Invariant signature-based modeling, classification and estimation
Introduction
In robotics, there is a growing need for efficient and robust recognition, classification, and characterization of rigid body motion trajectories. Example applications include the recognition of the motion trajectory of an object manipulated by a human or by a robot, and the extraction of a motion primitive from multiple demonstrations during programming by human demonstration. A coordinate-free representation of rigid body motion trajectories was developed in this research group by Professor De Schutter [1]. This representation can facilitate the tasks mentioned above.
The coordinate-free representation models the intrinsic differential geometric properties of the trajectory, and is invariant with respect to:
- The reference frame in which the motion is recorded.
- The reference point on the rigid body chosen to express the translational components of the motion.
- The parametrization of the trajectory (i.e. the motion profile).
- The time scale .
- The linear or angular scale of the motion.
The idea is to transform the measured motions to their invariant representation before applying algorithms for recognition, classification, comparison, averaging, etc., this way eliminating the dependency on the reference frame, reference point, parametrization, time scale, and angular or linear scale, leading to a large reduction in search space for the subsequent algorithms.
This research is part of the Application Project: "Optimal human-robot interaction" of OPTEC.
Figure 1: Two demonstrations of the same motion, performed in a different reference
frame, with different time scale. [2]
Figure 2: The twists (left) corresponding to the motions demonstrated in Figure 1 are clearly
different and cannot be used to recognize movements, the invariants representation (right)
of both motions is very similar. [2]
As can be seen from figure 2, the twists of motions recorded under different circumstances do not resemble each other and can therefore not be used for recognition purposes. The invariant representation of both movements however, are clearly similar. This representation thus eliminates the dependencies and allows the recognition and classification of movements even when they were recorded under widely varying conditions. The invariant representation greatly reduces the search space for subsequent algorithms, as can be seen in Figure 3.
Figure 3: Whereas recognition of motions based on the twist (left) needs several models to account for the different conditions under which a motion can be captured, recognition based on the invariants can be performed using only one model.
The invariants
Three types of invariants are proposed:
- Timebased invariants
- Geometric invariants
- Dimensionless Geometric invariants
The characteristics of each of these invariants are shown in Table 1. This table shows for each invariant type (and for the twist), which of the dependencies have been eliminated.
Table 1: For each of the three invariants (and the twist), the dependencies
which are eliminated are indicated. [3]
Current Research
Current research involves:
- Improving the pre-processing of the motion data.
- Experimental validation of the theory.
- Examining special motions.
- Developing a real-time implementation.
[1] J. De Schutter, Invariant description of rigid body motion trajectories, ASME Journal of Mechanisms and Robotics, 2008.
[2] T.Benoit,“Herkenning van menselijke en robot- bewegingen gebruikmakend van een coordinatenvrije beschrijving van 3d-beweging van starre lichamen,” Master’s thesis, K.U.Leuven, Departement Werktuigkunde, Celestijnenlaan 300, B-3001 Heverlee, 2011.
[3] T. Delabie, T. De Laet, J. F. M. De Schutter, R. Matthysen, J. De Schutter, Recognition of Everyday Movements Recorded In Different Conditions Using an Invariant Representation, 2010.
