This Appendix gives the details of the calculations by which a line is fitted to a set of sonar observations.

It is initially necessary to distinguish two cases; the creation of a new confirmed line and the updating of an existing confirmed line. In both cases the confirmed line is fitted to a number of contact points, one for each sonar reading which corresponds to the line. The only difference is in the way the contact points are determined.

A confirmed line is created by ‘upgrading’ a cluster of elementary line segments. As explained in Section 7.1, each line segment has two contact points. Since segments are added to the cluster if they share a sonar reading with a segment already in the cluster, it is common for a single sonar reading to correspond to more than one segment. To avoid giving unnecessary weight to these ‘multiple’ readings, the confirmed line is fitted to a single contact point for each sonar reading. It is therefore necessary to calculate an ‘average contact point’ if the sonar reading corresponds to multiple segments.

If, on the other hand, the confirmed line is to be updated then the line already has a number of contact points and a new one is to be added. As explained in Section 7.3, a contact point is obtained by taking a point at the measured distance from the robot in a direction normal to the line.