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

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

• phiSingleState - calculates the required phi to reach the evader using a single snapshot (issues with arctan2 range wrap)
• phiThetaHistory - calculates the required phi to reach the evader using previous theta history (solves the arctan2 wrap issue)
• phiPerturb - simple method based on phiThetaHistory but handles a detected loop by perturbing the pursuer phi

Evader strategies

• psiRandom - random direction changes every 20 steps
• psiTurn90 - every 5 steps, calculates new psi that is 90 degrees from a line drawn from pursuer to evader. Left vs right turn is handled depending on pursuer heading.

Current winning strategy: phiPerturb beats all pursuer methods
Caveat: this may be because of a flaw in the psiTurn90 algorithm

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.
• Running instructions (overall run with python3 main.py):
  • runAllSim runs all methods against each other and outputs results
  • runSim runs a specific method
  • animate.animate allows for animated python figure
• To-Do: rewrite using object oriented programming