An efficient grid-based distance-propagating dynamic system is proposed for real-time robot path planning in dynamic environments which incorporates safety margins around obstacles using local penalty functions. The path through which the robot travels minimizes the sum of the current known distance to a target and the cumulative local penalty functions along the path. The algorithm is similar to \tsup{D}{∗} but does not maintain a sorted queue of points to update. The resulting gain in computational speed is offset by the need to update all points in turn. Consequently, in situations where many obstacles and targets are moving at substantial distances from the current robot location, this algorithm is more efficient than \tsup{D}{∗}. The properties of the algorithm are demonstrated through a number of simulations. A sufficient condition for capture of a target is provided.