Comparison of rigid body motion trajectory descriptors for motion representation and recognition

Abstract

This paper presents an overview and comparison of minimal and complete rigid body motion trajectory descriptors, usable in applications like motion recognition and programming by demonstration. Motion trajectory descriptors are able to deal with potentially unwanted variations acting on the motion trajectory such as changes in the execution time, the motion's starting position, or the viewpoint from which the motion is observed. A suitable rigid body motion trajectory descriptor retains only the trajectory information relevant to the application. This paper compares different trajectory descriptors for rigid body motion and validates their usefulness for dealing with motion variation in a motion recognition experiment. Furthermore, a new type of invariant trajectory descriptor is introduced based on the Frenet-Serret formulas.

Bidirectional invariant representation of rigid body motions and its application to gesture recognition and reproduction

“…This limitation is overcome in [37], where Extended Frenet-Serret invariants (EFS) is proposed by considering also the orientation part of the motion. The EFS is not affected by affine transformations, time, linear and angular scale and motion profile.…”

“…As experimentally shown in Sec. 8, the sensitivity of numerical derivatives makes difficult to estimate reliably the invariant values in [37,6] and generates a non-negligible reconstruction error. On the contrary, the proposed DHB representation does not require high-order time derivatives.…”

“…Speed invariance -The invariance to the motion profile, or the speed of execution, can be obtained by expressing DHB invariants as a function of a degree of advancement, as described in [37]. Speed invariance can be achieved in theory.…”

“…This section describes theoretical relationships and differences between DHB and two state-of-the-art bidi-rectional invariant representations: EFS [37] and DS 4 [6]. To the best of our knowledge, EFS and DS are the only bidirectional representations which consider also the orientation part of the motion.…”

“…Cartesian trajectories describe the spatial motion of one or multiple points attached to the human (robot) body. In real scenarios, Cartesian trajectories are affected by two kinds of motion variations, depending on how and where the same motion is executed [37], which limit the applicability of Cartesian task descriptors in motion recognition and reproduction.…”