Real-Time Tracking of an Unpredictable Target Amidst Unknown Obstacles Cheng-Yu Lee Hector Gonzalez-Baños* Jean-Claude Latombe Computer Science Department Stanford University * Honda’s Fundamental Research Labs, Mountain View, CA, USA

The Problem observer target observer target 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: Pure visual servoing

Corner Example: Anticipating Occlusion

Corner Example

Related 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 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 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 Algorithm Acquire visibility region / Locate target Compute shortest escape paths Associate risk with every shortest escape path and compute risk gradient Compute motion command as recursive average of risk gradients

Target Acquisition of Visibility Region + Target Localization

Acquisition of Visibility Region

Steps of Tracking Algorithm Acquire visibility region / Locate target Compute shortest escape paths Associate risk with every shortest escape path and compute risk gradient Compute motion command as recursive average of risk gradients

observer target Shortest Escape Paths (Escape-Path Tree)

Steps of Tracking Algorithm Acquire visibility region / Locate target Compute shortest escape paths Associate risk with every shortest escape path and compute risk gradient Compute motion command as recursive average of risk gradients

Initial Risk-Based Strategy v e observer target Risk = 1/length of shortest escape path

v p e observer target e’ p’ Initial Risk-Based Strategy Risk = 1/length of shortest escape path

v p e observer target e” p”  i Improved Risk-Based Strategy reactive component look-ahead component

v e observer target Improved Risk-Based Strategy (other case) look-ahead component

Generic Risk Function v e observer target r h f(1/h) = ln ( + 1) h2h2h2h2 1  = = = =c r2r2r2r2 f(1/h) reactive look-ahead

Steps of Tracking Algorithm Acquire visibility region / Locate target Compute shortest escape paths Associate risk with every shortest escape path and compute risk gradient Compute motion command as recursive average of risk gradients

observer target Global Risk = Recursive Average Over Escape-Path Tree

Example

Steps of Tracking Algorithm Acquire visibility region / Locate target Compute shortest escape paths Associate risk with every shortest escape path and compute risk gradient Compute motion command as recursive average of risk gradients 0.1s

Adjustments for Real Robot Observer and target are modeled as disks Observer’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 Obstacles

Conclusion Observer successfully tracks swift targets despite paucity of its sensor Fast computation of escape-path tree and risk gradient (control rate is ~ 10Hz) Obvious potential improvement: Add camera for better target detection Future work: Multiple observers and multiple targets, more dynamic environments

Example