Reachability Subspace Exploration Using Continuation Methods

Reachability manifold computation suffers from the curse of dimensionality and for large state spaces is computationally intractable. This paper examines the use of continuation methods to address this issue by formulating the reachability sub-space manifold calculation into a number of initial valued problems. As a result of computing the reachability manifold for a subspace of interest, an exponential improvement in computational cost occurs. This concept is applied to a position subspace reachability problem of a spacecraft in a Keplerian orbit under maximum thrust constraints. Future work includes a comparison of the proposed method with computing reachability manifolds using viscosity solutions of the Hamilton Jacobi Bellman partial differential equation.