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