Geometric Probing with Light Beacons on Multiple Mobile Robots Sarah Bergbreiter CS287 Project Presentation May 1, 2002

Outline My Motivation Previous Work Problem Statement Algorithm Results and Analysis Conclusions and Future Work

Motivation: COTS-BOTS and Micro-robots Micro-robot fabricated using MEMs techniques (8mm x 3mm) Goal: Keep both robot platforms SIMPLE! Cots-Bots use off-the-shelf components to create an inexpensive, modular robot platform

Outline My Motivation Previous Work Problem Statement Algorithm Results and Analysis Conclusions and Future Work

Previous Work – Geometric Probing Originally associated with the problem of robot grasping – finger probes move toward the polygon on line L until contact at point p Extension to line probes where line slides over plane until contact with object Geometric Probe makes simple measurements to find location, size, and shape of an object L p Line Probe Finger Probe

Previous Work – Geometric Probes and Robots Finger probe model is similar to an exact sonar or laser range measurement (theory provides lower bounds on what is needed) Rekleitis, et al. have used two robots to sweep an environment using a camera to maintain line of sight But... We want to keep things even simpler than this (RISC robotics)

Outline My Motivation Previous Work Problem Statement Algorithm Results and Analysis Conclusions and Future Work

Problem Statement Given a polygonal obstacle and line of sight connectivity between mobile robots, define the obstacle Obstacle Line of Sight Connectivity Reconstructed Polygon

Why is this interesting? Only sensor required is light beacon (simple to implement on something of micro-robot size) Obstacle representation does not depend on surface properties of obstacle, camera calibration, etc.

Definitions Light Beacon is an omni-directional transmitter/receiver to determine line of sight Envelope Polygon is a polygon completely enclosing the obstacle polygon Tangent Line is a line segment which is tangent to the obstacle (at vertex or edge)

Assumptions (1) Polygon is a convex n-gon, n >= 3 (2) Beacons are infinitely powerful (can be detected at any distance) (3) Robots start far enough away so that minimum bounding circle and enclosing envelope do not intersect obstacle

Outline My Motivation Previous Work Problem Statement Algorithm Results and Analysis Conclusions and Future Work

Algorithm (1)(2)(3) (4)(5)

Algorithm Define min bounding circle Line of sight? Move robot on circle until visible # envelope vertices > 0 vertex(0) tangent? Envelope Poly Defined remove vertex from envelope, add to poly reduce envelope by adding intersection pts Done. The polygon has been defined No Yes DEMO!

Performance Metrics Accuracy: Measure displaced area normalized by area of obstacle Speed: Measure distance traveled (in radians) – did not implement

Outline My Motivation Previous Work Problem Statement Algorithm Results and Analysis Conclusions and Future Work

Simulation Results Used randomly placed robots to probe a fixed object (square, pentagon, etc) Performed each experiment 20 times for 3-6 robots

Multiple Robots Probing a Square

Multiple Robots Probing a Pentagon

Where do the errors come from? In the implementation, the robots take 2 o steps during each move – leads to numerical errors in finding vertices If vertex is close to obstacle (but not actually on the obstacle), it could still show up as tangent depending on how robot probe moves to check it

Analysis Error is maximum when robots = obstacle vertices. – perhaps less maneuverability to check tangent points Error decreases as robots increase (from number of obstacle vertices) Error decreases as robots decrease (from number of obstacle vertices)

Outline My Motivation Previous Work Problem Statement Algorithm Results and Analysis Conclusions and Future Work

Simple robot sensors are feasible for complex task of reconstructing a polygonal obstacle Would like to examine influence of odometry (position) error on outcome Remove assumption 3 (would likely have to add a collision sensor) Could use a better implementation of checking tangency, etc. in simulation