On the numerical solution of a free end-time homicidal chauffeur game

A functional formulation of the classical homicidal chauffeur Nash game is presented and a numerical framework for its solution is discussed. This methodology combines a Hamiltonian based scheme with proximal penalty to determine the time horizon where the game takes place with a Lagrangian optimal control approach and relaxation to solve the Nash game at a fixed end-time.

A Partitioning Scheme for a Switched Feedback Control Law in Two Agent Pursuit-Evasion Scenarios

A switched feedback control law is derived for an autonomous pursuing agent that attempts to intercept an evading agent whose dynamics are initially unknown. The model of the pursuer’s dynamics is known perfectly, and the evader is modeled as a disturbance. A new method is presented to efficiently update the pursuer’s control law as measurements of the parameters that govern the evader’s dynamics are received. Using a graph theoretical approach, the control law updates are limited to specific partitions of the state space, which eliminate many unneeded calculations. Results show increases in the time efficiency of the update calculations compared to traditional control law generation methods with a minimal loss in accuracy. An 11.6% overall decrease in calculation time over traditional methods and a 1% error rate compared to the true solution is achieved when solving the homicidal chauffeur game. We show how actual gains in time efficiency depend on the specific application of the controller and the size of the state space grid approximation. Both the theoretical development and implementation of the switched feedback controller are discussed.