legged locomotion planning kang zhao b659 intelligent robotics spring 2013 1
TRANSCRIPT
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Legged Locomotion Planning
Kang ZhaoB659 Intelligent RoboticsSpring 2013
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Planning Biped Navigation Strategies in Complex Environmentsโข Joel Chestnutt, James
Kuffner, Koichi Nishiwaki, Satoshi Kagami
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O Global terrain map MO GoalO Primitive set {Trans}O Search algorithm
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Algorithm - Biped Robot ModelO State:
O ฮธ: position and orientation relative to {U}
O One-step motion destination
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Algorithm- State transitionsO Footstep transition
โฆ
0
1
2 34
5 6
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A 16-transitions set
Branching factor
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Algorithm- EnvironmentO Terrain map
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Algorithm- State Evaluation
๐= ๐ (๐ ,๐ ,๐๐ ,๐๐)Location metric to
evaluate a locationโs cost
๐ฟ๐={ ๐ฟ๐ (๐ )โ ๐๐ ๐ฟ๐ (๐ )>๐ฟ๐
๐๐๐๐๐ก, ๐=1โฆ5
๐ฟ (๐ )=โ๐ค๐๐ฟ๐
Slope angle
Roughness
Stability
Largest bump
Safety
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Slope angle
Roughness
Stability
Largest bump
Safety
The slope angle of the surface at the candidate location. Perfectly horizontal surfaces are desired. The slope angle is computed by fitting a plane h(x, y) to the cells in the location.
1๐ โ
๐โ๐ถ
ยฟ๐ . h h๐๐๐ ๐กโh (๐ . ๐ฅ ,๐ . ๐ฆ )โจยฟยฟ
max {๐ . h h๐๐๐ ๐กโh (๐ . ๐ฅ ,๐ . ๐ฆ )โจ๐โ๐ถ }
Itโs purpose is to take into account the possible inaccuracy of foot positioning. This can be computed using the roughness and largest bump metrics, using the cells around the foot location
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Algorithm- State Evaluation
Step metric to evaluate cost
of taking a step
๐ (๐ ,๐ ,๐๐ )=๐ .๐๐๐ ๐ก+๐คhโจ๐ป (๐ ,๐๐ )โจยฟ
Cost of transition
โข Penalty for height changeโข Collision check
๐๐=๐ (๐ )๐ป={ ๐ป (๐ ,๐๐ )
โ ๐๐ ๐ป (๐ ,๐๐ )>๐ปโ๐๐๐๐๐ก
๐= ๐ (๐ ,๐ ,๐๐ ,๐๐)
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Algorithm- State Evaluation
Heuristic metric to evaluate
remaining cost
๐ (๐ ,๐๐)=๐ค๐๐ท (๐ ,๐๐ )+๐ค๐|ฦ (๐ ,๐๐ )|+๐คhโจ๐ป (๐ ,๐๐ )โจยฟ
Euclidean distance Relative angle Height
difference
๐= ๐ (๐ ,๐ ,๐๐ ,๐๐) The heuristic function estimates the cost to go from to a goal state
Its value is independent of the current search tree; it depends only on and the goal
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Best First SearchO It exploits state description to estimate how
โgoodโ each search node isO An evaluation function maps each node of
the search tree to a real number
O Greedy BFS
๐ (๐ ,๐๐)
h (๐ )=๐ (๐ ,๐๐)
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A* Search
h (๐ )=๐ (๐ ,๐๐)
๐ (๐ ,๐๐)
๐ฟ (๐๐ )+โ ๐ (๐๐ ,๐ ,๐๐)
Search tree
Searching the State SpaceA schematic view
Q s
Q g
Search tree
Searching the State SpaceA schematic view
Q s
Q g
T 1
T 2
Search tree
Searching the State SpaceA schematic view
Q s
Q g
Search tree
Searching the State SpaceA schematic view
Q s
Q g
Search tree
Searching the State SpaceA schematic view
Q s
Q g
Search tree
Searching the State SpaceA schematic view
Q s
Q g
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ResultsO Cluttered terrain
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ResultsO Multi-level terrain
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ResultsO Uneven ground with obstacles
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Comparisons
O Distance to goalO Transitions and obstacle effectsO Metric weights
23A 26-transitions set
A 40-transitions set BFS
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Performance comparison of A* and BFS for increasing numbers of stairs along the path
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๐ (๐ ,๐๐)=๐ค๐๐ท (๐ ,๐๐ )+๐ค๐|ฦ (๐ ,๐๐ )|+๐คhโจ๐ป (๐ ,๐๐ )โจยฟ
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Local-minimum problem
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Online Experiments
Stereo vision system
PlannerFootstep sequence
Trajectory generator
Walking area map
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Following work
O A tired planning Strategy for biped navigation, 2004O Biped navigation in rough environments using
on-board sensing, 2009
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Multi-Step Motion Planning for Free-climbing Robotsโข Tim Bretl, Sanjay Lall,
Jean-Claude Latombe, Stephen Rock