Only Truth Matters

1. 1 简介

针对一个富斯FS-i6发射机及其接收机来学习接收机方面的知识

1.1. 1.1 发射机

1.2. 1.2 接收机

• 型号：FS-iA6B
• 调制方式：GFSK
• 数据分辨率：1024级
• 电源标准：4.0-6.5V DC

1.3. 1.3 基本操作

• 开机：

1. 先开发射机Tx
2. 再开接收机Rx
3. 正常情况下接收机红色指示灯常亮

1. Compare Obstacle Avoidance Algorithm

1.1. 1 Bug algorithms

• Simple
• Non optimal
• May be trapped in maze structures

1.2. 2 Potential Field

Attractive Potential	Repulsive Potential

Combine Attractive Potential and Repulsive Potential

• Good for static and completely known environment

• Bad: may lead to a local minimum point

1. 1. Basics

• Figure
• Axes
• Axis
• Title

1. 1 Introduction (Prepare)

1.1. 1.1 Goal

Build a bicopter(a kind of frame) like this

1.2. 1.2 Pros & Cons

• Cheap : only 2 servos and 2 motors
• Unstable
• Hard to tune

1.3. 1.3 Hardware

• Servo $\times$ 2
• Motor $\times$ 2
• Flight Controller Board $\times​$ 1 : SP Racing F4 Pro
• Transmitter $\times$ 1 : FS-i6
• Receiver (Rx) $\times$ 1 : FS-iA6

1.4. 1.4 Software

• CleanFlight / BeteFlight / iNav (based on similar code)

1. 1 Introduction

Principal component analysis (PCA) is a common tool for data analysis

• Goal: reduce complex data set to a lower dimension
• Math tool: singular value decomposition (SVD)

1.1. 1.1 intuition

Many problem in real world can be expressed by a small number of variables. But we don’t know that, we just collect so many data and have no ideal how to deal with hundreds of variables. Also, there will be noise in our data, which makes the problem even more complicated.

PCA is to solve this problem by identify the most meaningful basis to re-express the data. Then we can delete the less important basis( variable)

1.2. 1.2 A little math

• $\mathbf{X}$ : the original data set $\rightarrow$ how to re-express $\mathbf{X}$
• row : variable ;
• column : measurements
• $\mathbf{Y}$ : transformed data set $\rightarrow$ how $\mathbf{Y}$ should look like $\rightarrow$ $\mathrm{C}_{\mathrm{Y}}$
• $\mathbf{P}​$ : transformation
• $\sigma_{\mathrm{ab}}^{2}​$ : covariance o f A and B
• $\sigma_{\mathrm{ab}}^{2} \equiv \frac{1}{n} \mathbf{a b}^{T}$ , $\mathbf{a}=\left[a_{1} a_{2} \ldots a_{n}\right]$ ,$\mathbf{b}=\left[b_{1} b_{2} \ldots b_{n}\right]$
• $\mathbf{C}_{\mathbf{X}} \equiv \frac{1}{n} \mathbf{X} \mathbf{X}^{T}$ : covariance matrix of $\mathbf{X}$, the covariance value reflect the noise and redundancy in the measurement
• large off-diagonal terms correspond to high redundancy

Assumption 1: bigger variance, more information
Assumption 2: If the covariance of 2 variable is big, one of them should be deleted.
Assumption 3: the principal components are orthogonal

1.3. 1.3 Goal in math

1. 1 Introduciton

1. 1 Introduction

1.1. 1.1 Deques

A deque, also known as a double-ended queue, is an ordered collection of items similar to the queue. It has two ends, a front and a rear, and the items remain positioned in the collection. In a sense, this hybrid linear structure provides all the capabilities of stacks and queues in a single data structure.

Simply speaking, deques is stacks + queues

1.2. 1.2 ADT

2. 2 Implementation

In practice, we just import deque from collections module

Adding and removing from the rear is $O(1)$

Adding and removing from the front is $O(n)​$

1. Problem

Goal: design evacuation plans at the Louvre in Paris

• Quic
• Safely

Difficuties: Diversity of visitors

• Language
• Group
• Disabled

Basic information:

• 5 floors, 2 of which are underground
• Entrance
• pyramid: main and most used
• Passage Richelieu
• Carrousel du Louvre
• Portes Des Lions
• Some other exit points, but may cause security problem

What to do:

• Design a adaptable model
• Indentify potential bottlenecks
• Validate your model
• How to implement it

1. 1 概论

大多数生产过程的效益取决于控制的好坏，因此控制很重要。

大多数过程可以分解为一些基本环节，掌握这些环节之后我们就可以进行改造、控制，并预估性能。

总目标：对于任意外部干扰$DV$，通过调节操作变量$MV$，使被控变量$CV/PV$维持在设定值$SP$

2. 2 过程动态特性

不同的过程动态特性不相同。

2.1. 2.1 典型动态特性，机理建模

自衡过程–纯滞后、单容、多容

非自衡–积分、指数

常用方程

1. 1 Error

There are two types of error:

• true error: $\operatorname { error } { \mathcal { D } } ( h ) \equiv \operatorname { Pr } { x \in \mathcal { D } } [ f ( x ) \neq h ( x ) ]$
• $D$ for distribution
• sample error: $error_s( h ) \equiv \frac { 1 } { n } \sum_ { x \in S } \delta ( f ( x ) \neq h ( x ) )$
• $\delta ( f ( x ) \neq h ( x ) )=1$ if $f ( x ) \neq h ( x )$

How well dose sample error estimate true error？

We can check

• Bias
• Variance

2. 2 Estimators

1. Choose sample $S$ of size $n$ according to $D$
2. measure $error_s(h)$
3. $\to$ sample error is an unbiased estimator for true error

e.g. with approximately $95%$ probability, true error lie in
$$
\operatorname { error } { S } ( h ) \pm 1.96\sqrt \frac { \text { errors } ( h ) \left( 1 - e r r o r { S } ( h ) \right) } { n }
$$