## 1. Information ¶

I plan to study a motion planning algorithm.

I will refer to the famous course from USC.

I will refer to the famous course from USC.

This is course information.

Instructor: Professor Nora Ayanian

Course: Coordinated Mobile Robotics

Instructor: Professor Nora Ayanian

Course: Coordinated Mobile Robotics

#### 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 = Distinct Situation for the world (x)
- State Transition Equation

x' = f(x, u)

- x : current state

- x': new state

- u : each action

- x : current state
- 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

- U(x): action space for each state x
- Xg: a set of goal states

- Formulation 2.1 = Discrete Feasible Planning

- A nonempty state space X, which is a finite or countably infinite set of states.

- For each state x ∈ X, a finite action space U(x).

- 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).

- An initial state x1 ∈ X.

- 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

- set of vertices = state space X

- A nonempty state space X, which is a finite or countably infinite set of states.