziegler%E2%80%93Nichols_method


ZN tuning is taught in engineering schools in the US. I even had a lab on it. As far as I remember it was kind of painful to work through and didn’t yield that much better results than hand tuning.

Ah I remembered something else… it needs to find the max Kp which in some cases is just not possible (or wise) to attempt with a real world plant.


On the contrary, ZN is taught is almost every undergrad control course — and not actually used industry. It’s a classic textbook method to demonstrate the concept in simulations but it has many downsides in practice (pushing the system to its boundaries is not a good idea).

Most professionals tune with starting values obtained using model inversion (IMC, direct synthesis) and then hand tune. There is also software like Loop Pro that analyzes the data and proposes tunings.


You can actually use that method for the remainder constants too. I built an analog motor controller for my control systems lab and the constants were just pots. We would increase the resistance until instability and back off a little. Rinse and repeated for the remainder two pots.


A lot of gaming doesn't really have the luxury of waiting for the oscillation to kick in, in order to then balance the system, though. By the time there's oscillation, it's already too late to fix, you need to preempt the oscillation.


Yes it does, you have to manipulate the expression to make it adimensional. But this rule-of-thumb is only valid for systems whose response time is less than 500ms.


I'm working on a 3d sonar to replace costly lidars.

Already have a state-of-the art prototype that has better performance than $3k lidars for under a hundred bucks.

Applications are robots that need to navigate autonomously in a non-cooperative environment (humanoid robots, delivery drones, etc). There's also a dozen other applications to use the sensor for (indoor millimeter-localization with beacons, insect detection and identification, passive localization of sound sources, etc).

I'd love to meet someone with a strong technical background but who could help me on all non-technical tasks (getting funding, finding an application to focus on, managing certifications, etc)

More context at [1] [2]

I'm currently based in France but would like to relocate in March when I finish my current internship.

[1]: https://www.alextoussaint.com/2021-04-28_How-I-built-an-ultr...

[2]: https://www.alextoussaint.com/

alex at alextoussaint.com


  Role: Six-month intern/fixed term job March-September 2024
  Location: Anywhere in the world (on-site), willing to relocate
  Skills: 

    * Digital signal processing, machine learning, computer vision, control theory, electronics, electrical engineering
    * C/C++/Assembly, Python, Go, Javascript, Django, React, Docker, OpenGL, OpenCV ...
    * High-speed pcb design, FPGA programming,
Hey! I’m Alex Toussaint, an engineering student at CentraleSupélec (France). I’m currently working on drone navigation algorithms, and I’m looking for a full-time second six month internship abroad in robotics/computer science.

I’ve been passionate about technology and robotics for as long as I can remember! Here are a few things I worked on:

- Co-founded, built and sold a no-code crypto trading bot editor startup when I was in high-school (kaktana.com)

- Built an ultrasonic 3d scanner that works in the air capable of scanning in 3D a 140deg*140deg*8meters volume at 60fps[1] [2]

- Built my own high-performance quadcopter flight controller pcb and code from scratch.

See my GitHub [3] and resume [4][5] above for more! I’m looking for a fast-paced environment and don’t mind working on very hard technical projects.

[1]: https://news.ycombinator.com/item?id=27090795

[2]: https://www.alextoussaint.com/2021-04-28_How-I-built-an-ultr...

[3]: https://github.com/alextousss

[4]: https://alextoussaint.com

[5]: https://alextoussaint.com/resumev2.pdf


Got my first internship building drone navigation systems after building my own quadcopter flight control board (software included) (https://github.com/alextousss/quadcopter)

By the way, looking for a second one March-September 2024 :)


  Role: Six-month intern/fixed term job March-September 2024
  Location: Anywhere in the world (on-site), willing to relocate
  Skills: 

    * Digital signal processing, machine learning, computer vision, control theory, electronics, electrical engineering
    * C/C++/Assembly, Python, Go, Javascript, Django, React, Docker, OpenGL, OpenCV ...
    * High-speed pcb design, FPGA programming,
Hey! I’m Alex Toussaint, an engineering student at CentraleSupélec (France). I’m currently working on drone navigation algorithms, and I’m looking for a full-time second six month internship abroad in robotics/computer science.

I’ve been passionate about technology and robotics for as long as I can remember! Here are a few things I worked on:

- Co-founded, built and sold a WYSIWYG crypto bot editor startup when I was in high-school (kaktana.com)

- Built an ultrasonic 3d scanner that works in the air capable of scanning in 3D a 140deg*140deg*8meters volume at 60fps[1] [2]

- Built my own high-performance quadcopter flight controller pcb and code from scratch.

See my GitHub [3] and resume [4][5] above for more! I’m looking for a fast-paced environment and don’t mind working on very hard technical projects.

[1]: https://news.ycombinator.com/item?id=27090795

[2]: https://www.alextoussaint.com/2021-04-28_How-I-built-an-ultr...

[3]: https://github.com/alextousss

[4]: https://alextoussaint.com

[5]: https://alextoussaint.com/resumev2.pdf


I'm surprised this does not include the excellent Alchitry boards [1] which are quite cheap and capable ($100 for an Artix-7 35T dev board is a steal)

[1]: https://www.sparkfun.com/categories/tags/alchitry


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