What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i...
Transcript of What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i...
![Page 1: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/1.jpg)
Motion Planning
Howie CHoset
![Page 2: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/2.jpg)
What is Motion Planning?
![Page 3: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/3.jpg)
What is Motion Planning?
• Determining where to go
![Page 4: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/4.jpg)
Overview
• The Basics
– Motion Planning Statement
– The World and Robot
– Configuration Space
– Metrics
![Page 5: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/5.jpg)
Algorithms
–Start-Goal Methods
–Map-Based Approaches
–Cellular Decompositions
![Page 6: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/6.jpg)
The World consists of...
• Obstacles
– Already occupied spaces of the world
– In other words, robots can’t go there
• Free Space
– Unoccupied space within the world
– Robots “might” be able to go here
– To determine where a robot can go, we need to discuss what a Configuration Space is
![Page 7: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/7.jpg)
Motion Planning Statement
If W denotes the robot’s workspace,
And Ci denotes the i’th obstacle,
Then the robot’s free space, FS, is
defined as:
FS = W - ( U Ci )
And a path c C0 is c : [0,1] g FS
where c(0) is qstart and c(1) is qgoal
![Page 8: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/8.jpg)
Example of a World (and Robot)
Obstacles
Free Space
Robot
x,y
![Page 9: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/9.jpg)
What is a good path?
![Page 10: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/10.jpg)
Basics: Metrics
• There are many different ways to measure a
path: • Time
• Distance traveled
• Expense
• Distance from obstacles
• Etc…
![Page 11: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/11.jpg)
1) head toward goal
2) if an obstacle is encountered,
circumnavigate it and remember
how close you get to the goal
3) return to that closest point (by
wall-following) and continue
Bug 1
“Bug 1” algorithm
Vladimir Lumelsky & Alexander Stepanov: Algorithmica 1987
• known direction to goal
• otherwise local sensing
walls/obstacles & encoders
But some computing power!
![Page 12: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/12.jpg)
1) head toward goal
2) if an obstacle is encountered,
circumnavigate it and remember
how close you get to the goal
3) return to that closest point (by
wall-following) and continue
Bug 1
“Bug 1” algorithm
Vladimir Lumelsky & Alexander Stepanov: Algorithmica 1987
But some computing power! • known direction to goal
• otherwise local sensing
walls/obstacles & encoders
![Page 13: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/13.jpg)
1) head toward goal
2) if an obstacle is encountered,
circumnavigate it and remember
how close you get to the goal
3) return to that closest point (by
wall-following) and continue
Bug 1
“Bug 1” algorithm
Vladimir Lumelsky & Alexander Stepanov: Algorithmica 1987
But some computing power! • known direction to goal
• otherwise local sensing
walls/obstacles & encoders
![Page 14: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/14.jpg)
Bug2
Call the line from the starting
point to the goal the m-line “Bug 2” Algorithm
![Page 15: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/15.jpg)
A better bug?
Call the line from the starting
point to the goal the m-line
1) head toward goal on the m-line
“Bug 2” Algorithm
![Page 16: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/16.jpg)
A better bug?
Call the line from the starting
point to the goal the m-line
1) head toward goal on the m-line
2) if an obstacle is in the way,
follow it until you encounter the
m-line again.
“Bug 2” Algorithm
![Page 17: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/17.jpg)
A better bug?
1) head toward goal on the m-line
2) if an obstacle is in the way,
follow it until you encounter the
m-line again.
3) Leave the obstacle and continue
toward the goal
OK ?
m-line “Bug 2” Algorithm
![Page 18: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/18.jpg)
A better bug?
1) head toward goal on the m-line
2) if an obstacle is in the way,
follow it until you encounter the m-
line again.
3) Leave the obstacle and continue
toward the goal
Goal
Start
“Bug 2” Algorithm
Better or worse than Bug1?
![Page 19: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/19.jpg)
A better bug?
1) head toward goal on the m-line
2) if an obstacle is in the way,
follow it until you encounter the
m-line again.
3) Leave the obstacle and continue
toward the goal
NO! How do we fix this?
Goal
Start
“Bug 2” Algorithm
![Page 20: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/20.jpg)
A better bug?
1) head toward goal on the m-line
2) if an obstacle is in the way,
follow it until you encounter the m-
line again closer to the goal.
3) Leave the obstacle and continue
toward the goal
Goal
Start
“Bug 2” Algorithm
![Page 21: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/21.jpg)
A better bug?
1) head toward goal on the m-line
2) if an obstacle is in the way,
follow it until you encounter the m-
line again closer to the goal.
3) Leave the obstacle and continue
toward the goal
“Bug 2” Algorithm
Better or worse than Bug1?
![Page 22: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/22.jpg)
Start-Goal Algorithm:
Lumelsky Bug Algorithms
![Page 23: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/23.jpg)
Lumelsky Bug Algorithms
• Unknown obstacles, known start and goal.
• Simple “bump” sensors, encoders.
• Choose arbitrary direction to turn (left/right) to make all turns, called
“local direction”
• Motion is like an ant walking around:
– In Bug 1 the robot goes all the way around each obstacle
encountered, recording the point nearest the goal, then goes around
again to leave the obstacle from that point
– In Bug 2 the robot goes around each obstacle encountered until it
can continue on its previous path toward the goal
![Page 24: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/24.jpg)
Assumptions?
![Page 25: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/25.jpg)
Assumptions
• Size of robot
• Perfect sensing
• Perfect control
• Localization (heading)
What else?
![Page 26: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/26.jpg)
Example of a World (and Robot)
Obstacles
Free Space
Robot
x,y
![Page 27: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/27.jpg)
Configuration Space: Accommodate Robot Size
Obstacles
Free Space
Robot
(treat as point object) x,y
![Page 28: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/28.jpg)
Trace Boundary of Workspace
Pick a reference point…
![Page 29: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/29.jpg)
Translate-only, non-circularly
symmetric
Pick a reference point…
![Page 30: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/30.jpg)
Translate-only, non-circularly
symmetric
Pick a reference point…
![Page 31: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/31.jpg)
The Configuration Space
• What it is
– A set of “reachable” areas constructed from
knowledge of both the robot and the world
• How to create it
– First abstract the robot as a point object. Then,
enlarge the obstacles to account for the robot’s
footprint and degrees of freedom
– In our example, the robot was circular, so we
simply enlarged our obstacles by the robot’s radius
(note the curved vertices)
![Page 32: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/32.jpg)
Start-Goal Algorithm:
Potential Functions
![Page 33: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/33.jpg)
Attractive/Repulsive Potential Field
– Uatt is the “attractive” potential --- move to the
goal
– Urep is the “repulsive” potential --- avoid
obstacles
![Page 34: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/34.jpg)
Artificial Potential Field Methods:
Attractive Potential
)(
)()(
goal
attatt
qk
qUqF
Quadratic Potential
![Page 35: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/35.jpg)
Distance
RRRd 22:
||||),( yyxx bababad
22 )()(),( yyxx bababad
![Page 36: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/36.jpg)
Path Length
Which is shortest?
![Page 37: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/37.jpg)
Path Length
Depends on metric
![Page 38: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/38.jpg)
Distance to Obstacle(s)
)(min)( qdqD i
![Page 39: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/39.jpg)
The Repulsive Potential
![Page 40: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/40.jpg)
Repulsive Potential
![Page 41: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/41.jpg)
Total Potential Function
+ =
)()()( repatt qUqUqU
)()( qUqF
![Page 42: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/42.jpg)
Local Minimum Problem with the Charge Analogy
![Page 43: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/43.jpg)
Local Min
![Page 44: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/44.jpg)
The Wavefront Planner
• A common algorithm used to determine the shortest paths between two points
– In essence, a breadth first search of a graph
• For simplification, we’ll present the world as a two-dimensional grid
• Setup:
– Label free space with 0
– Label start as START
– Label the destination as 2
![Page 45: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/45.jpg)
Representations
• World Representation – You could always use a large region and distances
– However, a grid can be used for simplicity
![Page 46: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/46.jpg)
Representations: A Grid
• Distance is reduced to discrete steps
– For simplicity, we’ll assume distance is uniform
• Direction is now limited from one adjacent cell to another
– Time to revisit Connectivity (Remember Vision?)
![Page 47: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/47.jpg)
Representations: Connectivity
• 8-Point Connectivity • 4-Point Connectivity – (approximation of the L1 metric)
![Page 48: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/48.jpg)
The Wavefront Planner: Setup
![Page 49: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/49.jpg)
The Wavefront in Action (Part 1)
• Starting with the goal, set all adjacent cells with
“0” to the current cell + 1
– 4-Point Connectivity or 8-Point Connectivity?
– Your Choice. We’ll use 8-Point Connectivity in our example
![Page 50: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/50.jpg)
The Wavefront in Action (Part 2)
• Now repeat with the modified cells
– This will be repeated until no 0’s are adjacent to cells with values >= 2
• 0’s will only remain when regions are unreachable
![Page 51: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/51.jpg)
The Wavefront in Action (Part 3)
• Repeat again...
![Page 52: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/52.jpg)
The Wavefront in Action (Part 4)
• And again...
![Page 53: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/53.jpg)
The Wavefront in Action (Part 5)
• And again until...
![Page 54: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/54.jpg)
The Wavefront in Action (Done)
• You’re done
– Remember, 0’s should only remain if unreachable regions exist
![Page 55: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/55.jpg)
The Wavefront, Now What?
• To find the shortest path, according to your metric, simply always
move toward a cell with a lower number
– The numbers generated by the Wavefront planner are roughly proportional to their
distance from the goal
Two
possible
shortest
paths
shown
![Page 56: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/56.jpg)
Wavefront (Overview)
• Divide the space into a grid.
• Number the squares starting at the start in
either 4 or 8 point connectivity starting at
the goal, increasing till you reach the start.
• Your path is defined by any uninterrupted
sequence of decreasing numbers that lead to
the goal.
![Page 57: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/57.jpg)
This is really a Continuous Solution
Not pixels
Waves bend
L1 distance
![Page 58: What is Motion Planning? · Motion Planning Statement If W denotes the robot’s workspace, And C i denotes the i’th obstacle, Then the robot’s free space, FS, is defined as:](https://reader035.fdocuments.in/reader035/viewer/2022071006/5fc3cffedd741b743512b6cd/html5/thumbnails/58.jpg)
Rapidly-Exploring Random Tree