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LERP, NLERP and SLERP

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WHAT IS THAT AND WHY DO YOU NEED THIS? Whenever you've got 2 numbers and you want something between them, you want some kind of interpolation. And the same in quaternions - you have to quaternions that describe the same no one is 100% correct but 100% incorrect either, so you want a quaternion that is a combination of these two. So you can use the simplest idea of combining two numbers: \[\mathbf{q}_{3}=\alpha \mathbf{q}_{1} +(1-\alpha)\mathbf{q}_{2} \label{eq:LERP}\] this is LERP ( linear interpolation ) but since, for orientation porpuse quaternion need to have norm of 1, after this interpolation you need to normalize result: \[\mathbf{q}_{3}=norm(\alpha \mathbf{q}_{1} +(1-\alpha)\mathbf{q}_{2}) \label{eq:NLERP}\] and that is NLERP ( normalized linear interpolation ) . Now, how these methods could be interpreted, and what are the consequences in real applications?  If we imagine a circle with a radius of 1 which is going across quaternions that we want to inter...
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ESC protocols overview with implementation on STM32

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 What is ESC protocol? When our flight controller calculates new values for each of the motors they need to be sent to ESC microcontroller which can then process these values and control MOSFETs. How exactly signals are received and then send to motors is ESC's software secret, which is another really interesting and complicated topic. For now, let's know that we can not control the motors or even MOSFETs from our FC, we need to send new values between two microcontrollers. And here is our topic: how to exchange this information efficiently and correctly?   Analog way The oldest and probably the most recognizable protocol is PWM signal, taken from servo controlling. All the analog protocols are based on this signal. Period and duty cycle changes, but the idea remains the same: the FC sends a signal, and the ESC measures the time of the high and low signal, and this measured value is treated as a new set for the motor. The main features of this approach are: simplicity ...
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Filters - Theory

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 Filters  In this post, I want to present the theory needed for digital filter design. Firstly, a quick description of mainly used filters in the continuous domain - I want to give you some intuition in interpreting the transform functions. Next, I will present practical discretization from the '$s$' domain into the '$z$' (discrete time). Finally, a difference equation will be provided which can be directly programmed on any microprocessor. In a future post, I will show the possible implementation of described filters. In essence, the filter should block undesirable frequencies and let others pass through without distortion. For our applications, we can divide filters into 4 main categories: Low-pass filters High-pass filters Band-pass filters Notch filters Low-pass filter As the name suggests this filter allows low frequencies to pass and suppress high ones. The simplest LPF is a system with one pole: \begin{gather}H(s)=\frac{\omega_{0}}{s+\omega_{0}}\end{gather} A typ...
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