# Robot_Study/Planning_Algorithm

## 1. Information ¶

I plan to study a motion planning algorithm.
I will refer to the famous course from USC.

This is course information.
Instructor: Professor Nora Ayanian
Course: Coordinated Mobile Robotics

## 3. Note ¶

### 3.1. Week 1 ¶

#### 3.1.1. Discrete Planning ¶

• All models are completely known and predictable
• Problem Solving and Planning are used as synonym

##### 3.1.1.2. Problem Formulation ¶
• State Space Model
• State = Distinct Situation for the world (x)
• Set of all possible states = State space (X) -> Countable
• State Transition Equation
x' = f(x, u)
• x : current state
• x': new state
• u : each action
• Set U of all possible actions over all states
U = set of U(x), x ∈ X
• U(x): action space for each state x
• For distinct x, x' ∈ X, U(x) and U(x') are not necessarily disjoint
• Xg: a set of goal states
• Formulation 2.1 = Discrete Feasible Planning
1. A nonempty state space X, which is a finite or countably infinite set of states.
2. For each state x ∈ X, a finite action space U(x).
3. A state transition function f that produces a state f(x,u) ∈ X for every x ∈ X and u ∈ U(x). The state transition equation is derived from f as x′ =f(x,u).
4. An initial state x1 ∈ X.
5. A goal set Xg ⊂ X.
=> Express as a "Directed State Transition Graph"
• set of vertices = state space X
• directed edge from x ∈ X to x′ ∈ X exists <=> exists an action u ∈ U(x) such that x′ = f(x,u)
• initial state and goal set are designated as special vertices in the graph

##### 3.1.1.3. Examples of Discrete Planning ¶
• Moving on a 2D Grid
• Rubik’s Cube Puzzle