The motion of a rigid object is expressed in a way, in which it will hold certain invariant properties with respect to several contextual dependencies of the recorded motion. Frenet Serret (FS) and Instantaneous Screw Axis (ISA) Invariant Descriptors are being used to describe a rigid body trajectory.
The motion recognition algorithms that are proposed, consist of a modified machine learning, distance-based, and a deep learning method. The amount of motions required to train the corresponding methods is kept to minimal and equal for every approach, so that a comparative basis can be established, and the invariance of the investigated motion representations favors the minimal amount of training data usage.
Motion Recognition Algorithms:
- Dynamic Time Warping (DTW-algorithm)
- DTW-based K-Nearest Neighbor
- LSTM Network
Description of Motion Trajectory via:
- Frenet serret Descriptors
- Instantaneous Screw Axis Descriptors
Parameterizations:
- Time-based
- Geometric
- Dimensionless Geometric
Invariant Descriptors Calculation Types:
- Analytical formulas
- Optimized Approach
The trajectory of a rigid body is represented by six (6) ISA - invariant descriptors, at each time moment. Below an example trajectory is illustrated, followed by the ISA-descriptors calculated with analytical formulas (blue) and optimized approach (red):
In this script the invariant descriptors for 1200 samples of 10 motion classes are constructed and then classified using the DTW-algorithm, using analytical formulas.
In this script the invariant descriptors for 1200 samples of 10 motion classes are constructed and then classified using the DTW-algorithm, using an optimized approach.
In this script a k-Nearest Neighbor algorithm is constructed using DTW-distance instead of the traditional Eucledian distance used in the literature, to classify the corresponding rigid body motions.
In this script an LSTM network is trained to classify the corresponding motions, while keeping the amount of training data to a minimal amount (about 8.3% of the whole dataset provided by KU Leuven). A brief representation of the network and the training accuracy and error are shown:
Due to the invariance of the descriptors, a minimal amount of training data are required in every approach, even in the LSTM approach. The amount of data that are used for training and testing are split in a similar manner for every method as follows:
- 8.3% (train)
- 91.7% (test)
- This project is my master thesis in collaboration with: KU Leuven, Robotics, Automation and Mechatronics (RAM), Leuven (Arenberg)
- Possible missing functions due to copyright issues, for further information email me at: konstgyftodimos@gmail.com