One the use of invariance in robotics-oriented redundant sensing

Invariant concepts are applied in connection with the redundant sensing of physical quantities in robotics-related applications. It is shown that, by utilizing the properties of invariant quantities associated with physical scalar, vector, and tensor variables, it is possible to verify the compatibility of measurements and, in some cases, to determine the relative orientation of the coordinated frames attached to each of the various sensors. A numerical example was introduced to illustrate the benefits of invariant concepts that led to the determination of the relative orientation of two different coordinate frames attached to the same rigid body by sheer matrix multiplications, thereby eliminating the complexity of nonlinear-equation solving. Invariance is shown to be applicable to compatibility verification and instrument calibration