Lecture 8: Motion Planning Flashcards
In the section of Representation, what is workspace?
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?
In the section of Representation, what does configuration space describe?
(the f sta of the rob in the w)
the full state of the robot in the world (actuator positions, orientation, etc.)
Positions in configure space tend to be?
Close together for the robot
Using configure space can make it easier to do what 2 things?
(Solving coll checks, join nrby poses)
Solve collision checks and join nearby poses
Configure space allows a level of abstraction that means?
(Sol meth can s a wider r o p)
solution methods can solve a wider range of problems
What is very common to do after converting a planning problem to some kind of graph?
use one of a variety of existing search algorithms on the graph
What 2 things are structured?
(OccuGr, DisFiel)
Occupancy Grids and Distance Fields
What 3 things are structured
(PoiClou, Mesh, Exa)
Point Clouds, Meshes, Exact
What has both unstructured and structured
Graphs
The edges of a directed graph have ?
direction
The edges of a weighted graph have? (c)
costs
What does Discrete State Space Representation do to Continuous State Space?
reduces it to a finite set of discrete states
When ti goes from a grid to a graph, what are states and transitions considered?
S as v, T as DE
States as vertices; transitions as directed edges
What is the process of a graph?
(Xs, Xg, X*A–>R^+)
Add a start node(Xs), goal node(Xg), and cost function(C: X*A→R^+)
What can be treated as a graph search problem?
Finding the shortest path
What are the 4 issues with grid-based representation?
(loss of precision,
appropriate grid res,
limit output path,
poor scaling in higher dim)
suffer some loss of precision, selecting an appropriate grid resolution, limit the type of output path, poor scaling in higher dimensions
How do you create a grid lattice?
(Cre,Constr)
first make a set of feasible motion primitives and construct a tree/graph that chains the motions into a sequence/plan
What does a visibilty graph create between all pairs of mutually visible vertices?
(e)
edges
Is visibility the optimal plan?
Yes
What graphs require careful consideration to construct graphs with guarantees?
(R-S Gra)
Randomly-sampled graphs
Randomly-sampled graphs are popular for what?
(S-based meth)
sample-based methods
3 steps to solve planning problem
(Conv prob, srch, pro)
Convert problem to graph
Search the graph
Profit!
What edges are generally considered in graph search?
(+)
positive edge weights
What are the 4 graph search methods?
BFS, DFS, Dijkstra’s Algorithm, A*
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)
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
In CLOSED SET, what are the 2 characteristics
(Set keeps track of …..
For each n, found l-c p)
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
Time complexity of Breadth-first search?
O(|V|+|E|)
What guarantees to find the shortest path?
BFS
How does DFS search?
starts at the root node and explores as far as possible along each branch before backtracking; has a stack queue
What has a lower memory footprint: BFS or DFS?
DFS
Is DFS complete for infinite trees?
No because it may explore an incorrect branch infinitely deep, it may never come back up
Dijkstra’s algorithm was published when by who?
Edsger Dijkstra in 1959
Basic idea of Dijkstra’s algorithm?
(expanding in ord of c - st)
expanding in order of closest to start (BFS with edge costs)
What is Dijkstra’s algorithm known as
(asymp the fast.. known s-s p algo for arbitrary dg)
Asymptotically the fastest known single-source shortest path algorithm for arbitrary directed graphs
Manhattan Distance and Euclidean Distance are examples of what?
A* Heuristic Search
What is the equation of A* Priority?
f(n) = g(n) + h(n); g(n) is the cost to arrive and h(n) is the heuristic cost to goal
3 Valid Heuristics
Euclidean Distance,
Manhattan Distance,
Zero(Dijkstra’s algorithm)
What are the 3 limitations of A* Search?
(need to …..,
sometimes and admissible heu func is diff to f,
not good rep of prob)
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
2 types of uncertainties?
Environment uncertainty, Motion uncertainty
Are potential field methods relatively simple to implement?
Yes
What do Potential fields design?
a function such that descending the gradient leads to a collison-free path to the goal
What are two examples of hierarchical planning?
Global planner over the whole search space
Local planner to respond to changes in environment, avoid collisions, stay on global path
Graphs are constructions of what two things?
(vert and CE)
vertices and connecting edges
Configuration space is what?
the robot’s configuration(joint angles etc) in the world
What is work space?
the world without the robot
