Sensor-based discovery path planning is problematic because the path needs to be continually recomputed as new information is discovered. A process-based clientserver approach is presented that permits concurrent sensor-based map and localization-correction updates as well as concurrent path computation and execution. Laplace’s equation is constantly solved (i.e., a harmonic function) by using an iteration kernel convolved with an occupancy-grid representation of the current free space. The path produced (i.e., by steepest gradient descent on the harmonic function) is optimal in the sense of minimizing the distance to the goal as well as a hitting probability. This helps alleviate the influence of uncertainty on path planning. An initial heuristic estimate provides the path planner with instantaneous response (i.e., reactive), but with some deliberation it able to produce optimal paths. In addition, the computation time for generating the path is insignificant provided that the harmonic function has converged. On a regular grid, the computation of the harmonic function is linear in the total number of grid elements. A quad-tree representation is used to minimize the computation time by reducing the number of grid elements and minimally representing large spaces void of obstacles and goals.