Robot Study/Planning Algorithm: Difference between revisions

Revision as of 09:41, 12 February 2020

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

Read Chapter 2

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)

  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

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 == Note ==
 === Week 1 ===
+Read Chapter 2
+==== Discrete Planning ====
+* All models are completely known and predictable
+* Problem Solving and Planning are used as synonym
+===== Introduction to Discrete Feasible Planning =====
+====== 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
+## 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
 == Comments ==