cs-417 introduction to robotics and intelligent systemsyiannis/417/2013/lectureslides/09... · ·...
TRANSCRIPT
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Ioannis Rekleitis
Motion Planning
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Outline
• Path Planning
– Visibility Graph
– Bug Algorithms
– Potential Fields
– Skeletons/Voronoi Graphs
– C-Space
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Motion Planning
• The ability to go from A to B
– Known map – Off-line planning
– Unknown Environment –Online planning
– Static/Dynamic Environment
CS-417 Introduction to Robotics and Intelligent Systems 3
qgoalqinit
qgoal
qgoalqinit
qinit
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Path Planning
Robot Map
World
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Path Planning
Robot Map
World
•Indoor/Outdoor•2D/2.5D/3D•Static/Dynamic•Known/Unknown•Abstract (web)
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Path Planning
Robot Map
World
•MobileIndoor/OutdoorWalking/Flying/Swimming
•Manipulator•Humanoid•Abstract
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Path Planning
Robot Map
World
•Topological•Metric•Feature Based•1D,2D,2.5D,3D
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Path Planning
Robot Map
World
•Topological•Metric•Feature Based•1D,2D,2.5D,3D
•MobileIndoor/OutdoorWalking/Flying/Swimming
•Manipulator•Humanoid•Abstract
•Indoor/Outdoor•2D/2.5D/3D•Static/Dynamic•Known/Unknown•Abstract (web)
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Path Planning: Assumptions
• Known Map
• Roadmaps (Graph representations)
• Polygonal Representation
qgoal
qinit
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Visibility Graph
• Connect Initial and goal locations with all the visible vertices
qgoal
qinit
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Visibility Graph
• Connect initial and goal locations with all the visible vertices
• Connect each obstacle vertex to every visible obstacle vertex
qgoal
qinit
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Visibility Graph
• Connect initial and goal locations with all the visible vertices
• Connect each obstacle vertex to every visible obstacle vertex
• Remove edges that intersect the interior of an obstacle
qgoal
qinit
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Visibility Graph• Connect initial and goal locations with all the visible vertices
• Connect each obstacle vertex to every visible obstacle vertex
• Remove edges that intersect the interior of an obstacle
• Plan on the resulting graph
qgoal
qinit
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Visibility Graph• An alternative path
• Alternative name: “Rubber band algorithm”
qgoal
qinit
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Major Fault• Point robot
• Path planning like that guarantees to hit the obstacles
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Limited-knowledge path planning
• known direction to goal
• otherwise local sensing
walls/obstacles encoders
•“reasonable” world
1. finitely many obstacles in any finite disc
2. a line will intersect an obstacle finitely many times
Goal
Start
• Path planning with limited knowledge
– Insect-inspired “bug” algorithms
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Not truly modeling bugs...
Insects do use several cues for navigation:
neither are the current bug-sized robots
visual landmarks
polarized light
chemical sensing
Other animals use information from
magnetic fields
electric currents
temperature
they’re not ears...
migrating bobolinkbacteria 17CS-417 Introduction to Robotics and Intelligent Systems
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Bug Strategy
“Bug 0” algorithm
• known direction to goal
• otherwise only local sensing
walls/obstacles encoders
1) head toward goal
2) follow obstacles until you can
head toward the goal again
3) continue
Insect-inspired “bug” algorithms
CS-417 Introduction to Robotics and Intelligent Systems 18
assume a
left-turn robot
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Does It Work?
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“Bug 1” algorithm
• known direction to goal
• otherwise only local sensing
walls/obstacles encoders
1) head toward goal
Insect-inspired “bug” algorithms
Bug 1
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“Bug 1” algorithm
• known direction to goal
• otherwise only local sensing
walls/obstacles encoders
1) head toward goal
2) if an obstacle is encountered,
circumnavigate it and remember
how close you get to the goal
Insect-inspired “bug” algorithms
Bug 1
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“Bug 1” algorithm
• known direction to goal
• otherwise only local sensing
walls/obstacles encoders
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
Insect-inspired “bug” algorithms
Vladimir Lumelsky & Alexander Stepanov Algorithmica 1987
Bug 1
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Distance Traveled What are bounds on the path
length that the robot takes?
Lower and upper bounds?
Available Information:
D = straight-line distance from start to goal
Pi = perimeter of the i th obstacle
Lower bound:
Upper bound:
Bug 1 analysis
CS-417 Introduction to Robotics and Intelligent Systems 23
D
P1
P2
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Distance Traveled What are bounds on the path
length that the robot takes?
Lower and upper bounds?
Available Information:
D = straight-line distance from start to goal
Pi = perimeter of the i th obstacle
Lower bound: D
Upper bound:
Bug 1 analysis
CS-417 Introduction to Robotics and Intelligent Systems 24
D
P1
P2
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Distance Traveled What are bounds on the path
length that the robot takes?
Lower and upper bounds?
Available Information:
D = straight-line distance from start to goal
Pi = perimeter of the i th obstacle
Lower bound: D
Upper bound: D + 1.5 Pii
How good a bound?
How good an algorithm?
Bug 1 analysis
CS-417 Introduction to Robotics and Intelligent Systems 25
D
P1
P2
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Bug Mapping
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“Bug 2” algorithmCall the line from the starting
point to the goal the s-line
A better bug?
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“Bug 2” algorithmCall the line from the starting
point to the goal the s-line
1) head toward goal on the s-line
A better bug?
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“Bug 2” algorithmCall the line from the starting
point to the goal the s-line
1) head toward goal on the s-line
2) if an obstacle is in the way,
follow it until encountering the s-
line again.
A better bug?
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“Bug 2” algorithm
1) head toward goal on the s-line
2) if an obstacle is in the way,
follow it until encountering the s-
line again.
3) Leave the obstacle and continue
toward the goal
OK ?
s-line
A better bug?
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“Bug 2” algorithm
1) head toward goal on the s-line
2) if an obstacle is in the way,
follow it until encountering the s-
line again closer to the goal.
3) Leave the obstacle and continue
toward the goal
OK ?
A better bug?
CS-417 Introduction to Robotics and Intelligent Systems 31
Goal
Start
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Distance Traveled What are bounds on the path
length that the robot takes?
Lower and upper bounds?
Available Information:
D = straight-line distance from start to goal
Pi = perimeter of the i th obstacle
Lower bound:
Upper bound:
Bug 2 analysis
CS-417 Introduction to Robotics and Intelligent Systems 32
Goal
Start
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Distance Traveled What are bounds on the path
length that the robot takes?
Lower and upper bounds?
Available Information:
D = straight-line distance from start to goal
Pi = perimeter of the i th obstacle
Lower bound:
Upper bound:
Ni = number of s-line intersections
with the i th obstacle
Bug 2 analysis
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Goal
Start
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Distance Traveled What are bounds on the path
length that the robot takes?
Lower and upper bounds?
Available Information:
D = straight-line distance from start to goal
Pi = perimeter of the i th obstacle
Lower bound: D
Upper bound:
Ni = number of s-line intersections
with the i th obstacle
Bug 2 analysis
CS-417 Introduction to Robotics and Intelligent Systems 34
Goal
Start
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Distance Traveled What are bounds on the path
length that the robot takes?
Lower and upper bounds?
Available Information:
D = straight-line distance from start to goal
Pi = perimeter of the i th obstacle
Lower bound: D
Upper bound: D + 0.5 Ni Pi
Ni = number of s-line intersections
with the i th obstacle
i
Bug 2 analysis
CS-417 Introduction to Robotics and Intelligent Systems 35
Goal
Start
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head-to-head comparison
What are worlds in which Bug 2 does
better than Bug 1 (and vice versa) ?
Bug 2 beats Bug 1
or thorax-to-thorax, perhaps
Bug 1 beats Bug 2
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head-to-head comparison
What are worlds in which Bug 2 does
better than Bug 1 (and vice versa) ?
Bug 2 beats Bug 1
or thorax-to-thorax, perhaps
Bug 1 beats Bug 2
CS-417 Introduction to Robotics and Intelligent Systems 37
“zipper world”
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Other bug-like algorithms
The Pledge maze-solving algorithm 1. Go to a wall
2. Keep the wall on your right
3. Continue until out of the maze
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Other bug-like algorithms
The Pledge maze-solving algorithm 1) Go to a wall
2) Keep the wall on your right
3) Continue until out of the maze
mazes of unusual origin
int a[1817];main(z,p,q,r){for(p=80;q+p-80;p=2*a[p])
for(z=9;z--;)q=3&(r=time(0)+r*57)/7,q=q?q-1?q-2?1-p%79?-
1:0:p%79-77?1:0:p<1659?79:0:p>158?-
79:0,q?!a[p+q*2]?a[p+=a[p+=q]=q]=q:0:0;for(;q++-
1817;)printf(q%79?"%c":"%c\n"," #"[!a[q-1]]);}
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###############################################################################
IOCCC random maze generator
discretized RRT39CS-417 Introduction to Robotics and Intelligent Systems
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Tangent Bug
• Limited Range Sensor
• Tangent Bug relies on finding endpoints of finite, continues segments of the obstacles
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Tangent Bug
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Contact Sensor Tangent Bug
1. Robot moves toward goal until it hits obstacle 1 at H12. Pretend there is an infinitely small sensor range and the direction which
minimizes the heuristic is to the right3. Keep following obstacle until robot can go toward obstacle again4. Same situation with second obstacle5. At third obstacle, the robot turned left until it could not increase heuristic6. D_followed is distance between M3 and goal, d_reach is distance between
robot and goal because sensing distance is zero
42CS-417 Introduction to Robotics and Intelligent Systems
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Limited Sensor Range Tangent-Bug
43CS-417 Introduction to Robotics and Intelligent Systems
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Infinite Sensor Range Tangent Bug
44CS-417 Introduction to Robotics and Intelligent Systems