Path Planning in Kinematic Image Space Without the Study Condition

Abstract

This article proposes a new dual quaternion based approach for motion interpolation. The highlight is that dual quaternions act in the usual way on points, even if the Study condition is not fulfilled. This induces a fibration of kinematic image space into straight lines that describe the same rigid body displacement. This allows to use standard interpolation schemes for (piecewise) rational curves in a linear space rather than on the curved Study quadric.