Fundamentals of Robotics and Artificial Intelligence - APS

It will mainly delivery contents of the world’s leading robotics and AI institutions and their specific research directions, fundamental concepts of robotics and AI, essential mathematics for robotics, structure of robots (fundamental structure of different types of robots), robot kinematics and rigid multibody system dynamics, expression and reasoning of knowledge, problem solving on the basis of searching, artificial neural network and deep learning, basic control and system integration, AI used on robots, etc.

1. Mainstream institutions of robotics and AI and

their characteristics

1.1 CMU Carneige Mellon University- Robotics Institute

• Manipulation, Locomotion, control,ML & CV

• HERE

  

1.2 MIT-CSAIL

• AI / System / Theory
• Artificial Muscle

1.3 Stanford- SAIL

• CV & NLP

1.4 Google

• AlphaGo

1.5 Waseda University

humanoid robot

1.6 Nagoya University

surgical robots

2. Robotics &AI

2.1 R-Concept

• Mechanical Eng.
  • Eng. Physics Material science
  • Design, Analysis, Manufacturing, Maintenance
• Electrical Eng.
  • Electricity, Electronics, Electromagnetism
  • Power, Drive, Sensor, Control
• Computer Eng.
  • Theory, Experimentation, Eng.
  • Computation, ML, CV,

2.2 R-Allpication

• Dangerous Enviroment
• Areas human can’t survive
• Manufacturing process

2.3 AI-Concept

1.0 act like human

• Turing Test

2.0 think like human

• cognitive science
• decision make, problem solve, learning

3.0 think rationaly

4.0 think intelligently

2.4 Three laws of Robotics

• [Law 0] humanity the first
• [Law I] no harm to human
• [Law II] obey the orders, under Law I
• [Law III] protect itself, under Law I &II

2.5 Example of Salto to Galago

3. Fundamental mathematics for robotics

3.1 Vector[a b c d]

• d: Scale
• $a\cdot b=xx+yy+zz$
• $a\times b=||$
• Plane: $P=[a\quad b\quad c\quad d]$
  • to 0: $-\dfrac{d}{m}, m=\sqrt{a^2+b^2+c^2}$
• Vector: $PV=0,on\PV>0,above\PV<0,under$

$v=Hu\H=Trans(a, b, c)=\left(\begin{matrix}1&0&0&a\0&1&0&b\0&0&1&c\0&0&0&1\end{matrix}\right)$

3.2 Rotational Transformation

3.3 Robot coordinates

3.3.1 DOF degree of freedom

$T_6=A_1 A_2 A_3 A_4 A_5A_6\\quad=\left(\begin{matrix}n_x&o_x&a_x&p_x\n_y&o_y&a_y&p_y\n_z&o_z&a_z&p_z\0&0&0&1\end{matrix}\right)$

3.3.2 Euler Angle

$Euler(\varphi,\theta,\psi)=Rot(z,\varphi)Rot(y,\theta)Rot(z,\psi)$

• X: Yaw
• Y: Pitch
• Z: Roll

3.3.3 Coordinates

• Cartesian Coordinate

  $T=T_{cart}=\left(\begin{matrix}1&0&0&p_x\0&1&0&p_y\0&0&1&p_z\0&0&0&1\end{matrix}\right)$

• Cylindrical Coordinate

  

• Spherical Coordinate

  

• Chain Coordinate

3.4 Position Kinematics

• Rotate joints

  

• Prismatic joints

  

• Example

  

  

$A_n=Rot(z,\theta_n)Trans(0,0,d_n)Trans(a_n,0,0)Rot(x,a_n)$

3.5 Velocity Kinematics

$\dot{x}=J(q)\dot{q}\x=\left[\begin{matrix}v\w\end{matrix}\right]\\left[\begin{matrix}v\w\end{matrix}\right]=\left[\begin{matrix}J_{l1}&J_{l2}&\dots&J_{ln}\J_{a1}&J_{a2}&\dots&J_{an}\end{matrix}\right]\left[\begin{matrix}\dot{q_1}\\dot{q_2}\\dots\\dot{q_n}\end{matrix}\right]$

4. Knowledge representation and reasoning

4.1 Definition

• Descriptive k
• Judgment k

• Procedural k

• Object-level

• Meta-level

4.2 Knowledge representation methods

4.2.1 Predicate Logic

• P, Q, R, S
• T, F
• 

• 

• 

4.2.2 Production representation

• $P\rightarrow Q $: If P then Q

• deterministic factual knowledge

  • (object, property, value)
  • (relationship, object1, object2)

  

• uncertainty factual knowledge

  • (object, property, value, credibility)
  • (relationship, object1, object2, credibility)

  

• Production system components

  

4.2.3 Semantic network representation

• NLP Natural Language Processing

• (Node 1, Arc, Node 2)

  

• Relationship

  • Category: kind / member
  • Inclusive: part
  • Attribute: have /can
  • Time: before / after
  • Locational
  • Similarity
  • Causal
  • Composition

• 

4.2.4 The frame Representation

4.3 Deterministic reasoning

4.3.1 Definetion

• Deductive r
• Inductive r

• Default r

• Deterministic r

• Uncertainly

• Heuristic r

• Non-heuristic

4.3.2 Logic basis

• predicate logic

4.3.3 Natural deductive reasoning

4.4 Uncertainty knowledge representation and reasoning

• Randomness

• Fuzzy

  • IF E THEN R (CF,$\lambda$)

    • CF: Certainly Factor

  • Fuzzy logic control

    

    

    

• Incompleteness of knowledge

5. Search to slove

• And-Or Graph

  

  decomposition the problem(TV)

• TSP Traveling Salesman Problem

  • each city once
  • shortest route
• GA Genetic Algorithm
• PSO Particle Swarm Optimization

6. Artificial Neural Network

weight and biases to minimize the cost function

• neuro: number
• get the cost function: Gradient Descent

• Least-squares fitting (最小二乘法拟合)

  • $z=Xw+e$

  • mean-square error(MSE-均方误差)

    

• Adaptive linear systems

• Non-linear adaptive units
• Single Neuron Neural Network
• BP Backpropagation Neural Network
  • 3 layers (1 hidden)
  • change the weight and biases from the result