We introduced the concept of C-space entropy recently in [1-3] as a measure of knowledge of C-space for sensor-based path planning and exploration for general robot-sensor systems. The robot plans the next sensing action to maximally reduce the expected C-space entropy, also called the maximal expected entropy reduction, or MER criterion. The expected C-space entropy computation, however, made two idealized assumptions. The first was that the sensor field of view (FOV) is a point; and the second was that no occlusion (or visibility) constraints are taken into account, i.e., as if the obstacles are transparent. We extend the expected C-space entropy formulation where these two assumptions are relaxed, and consider a generic range sensor with non-zero volume FOV and occlusion constraints, thereby modelling a real range sensor. Planar simulations show that (ⅰ) MER criterion results in significantly more efficient exploration than the naive physical space based criterion (such as maximize the unknown physical space volume), (ⅱ) the new formulation with non-zero volume FOV results in further improvement over the point FOV based MER formulation.
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