Estimating the Coverage Measure and the Area Explored by a Side-Scan Sonar

Estimating the Coverage Measure and the Area Explored by a Line-Sweep Sensor on the Plane

“…In [8] a relation between the coverage measure of a point in the plane and the topological degree has been explored. Here we give a general axiomatic definition of the notion of topological degree and recap the main properties that we use.…”

“…Now let f represent the sweep function, mapping from the Waterfall Space W , which is homeomorphic to D 2 , to the Mosaic Space M . According to (8) and under hypothesis (5), for p ∈ R n \f (∂W ),…”

“…When the robot's pose and its visible set are well defined, the coverage measure of all the points in the environment during a mission can be uniquely determined. However, if we adopt the method proposed by [8], using relation (10), the coverage measure of a point p ∈ γ will be undefined considering the definition of winding numbers. γ p 1 p 2 Fig.…”

“…We demonstrate that the whole environment can be characterized from very basic information on the robot's state and on the range of visibility of the exploration sensors, resulting in a method of low computational complexity. This approach has already been explored at [8], but here we deepen its mathematical definition and extend it to address previous limitations such as the coverage measure of points on the maximal range of visibility and of points that are swept on the opposite direction of movement.…”