1. Pursuit and Evasion CS326A: Motion Planning Spring 2003 Final Project Eric Ng Huy Nguyen

2. Introduction Problem description:  Pursuer – find an adversarial target within an environment  Evader – avoid discovery by a pursuer within an environment  Omnidirectional visibility - line of sight blocked only by walls  Visibility capture – Pursuer “wins” if, at any point, the Evader is contained within its visibility polygon Problem described in [ LaValle, et al. 1997 ], but evasion strategy is not addressed Evaluate performance by providing victory conditions for Evader  Exit – Evader reaches exit before being discovered  Time Expired – Evader can avoid being discovered for a finite amount of time

3. Evader Strategies Dense PRM provides Evader many path choices for reaching goals  Try to connect each point added to PRM to every other point Shortest Euclidean distance to goal  Simulates a “panic” response  Weight edges in PRM by Euclidean distance Lowest visibility path to goal  Simulates a “cautious” response  Weight edges by area of visibility polygon at midpoint

4. Pursuer Strategies Since there is only one Pursuer, it is not guaranteed to find the Evader, so we can’t use [ LaValle, et al. 1997 ] directly Since the Pursuer can’t always clear the map, how should it move?  Define helpful goals Patrol exits  Use heuristics to explore map Bias towards exploration of new territory Greedy free-edge decontamination

5. Pursuer Strategies Patrol exits  Patrol policy Touch Exit – Touch each exit See Exit – Only move far enough to see the exit  Path planning Lowest Visibility using dense PRM – try to find Evader by matching his likely strategy Medial-Axis – move along medial axis to maximize visibility along path Greedy Free-Edge Decontamination

6. 1) Perform cell decomposition as described in [LaValle, et al. 1997] to define critical points where free edges in the visibility polygon change 2) Sample a grid over the visibility polygon at the current location 3) Move to sampled point, updating the contamination values of the visibility polygons at each intersection with the cell decomposition 4) Move back to starting location, updating contamination values 5) Select the best point based on the “change in knowledge” about contamianted free edges, breaking ties by biasing towards unexplored areas 6) Can recursively repeat 2-5 from the second point, etc. to generate a multistep path

7. Step 1) Generate cell decomposition

8. Step 2) Sample the visibility polygon

9. Steps 3-5 sampled point Although the visible area is greater at the sampled point on the bottom, moving to the sampled point at the top results in two decontaminated edges, so the top point will be preferred.

10. Change in Knowledge The topology of a visibility polygon changes as the agent moves, but not all of those changes are informative Uninformative changes  Obstacle edges becoming decontaminated free edges  Two decontaminated (or two contaminated) edges merging  A decontaminated (or contaminated) edge splitting

11. Change in Knowledge Informative changes Type 1: Contaminated edge becoming an obstacle edge Type 2: Contaminated edge merging with uncontaminated edges Track informative changes to determine quality of path  Paths with many Type 1 changes are good  Paths with many Type 2 changes are bad

12. Results By patrolling exits, the pursuer is able to capture the evader most of the time. Decontamination strategy is less successful, because it tends to cover less area in the same period of time. Least visibility pathways appear to be promising in “cluttered” maps which offer low visibility regions. This allows the evader to safely maneuver to an exit without being caught.

13. Future Work Evader strategy technique: blend of “shortest distance to goal” and “low visibility path”. Multi-Pursuer/Evader Strategies Capture by touch vs vision Agents having limited viewing angles