  This paper extends the capabilities of the harmonic potential field (HPF)
approach to planning. The extension covers the situation where the workspace of
a robot cannot be segmented into geometrical subregions where each region has
an attribute of its own. The suggested approach uses a task-centered,
probabilistic descriptor of the workspace as an input to the planner. This
descriptor is processed, along with a goal point, to yield the navigation
policy needed to steer the agent from any point in its workspace to the target.
The approach is easily adaptable to planning in a cluttered environment
containing a vector drift field. The extension of the HPF approach is based on
the physical analogy with an electric current flowing in a nonhomogeneous
conducting medium. The resulting potential field is known as the gamma-harmonic
potential (GHPF). Proofs of the ability of the modified approach to avoid
zero-probability (definite threat) regions and to converge to the goal are
provided. The capabilities of the planer are demonstrated using simulation.
