Lecture6 - KAISTsglab.kaist.ac.kr/~sungeui/MPA/Slides/Lecture6.pdf · 2019. 10. 15. · Microsoft...
Transcript of Lecture6 - KAISTsglab.kaist.ac.kr/~sungeui/MPA/Slides/Lecture6.pdf · 2019. 10. 15. · Microsoft...
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CS686:RRT
Sung-Eui Yoon(윤성의)
Course URL:http://sgvr.kaist.ac.kr/~sungeui/MPA
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Class Objectives● Understand the RRT technique and its
recent advancements● RRT*● Kinodynamic planning
● Last time● Probabilistic roadmap techniques● Sampling and re-sampling techniques
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Question● PRM assumes that we know the global
map, but how can we handle the case where we have only a partial map due to the limited sensor range?● 지난시간에 배운 PRM 기법들은 글로벌 맵을 알고
있어야 문제 해결이 가능한데, 전체 맵의 일부분(센서탐지거리 제약 등으로)만을 알고 있는 상황에서PRM알고리즘을 적용하려면 어떤 방식으로 해야하는지요?
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Rapidly-exploring Random Trees (RRT) [LaValle 98]● Present an efficient randomized path
planning algorithm for single-query problems● Converges quickly● Probabilistically complete● Works well in high-dimensional C-space
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Rapidly-Exploring Random Tree● A growing tree from an initial state
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RRT Construction Algorithm● Extend a new vertex in each iteration
● Alternatively, one can simply connect
qinit
ε
qqnear
qnew
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Overview – Planning with RRT● Extend RRT until a nearest vertex is close
enough to the goal state● Can handle nonholonomic constraints and high
degrees of freedom
● Probabilistically complete, but does not converge to the optimal one
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RRT Construction Algorithm
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Voronoi Region● An RRT is biased by large Voronoi regions
to rapidly explore, before uniformly covering the space
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Overview – With Dual RRT● Extend RRTs from both initial and goal
states● Find path much more quickly
737 nodes are used
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● Aggressively connect the dual trees using a greedy heuristic
● Extend & connect trees alternatively
Overview – With RRT-Connect
42 nodes are used
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RRT*● RRT does not converge to the optimal
solution
RRT
RRT*
From Sertac’s homepage
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RRT*- Asymptotically optimal without a substantial
computational overhead
- YnRRT* : cost of the best path in the RRT*
- c* : cost of an optimal solution- Mn
RRT : # of steps executed by RRT at iteration n- Mn
RRT*: # of steps executed by RRT* at iteration nFrom DH’s homepage
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Key Operation of RRT*● RRT
● Just connect a new node to its nearest neighbor node
● RRT*: refine the connection with re-wiring operation● Given a ball, identify neighbor nodes to the
new node● Refine the connection to have a lower cost
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Example: Re-Wiring Operation
From ball tree paper
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Example: Re-Wiring Operation
Generate a new sample
From ball tree paper
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Example: Re-Wiring Operation
Identify nodes in a ball
From ball tree paper
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Example: Re-Wiring Operation
Identify which parent gives the lowest cost
From ball tree paper
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Example: Re-Wiring Operation
From ball tree paper
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Example: Re-Wiring Operation
Identify which child gives the lowest cost
From ball tree paper
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Example: Re-Wiring Operation
From ball tree paper
Video showing benefits with real robot
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Kinodynamic Path Planning
● Consider kinematic + dynamic constraints
Gait and Trajectory Optimization for Legged Systems through Phase-based End-Effector Parameterization
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State Space Formulation● Kinodynamic planning → 2n-dimensional
state spacespace thedenote C-C
space state thedenote X
XxCqqqx ∈∈= ,for ),,(
] [ 2121 dt
dqdt
dqdtdqqqqx n
n =
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Constraints in State Space
● Constraints can be written in:nm,m,i
xxGqqqh ii
2 and 1for ,0),( becomes 0),,(
<===
),( uxfx =
inputsor controls allowable ofSet : , UUu ∈
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Rapidly-Exploring Random Tree● Extend a new vertex in each iteration
qinit
qqnear
qnewu
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Results – 200MHz, 128MB● 3D translating● X=6 DOF● 16,300 nodes● 4.1min
● 3D TR+RO● X=12 DOF● 23,800 nodes● 8.4min
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RRT at work: Successful Parking Maneuver
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Some Works of Our Group● Narrow passages
● Identify narrow passage with a simple one-dimensional line test, and selectively explore such regions
● Selective retraction-based RRT planner for various environments, Lee et al., T-RO 14
● http://sglab.kaist.ac.kr/SRRRT/T-RO.html
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Retration-based RRT [Zhang & Manocha 08]
● Retraction-based RRT technique handling narrow passages
● General characteristic: Generates more samples near the boundary of obstacles
image from [Zhang & Manocha 08]
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RRRT: Pros and Cons
with narrow passages without narrow passagesimages from [Zhang & Manocha 08]
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RRRT: Pros and Cons
with narrow passages without narrow passagesimages from [Zhang & Manocha 08]
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Bridge line-test [Lee et al., T-RO 14]● To identify narrow passage regions
● Bridge line-test1. Generate a random line 2. Check whether the line meets any obstacle
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Results
Video
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Related Works of Our Group●Handling narrow passages ●Handling uncertainty and dynamic objects
● Anytime RRBT for handling uncertainty and dynamic objects, IROS 16
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Handling Sensor Errors● Uncertainty caused by:
● Various sensors● Low-level controllers
Sensor noise Controller noise
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Rapidly-exploring Random Belief Tree[Bry et al., ICRA 11]
Use Kalman filter to propagate Gaussian states Improve solutions toward optimal
Number of iteration
500 1000 1500Preserve optimal path
Multiple belief nodes in the same vertex
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Main Contribution: Anytime Extension [Yang et al.,IROS 16]
Measurement region
Goalregion
Bigger circle means higher uncertainty
The robot computes better path while
executing the path
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Main Contribution:Anytime Extension
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Velocity Obstacle:Local Geometric Analysis
“The hybrid reciprocal velocity obstacle” TRO11 J Snape, J van den Berg, SJ Guy“Reciprocal velocity obstacles for real-time multi-agent navigation” J van den Berg“Generalized Velocity Obstacles” IROS09, D Wilkie, J Van den Berg
• Used for collision avoidance among multiple robots• When v for Robot is in the VO, we will have collision
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Uncertainty-aware Velocity Obstacle as Local Geometry Analysis
Conservative collision checking
“The hybrid reciprocal velocity obstacle” TRO11 J Snape, J van den Berg, SJ Guy“Reciprocal velocity obstacles for real-time multi-agent navigation” J van den Berg“Generalized Velocity Obstacles” IROS09, D Wilkie, J Van den Berg
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Intersection scene – with UVO
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Class Objectives were:● Understand the RRT technique and its
recent advancements● RRT* for optimal path planning● Kinodynamic planning● Some related techniques to RRT
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Summary
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Next Time..● Basic concepts of reinforcement learning
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Homework for Every Class● Submit summaries of 2
ICRA/IROS/RSS/CoRL/TRO/IJRR papers● Go over the next lecture slides● Come up with three question before the mid-
term exam