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Legged Locomotion Planning. Kang Zhao B659 Intelligent Robotics Spring 2013. Planning Biped Navigation Strategies in Complex Environments Joel Chestnutt , James Kuffner , Koichi Nishiwaki , Satoshi Kagami. Global terrain map M Goal Primitive set {Trans} Search algorithm. - PowerPoint PPT Presentation
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Legged Locomotion Planning
Kang ZhaoB659 Intelligent RoboticsSpring 2013
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Planning Biped Navigation Strategies in Complex Environments• 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 θ: position and orientation relative to {U}
O One-step motion destination
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Algorithm- State transitionsO Footstep transition
…
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
𝑉= 𝑓 (𝑄 ,𝑇 ,𝑄𝑐 ,𝑄𝑔)Location metric to
evaluate a location’s cost
𝐿𝑖={ 𝐿𝑖 (𝑄 )∞ 𝑖𝑓 𝐿𝑖 (𝑄 )>𝐿𝑖
𝑙𝑖𝑚𝑖𝑡, 𝑖=1…5
𝐿 (𝑄 )=∑𝑤𝑖𝐿𝑖
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.
1𝑁 ∑
𝑐∈𝐶¿𝑐 . h h𝑒𝑖𝑔 𝑡−h (𝑐 . 𝑥 ,𝑐 . 𝑦 )∨¿¿
max {𝑐 . h h𝑒𝑖𝑔 𝑡−h (𝑐 . 𝑥 ,𝑐 . 𝑦 )∨𝑐∈𝐶 }
It’s 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
𝑆 (𝑄 ,𝑇 ,𝑄𝑐 )=𝑇 .𝑐𝑜𝑠𝑡+𝑤h∨𝐻 (𝑄 ,𝑄𝑐 )∨¿
Cost of transition
• Penalty for height change• Collision check
𝑄𝑐=𝑇 (𝑄 )𝐻={ 𝐻 (𝑄 ,𝑄𝑐 )
∞ 𝑖𝑓 𝐻 (𝑄 ,𝑄𝑐 )>𝐻❑𝑙𝑖𝑚𝑖𝑡
𝑉= 𝑓 (𝑄 ,𝑇 ,𝑄𝑐 ,𝑄𝑔)
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Algorithm- State Evaluation
Heuristic metric to evaluate
remaining cost
𝑅 (𝑄 ,𝑄𝑔)=𝑤𝑑𝐷 (𝑄 ,𝑄𝑔 )+𝑤𝜃|Ɵ (𝑄 ,𝑄𝑔 )|+𝑤h∨𝐻 (𝑄 ,𝑄𝑔 )∨¿
Euclidean distance Relative angle Height
difference
𝑉= 𝑓 (𝑄 ,𝑇 ,𝑄𝑐 ,𝑄𝑔) 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
“good” each search node isO An evaluation function maps each node of
the search tree to a real number
O Greedy BFS
𝑅 (𝑄 ,𝑄𝑔)
h (𝑁 )=𝑅 (𝑄 ,𝑄𝑔)
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A* Search
h (𝑁 )=𝑅 (𝑄 ,𝑄𝑔)
𝑅 (𝑄 ,𝑄𝑔)
𝐿 (𝑄𝑐 )+∑ 𝑆 (𝑄𝑖 ,𝑇 ,𝑄𝑐)
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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ComparisonsO 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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𝑅 (𝑄 ,𝑄𝑔)=𝑤𝑑𝐷 (𝑄 ,𝑄𝑔 )+𝑤𝜃|Ɵ (𝑄 ,𝑄𝑔 )|+𝑤h∨𝐻 (𝑄 ,𝑄𝑔 )∨¿
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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 workO 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 Robots• Tim Bretl, Sanjay Lall,
Jean-Claude Latombe, Stephen Rock
