  Let $\Omega$ in $R^M$ be a compact connected $M$-dimensional real analytic
domain with boundary and $\phi$ be a primal navigation function; i.e. a real
analytic Morse function on $\Omega$ with a unique minimum and with minus
gradient vector field $G$ of $\phi$ on the boundary of $\Omega$ pointed inwards
along each coordinate. Related to a robotics problem, we define a sequential
hybrid process on $\Omega$ for $G$ starting from any initial point $q_0$ in the
interior of $\Omega$ as follows: at each step we restrict ourselves to an
affine subspace where a collection of coordinates are fixed and allow the other
coordinates change along an integral curve of the projection of $G$ onto the
subspace. We prove that provided each coordinate appears infinitely many times
in the coordinate choices during the process, the process converges to a
critical point of $\phi$. That critical point is the unique minimum for a dense
subset in primal navigation functions. We also present an upper bound for the
total length of the trajectories close to a critical point.
