In this paper, we consider Lipschitz conditions for tri-quadratic functional equations. We introduce a new notion similar to that of the left invariant mean and prove that a family of functions with this property can be approximated by tri-quadratic functions via a Lipschitz norm.
The paper presents Potential-Based Scan Matching (PSCM) method used for simultaneous localization and mapping of mobile robot in unknown environment. The method is based on matching two proximity sensor scans from different robot locations. The resistance of the method against errors in sensor readings is investigated using both general sensor error model and error model for LMS 200 laser scanner. The method proved to be highly resistent for the noise levels exceeding the commonly used instruments.