Lecture 8: Motion Planning

Question 1

In the section of Representation, what is workspace?

Answer 1

is often the representation of the world, possibly independent of the robot itself. Often describes some notion of reachability, what space is free or occupied?

Question 2

In the section of Representation, what does configuration space describe?
(the f sta of the rob in the w)

Answer 2

the full state of the robot in the world (actuator positions, orientation, etc.)

Question 3

Positions in configure space tend to be?

Answer 3

Close together for the robot

Question 4

Using configure space can make it easier to do what 2 things?
(Solving coll checks, join nrby poses)

Answer 4

Solve collision checks and join nearby poses

Question 5

Configure space allows a level of abstraction that means?
(Sol meth can s a wider r o p)

Answer 5

solution methods can solve a wider range of problems

Question 6

What is very common to do after converting a planning problem to some kind of graph?

Answer 6

use one of a variety of existing search algorithms on the graph

Question 7

What 2 things are structured?
(OccuGr, DisFiel)

Answer 7

Occupancy Grids and Distance Fields

Question 8

What 3 things are structured
(PoiClou, Mesh, Exa)

Answer 8

Point Clouds, Meshes, Exact

Question 9

What has both unstructured and structured

Answer 9

Graphs

Question 10

The edges of a directed graph have ?

Answer 10

direction

Question 11

The edges of a weighted graph have? (c)

Answer 11

costs

Question 12

What does Discrete State Space Representation do to Continuous State Space?

Answer 12

reduces it to a finite set of discrete states

Question 13

When ti goes from a grid to a graph, what are states and transitions considered?
S as v, T as DE

Answer 13

States as vertices; transitions as directed edges

Question 14

What is the process of a graph?
(Xs, Xg, X*A–>R^+)

Answer 14

Add a start node(Xs), goal node(Xg), and cost function(C: X*A→R^+)

Question 15

What can be treated as a graph search problem?

Answer 15

Finding the shortest path

Question 16

What are the 4 issues with grid-based representation?
(loss of precision,
appropriate grid res,
limit output path,
poor scaling in higher dim)

Answer 16

suffer some loss of precision, selecting an appropriate grid resolution, limit the type of output path, poor scaling in higher dimensions

Question 17

How do you create a grid lattice?
(Cre,Constr)

Answer 17

first make a set of feasible motion primitives and construct a tree/graph that chains the motions into a sequence/plan

Question 18

What does a visibilty graph create between all pairs of mutually visible vertices?
(e)

Answer 18

edges

Question 19

Is visibility the optimal plan?

Answer 19

Yes

Question 20

What graphs require careful consideration to construct graphs with guarantees?
(R-S Gra)

Answer 20

Randomly-sampled graphs

Question 21

Randomly-sampled graphs are popular for what?
(S-based meth)

Answer 21

sample-based methods

Question 22

3 steps to solve planning problem
(Conv prob, srch, pro)

Answer 22

Convert problem to graph
Search the graph
Profit!

Question 23

What edges are generally considered in graph search?
(+)

Answer 23

positive edge weights

Question 24

What are the 4 graph search methods?

Answer 24

BFS, DFS, Dijkstra’s Algorithm, A*

Question 25

In OPEN SET, what are the 4 characteristics? (Maintains a list of frontier ... Keeps track of what .... Often stored as a .. For each n, know at least 1)

Answer 25

maintains a list of frontier (unexpanded) plans Keeps track of what nodes to expand next Often stored as a priority queue For each node in the open list, we know of at least one path to it from the start

Question 26

In CLOSED SET, what are the 2 characteristics (Set keeps track of ..... For each n, found l-c p)

Answer 26

set keeps track of nodes that have been expanded For each node in the closed list, we’ve already found the lowest-cost path to it from the start

Question 27

Time complexity of Breadth-first search?

Answer 27

O(|V|+|E|)

Question 28

What guarantees to find the shortest path?

Answer 28

BFS

Question 29

How does DFS search?

Answer 29

starts at the root node and explores as far as possible along each branch before backtracking; has a stack queue

Question 30

What has a lower memory footprint: BFS or DFS?

Answer 30

DFS

Question 31

Is DFS complete for infinite trees?

Answer 31

No because it may explore an incorrect branch infinitely deep, it may never come back up

Question 32

Dijkstra's algorithm was published when by who?

Answer 32

Edsger Dijkstra in 1959

Question 33

Basic idea of Dijkstra's algorithm? (expanding in ord of c - st)

Answer 33

expanding in order of closest to start (BFS with edge costs)

Question 34

What is Dijkstra's algorithm known as (asymp the fast.. known s-s p algo for arbitrary dg)

Answer 34

Asymptotically the fastest known single-source shortest path algorithm for arbitrary directed graphs

Question 35

Manhattan Distance and Euclidean Distance are examples of what?

Answer 35

A* Heuristic Search

Question 36

What is the equation of A* Priority?

Answer 36

f(n) = g(n) + h(n); g(n) is the cost to arrive and h(n) is the heuristic cost to goal

Question 37

3 Valid Heuristics

Answer 37

Euclidean Distance, Manhattan Distance, Zero(Dijkstra’s algorithm)

Question 38

What are the 3 limitations of A* Search? (need to ....., sometimes and admissible heu func is diff to f, not good rep of prob)

Answer 38

You need to construct a graph Sometimes an admissible heuristic function is difficult to find(as hard as the problem) A grid may not be a good representation of your problem

Question 39

2 types of uncertainties?

Answer 39

Environment uncertainty, Motion uncertainty

Question 40

Are potential field methods relatively simple to implement?

Answer 40

Yes

Question 41

What do Potential fields design?

Answer 41

a function such that descending the gradient leads to a collison-free path to the goal

Question 42

What are two examples of hierarchical planning?

Answer 42

Global planner over the whole search space Local planner to respond to changes in environment, avoid collisions, stay on global path

Question 43

Graphs are constructions of what two things? (vert and CE)

Answer 43

vertices and connecting edges

Question 44

Configuration space is what?

Answer 44

the robot’s configuration(joint angles etc) in the world

Question 45

What is work space?

Answer 45

the world without the robot