Locating object surfaces with an ultrasonic range sensor

Ultrasonic range sensing has attracted attention in the robotics community because of its simple construction and low cost. However, determining range direction is made difficult by the signal beam spread of the transducer. This direction ambiguity can be reduced to some extent by increasing the operating frequency or diameter of the sensor but some ambiguity will still remain. A technique is described for obtaining the true surface normals to a planar surface using three sensors or three positions of one sensor. The solution is quite complex in direct form. A simplifying transformation applied to the direct form and a further simplifying sensor configuration are described which greatly reduces the solution complexity. An alternate formulation of the problem is described from which geometrical insight can be obtained. This alternate solution also lends itself to the generation of tangential constraint surfaces for bounding curved object surfaces.