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# System prepended metadata

title: Force Prediction in the Real World

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# Force Prediction in the Real World
## Comparison of Curriculum and No Curriculum
From last time, the final stage in the curriculum learning procedure produced the model:
![](https://i.imgur.com/hLEjt0c.png)


Now, we collect a single dataset by performing a random walk in the 'n', 'e', and 'd' directions:
![](https://i.imgur.com/6FSrRIY.png)
![](https://i.imgur.com/SoUBcaH.png)

Why might the curriculum learning procedure be advantageous (outside of practical reasons)?
Curse of dimensionality: It is harder to sample points in $\mathbb{R}^3$ than it is in $\mathbb{R}^2$. 

## Real World Experiments: Stage 1
'U1' is performing a random walk 1.75m below 'U2'.
![](https://i.imgur.com/G7GLdSw.png)
![](https://i.imgur.com/FbtXAhO.png)
![](https://i.imgur.com/gZo2K67.png)
We observe very large biases ($>1 m/s^2$) in the down direction. We can make these biases smaller in magnitude using a thrust stand (Peter and Ajay).
![](https://i.imgur.com/fEiQSCh.jpg)



### Online Bias Estimation
One possible way by which to zero out the bias is to add  the online bias estimation, $u_{\text{bias}}$, to $u$. However, $u_{\text{bias}}$ also measures the downwash forces. This results in the prediction of negative forces after 'U1' passes under 'U2'.
![](https://i.imgur.com/BdxoNxg.png)
![](https://i.imgur.com/qwL4ThR.png)

These negative forces might be reasonable, though. Neural-Swarm 1 has similar patterns in their predicted/ground truth forces:
![](https://i.imgur.com/uDfbZTu.png)



### Oscillations in the 'n' and 'e' directions
When U1 approaches U2 in the n and e directions, it experiences sinusoidal oscillations that create similar sinusoidal patterns in the force predictions.
![](https://i.imgur.com/fLOJ4DA.png)
![](https://i.imgur.com/Zf6EHR4.png)

Are these oscillations part of the downwash effect that we should model, or are they due to something else (ex. interaction of U1's ground effect with the downwash effect)?
Ajay: These effects are due to a combination of the ground effect and the magnitude of the acceleration.

### Predictions Using Force Dynamics
So far, we have modeled assumed a memoryless state model: the forces at time $t$ are a function only of the drones' relative states at time $t$. What if this were not the case, though? 

The drone's force at time $t$ is both a function of the drones' relative state at time $t$ and the forces the drone felt at the previous $K$ timestep(s).

Perhaps we should model this as (at least) a Markovian state, such that $f_{ext}(t) = H(X_t)$, where $X_t = [p^{rel}(t),v^{rel}(t),f_{ext}(t-1)]^T$. 

The modeling question is very important. Likely where the novelty of our approach comes in (compared to Neural-Swarm). See [*Machine Learning for Sequential Data: A Review*](https://web.engr.oregonstate.edu/~tgd/publications/mlsd-ssspr.pdf). 

> Physics-based evidence for recurrence/Markov-transition dynamics for the force field. @Ajay.