EE562: Robot Motion Planning Slides on Discrete Planning Abubakr - - PowerPoint PPT Presentation

EE562: Robot Motion Planning

Slides on Discrete Planning Abubakr Muhammad

Discrete Planning

• Planning (robotics) or Problem Solving (AI) ?
• We will study

– Discrete configuration spaces or state spaces – Modeling planning problems as graph search algorithms (feasible planning) – Optimal planning (dynamic programming)

• No geometric models or differential equations
• Key towards a unified approach towards planning

problems

• Reference: Planning Algorithms by LaValle Ch 2

State Space Models

• A distinct situation is a state, say x
• Set of all possible states is State Space X
• World is transformed through actions (controls)
• Actions are chosen by a planner
• Each action u, when applied to state x, produces

a new state x’, via State transition function f

x’ = f(x,u)

Discrete Feasible Planning

• U(x) : set of all actions that can be applied

from state x.

• Choose controls to stear state to the goal.

Example: A labyrinth

Example: An infinite tiled floor

Example 2: Puzzle games

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Example 3: Reconfigurable systems / Dynamic Networks

• Robotic warehousing
• KIVA Systems video (0-45 sec)

http://www.youtube.com/watch?v=lWsMdN7HMuA#

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Reconfigurable systems / Dynamic Networks

• Lab on a chip
• Coordinated drop movement

Courtesy: Duke digital microfluidics Courtesy: RPI robotics

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Common themes ….

• Agents are constrained to occupy “positions”
• Agents cannot bump into each other (collision

avoidance)

• The positions of all agents collectively make a

configuration

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Configuration Space

• Set of all configurations is a configuration

space

• Reconfiguration: Moving from one

configuration to another

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Example 3: Distributed Robotics

• What is the configuration space?

Sounds familiar?

• When state space is finite

– Finite state machines (Mealy/Moore machines) – Deterministic Finite automata (DFA)

Graphs

Ex: Graphs from Grids

Planning as Graph Search Problem

• 1. Construct a graph representing the planning

problem

• 2. Search the graph for a (hopefully, close-to-
• ptimal) path

The two steps above are often interleaved

Examples of Graph Construction

Search in Path Planning

• Find a path between two locations in an
• unknown, partially known, or known
• environment
• Search Performance

– Completeness / systematic – Optimality → Operating cost – Space Complexity – Time Complexity

Graph Search Types

Uninformed Search

• Use no information obtained from the

environment

• Blind Search: BFS (Wavefront), DFS

Informed Search

• Use evaluation function
• More efficient
• Heuristic Search: A*, D*, etc.

General forward search

Ex1: Breadth First Search

Running time complexity = O(V+E)

Ex2: Depth First Search

Running time complexity = O(V+E)

General forward search

• States

– Unvisited – Dead – Alive

• Set of alive states kept in a priority queue
• Implementation details (omitted)

– How to determine whether x is in XG (representation) [Line 4] – How to verify whether x has been visited? (lookup tables? Hashing?) [Line 8] – How to sort the queue?

Backward Search

Bidirectional Search

Systematic searches

BFS is systematic DFS is systematic for finite graphs For finite graphs all searches are systematic Requirement: systematic

• keep track of visited states
• visit every reachable state)