real-time tracking of an unpredictable target amidst unknown obstacles cheng-yu lee hector...
Post on 19-Dec-2015
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Real-Time Tracking of an Real-Time Tracking of an Unpredictable Target Amidst Unpredictable Target Amidst
Unknown ObstaclesUnknown ObstaclesCheng-Yu Lee
Hector Gonzalez-Baños*Jean-Claude Latombe
Computer Science DepartmentStanford University
* Honda’s Fundamental Research Labs, Mountain View, CA, USA
The ProblemThe Problem
observertarget
observertarget
observer’s visibility region
Goal: Keep the target in field of view despite obstacles
• No prior map of workspace• Unknown target’s trajectory
Corner Example:Corner Example:Pure visual servoingPure visual servoing
Corner Example:Corner Example:Anticipating OcclusionAnticipating Occlusion
Corner ExampleCorner Example
Related ProblemsRelated Problems
Missile control Occlusions are not the main concern
Visual tracking, visual servo-control No attempt to exploit sensor’s mobility to avoid undesirable occlusions
Guarding an art gallery Many fixed sensors, instead of a moving one
Previous Similar WorkPrevious Similar Work
Off-line backchaining planning Offline game-theoretic planning Prior knowledge of workspace and target’s
trajectory
On-line game-theoretic planning Probabilistic model of target’s behavior Prior knowledge of workspace Localization issue Computationally intensive
Multi-observer/Multi-target case
Our Risk-Based ApproachOur Risk-Based Approach
Observer’s visibility region is obtained by sensing No prior model of workspace No localization issue Tolerance to transient objects
At each step observer minimizes the risk that target may escape its visibility region No prior model of the target’s behavior
Risk combines a reactive and a look-ahead term Works well with aggressive targets
Steps of Tracking AlgorithmSteps of Tracking Algorithm
Acquire visibility region / Locate target
Compute shortest escape paths
Associate risk with every shortest escape pathand compute risk gradient
Compute motion command as recursive averageof risk gradients
Target
Acquisition of Visibility Acquisition of Visibility RegionRegion
+ Target Localization+ Target Localization
Acquisition of Visibility Acquisition of Visibility RegionRegion
Acquisition of Visibility Acquisition of Visibility RegionRegion
Steps of Tracking AlgorithmSteps of Tracking Algorithm
Acquire visibility region / Locate target
Compute shortest escape paths
Associate risk with every shortest escape pathand compute risk gradient
Compute motion command as recursive averageof risk gradients
observer
target
Shortest Escape PathsShortest Escape Paths
(Escape-Path Tree)(Escape-Path Tree)
Steps of Tracking AlgorithmSteps of Tracking Algorithm
Acquire visibility region / Locate target
Compute shortest escape paths
Associate risk with every shortest escape pathand compute risk gradient
Compute motion command as recursive averageof risk gradients
Initial Risk-Based StrategyInitial Risk-Based Strategy
v
e
observer
target
Risk = 1/length of shortest escape path
v
p
e
observer
targete’
p’
Initial Risk-Based StrategyInitial Risk-Based Strategy
Risk = 1/length of shortest escape path
v
p
e
observer
targete”
p”
i
Improved Risk-Based Improved Risk-Based StrategyStrategy
reactive component
look-ahead component
v
e
observer
target
Improved Risk-Based Improved Risk-Based StrategyStrategy
(other case)(other case)
look-ahead component
Generic Risk FunctionGeneric Risk Function
v
e
observer
target
r
h
f(1/h)f(1/h) = = lnln ( + ( + 1) 1) hh22
11
= = c c rr22 f(1/h)
reactivelook-ahead
Steps of Tracking AlgorithmSteps of Tracking Algorithm
Acquire visibility region / Locate target
Compute shortest escape paths
Associate risk with every shortest escape pathand compute risk gradient
Compute motion command as recursive averageof risk gradients
observer
target
Global Risk = Recursive Global Risk = Recursive Average Over Escape-Path Average Over Escape-Path
Tree Tree
ExampleExample
Steps of Tracking AlgorithmSteps of Tracking Algorithm
Acquire visibility region / Locate target
Compute shortest escape paths
Associate risk with every shortest escape pathand compute risk gradient
Compute motion command as recursive averageof risk gradients
0.1s
Adjustments for Real RobotAdjustments for Real Robot
Observer and target are modeled as disksObserver’s sensor has limited range (8m) and scope (180dg)Observer is nonhololomic with zero turning radius
Imagine yourself tracking a moving target in an unknown environment using
a flashlight projecting only a plane of light!
Transient ObstaclesTransient Obstacles
ConclusionConclusion
Observer successfully tracks swift targets despite paucity of its sensorFast computation of escape-path tree and risk gradient (control rate is ~ 10Hz)Obvious potential improvement: Add camera for better target detectionFuture work: Multiple observers and multiple targets, more dynamic environments
ExampleExample