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This paper extends the capabilities of the harmonic potential field approach to planning to cover the situation where the workspace of a robot cannot be segmented into geometrical subregions each having an attribute of its own. Instead, a task-centered, probabilistic descriptor of the workspace is used as an input. This descriptor is processed along with a goal point to yield the navigation policy. The approach is also used for planning in a cluttered environment containing a vector drift field that influences the ability of an agent to alter its state. The planner can guide the agent to a target zone, avoid clutter and marginalize the influence of drift on motion or exploit its presence in carrying out a task. The extension is based on the physical analogy with an electric current flowing in a nonhomogeneous conducting medium. Proofs of the ability of the modified approach to avoid zero-probability (definite threat) regions and converge to the goal are provided. The capabilities of the planner are demonstrated using simulation.