Symbolic Derivation & Interactive Simulation with SymPy

Live demo

An interactive marimo notebook exploring Rufus Isaacs' foundational pursuit-evasion problem from his 1951 RAND Corporation research. Every equation is derived symbolically with SymPy, then brought to life through numerical simulation with interactive parameter sliders.

The Homicidal Chauffeur problem asks: Can a fast but clumsy car catch a slow but agile pedestrian? A pursuer (high speed, constrained turning radius) chases an evader (low speed, unlimited maneuverability) on an unbounded plane — a canonical model for missile guidance, UAV pursuit, and autonomous vehicle collision avoidance.

• Problem history — Isaacs, RAND, and the torpedo-vs-ship origin (1951)
• Absolute & reduced kinematics — 5-DOF dynamics reduced to a 2-DOF body-frame system
• Differential game formulation — zero-sum structure, value function, Hamilton-Jacobi-Isaacs PDE
• Hamiltonian & optimal controls — symbolic derivation of bang-bang pursuer and gradient-aligned evader strategies
• Costate equations — adjoint system, costate norm conservation proof
• Singular surfaces — Merz's taxonomy: dispersal, universal, equivocal, and focal lines
• Numerical trajectory simulation — interactive sliders for evader speed, turn rate, and capture radius
• Backward reachable sets — isochrones computed via method of characteristics
• Verification & validation — 20 automated tests (symbolic + numerical) cross-checking the derivations

Requires Python >= 3.10 and uv.

git clone https://github.com/mzargham/hc-marimo.git
cd hc-marimo
uv sync
uv run marimo edit homicidal_chauffeur.py

For read-only app mode (sliders work, code hidden):

uv run marimo run homicidal_chauffeur.py

marimo, SymPy, NumPy, SciPy, matplotlib — see pyproject.toml for pinned versions.

• R. Isaacs, Games of Pursuit, RAND Corporation P-257 (1951)
• R. Isaacs, Differential Games, John Wiley & Sons (1965), pp. 297–350
• A.W. Merz, The Homicidal Chauffeur — a Differential Game, PhD Thesis, Stanford (1971)
• V.S. Patsko & V.L. Turova, "Homicidal Chauffeur Game: History and Modern Studies," Advances in Dynamic Games, Annals of the ISDG Vol. 11 (2011)
• S. Coates & M. Pachter, "The Classical Homicidal Chauffeur Game," Dynamic Games and Applications 9(1), 2019