Abstract-We describe and implement an algorithm for computing the set of reachable states of a continuous dynamic game. The algorithm is based on a proof that the reachable set is the zero sublevel set of the viscosity solution of a particular time-dependent Hamilton-Jacobi-Isaacs partial differential equation. While alternative techniques for computing the reachable set have been proposed, the differential game formulation allows treatment of nonlinear systems with inputs and uncertain parameters. Because the time-dependent equation's solution is continuous and defined throughout the state space, methods from the level set literature can be used to generate more accurate approximations than are possible for formulations with potentially discontinuous solutions. A numerical implementation of our formulation is described and has been released on the web. Its correctness is verified through a two vehicle, three dimensional collision avoidance example for which an analytic solution is available.
Numerical computation of the reachable sets of hybrid systems by means of partial differential equations REF has been applied to design and verify the safety of collision avoidance systems for which an analytic solution is available.
A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games
IEEE Transactions on Automatic Control
IEEE Transactions on Automatic Control
Computer Science Mathematics