/differential-games

Primary LanguagePython

Differential Games

Simulating differential games (specifically pursuit/evasion scenarios) using python.

Homicidal Chauffeur Problem - 2 Body Pursuit/Evasion

Differential equations

source: Fundamentals of Aerospace Navigation and Guidance by Kabamba & Girard

Differential equation solver
Python/Scipy solv_ivp or could implement as a discrete time system...

Player strategy ideas (for choosing heading angles)

  • Minimize/maximize distance
  • Move in tangential direction of attacker
  • Knowing previous history of other player or not
  • Neural network / machine learning for creating strategy using sklearn libraries (maybe...)

Pursuer strategies

  • phiCalcSingleState - calculates the required phi to reach the evader using a single snapshot (issues with arctan2 range wrap)
  • phiCalcThetaHistory - calculates the required phi to reach the evader using previous theta history (solves the arctan2 wrap issue)

Evader strategies

  • randomPsi - random direction changes every 20 steps

Algorithms

  1. Initialize with some set of parameters.
  2. Simulate first step using ODE solver.
  3. Choose heading angles using strategy.
  4. Repeat 2 and 3 until time runs our or collision occurs.

Notes

  • wavy behavior exhibited when using phiCalcSingleState is solved using np.unwrap with previous history in phiCalcThetaHistory
    • not sure if this is a bug or not: whenever the pursuer misses, it makes a loop.