# Update: Jason 2018-11-30

I wish to identify flow disturbance effect on quadcopters, so that we can do better position tracking, and predictions under large flow disturbances (wind gusts, large shear flow).

To experimentally produce the flow disturbance, I have set-up experiments to produce an open jet utilizing a square nozzle. This set-up will help us to produce repeatable, characterized flow disturbances so that we can conduct quantitative analysis for the flow acting on the quadcopter.

This week I have done some preliminary flow disturbance tests using the nozzle set-up, and tried to analyze the flow.

After today’s meeting, we obtained the conclusion that the order of magnitude for disturbance torque is too high (~0.1 Nm)

$\left[\underline{n_{D}}\right]^{B}=\left[\underline{J_{B}^{B}}\right]^{B}\left[\underline{D^{B}\gamma}\right]^{B}-\left[\underline{n_{B}}\right]^{B}$

After the meeting, I have thought about that and I re-plotted disturbance torque using the estimated angular velocity.

I think using estimated angular velocity is more desirable  for two reasons

1. The estimator utilizes mocap data, which reduces the error between the rate gyro data and the real angular velocity on the body.
2. The filter is applied to the estimator, so smoother signal results in less noisy results after differentiation (e.g. forward Euler).
Resulting equation is,

$\left[\underline{n_{D}}\right]^{B}=\left[\underline{J_{B}^{B}}\right]^{B}\left[\underline{D^{B}\omega^{BE}}\right]^{B}-\left[\underline{n_{B}}\right]^{B}$,

where $\left[\underline{n_{D}}\right]^{B}$ is disturbance torque, and $\left[\underline{n_{B}}\right]^{B}$ is motor torque on body frame.

Fig. 1. Disturbance torque, $\left[\underline{n_{D}}\right]^{B}$ 2. Motor torque, $\left[\underline{n_{B}}\right]^{B}$   3. Inertia multiplied by angular acceleration, $\left[\underline{J_{B}^{B}}\right]^{B}\left[\underline{D^{B}\omega^{BE}}\right]^{B}$ 4. Disturbance force

I have obtained Disturbance torque by subtracting ‘2. Motor torque’ from ‘3. Inertia multiplied by angular acceleration’.

For the angular acceleration term, I have used first order forward Euler method to calculate the derivatives of the estimated angular velocity. The order of magnitude is ~0.04 Nm at max., which is more reasonable than the result using derivatives of rate gyro data (~0.1 Nm). However, still the value of torque disturbance is higher compared to the torque produced by motors (~0.006 Nm at max.)

Although I am not sure whether the order of magnitude 0.04 Nm is reasonable, qualitatively, it makes sense to have higher value of z-torque, since flow is acting on the vehicle by x-axis.

This week, I have leaned that

• How to write a python script for analyzing/plotting pickle data
• A way to calculate force and torque due to disturbance
• How to reason about the given plots
• Better way of presentation slides/methods of my research for a potential sponsor

Next week, I will focus more on flow part of the nozzle. Specifically,

• I will locate the hot-wire where the miniquad was located during the preliminary test, and see the velocity values. I am also planning to compare the result with theoretical velocity, which only holds for laminar flow, and see whether the result matches
• I will also re-do the test near to the nozzle, and see if that makes a much difference to the disturbance effect
• I will make a full preparation of sponsor presentation on next Thursday based on the  comments that I got from yesterday’s mock-up presentation.
• I will read the paper named “External Wrench Estimation, Collision Detection, and Reflex Reaction for Flying Robots” https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=8059847,
which is about detecting other environmental effects to avoid collision. That would help me to provide some intuition of analyzing flow disturbance effects of our case
• I forgot to ask Prof. Makiharju that whether we can utilize Particle Image Velocimetry (PIV) of his lab. and doing some flow analysis of quadcopters such as the figures of the paper “Wind Characterization Using Onboard IMU of sUAS” https://arc.aiaa.org/doi/abs/10.2514/6.2018-2986. It might be worth to discuss this with him.

Fig. Flow effect of rotors utilizing PIV technique (ref. from the paper)
• In a month, I am aiming to finish the static drone test (make it hover in one position with fan on) with jet flow characterization utilizing hot wire sensor.