A Data Set for Research on Differential-Drive Mobile Robots in the Context of EDMD

<h3>General</h3>
This dataset contains real-world measurement data for data-based modeling of a differential-drive robot.
The dataset is especially tailored for data-based modeling using Extended Dynamic Mode Decomposition (EDMD) for control-affine systems.
It contains predecessor and successor pose data of the wheeled mobile robot (i.e., its position in the plane of an inertial frame of reference as well as its orientation w.r.t. the x-axis) when constant control inputs are applied to the robot, which is done for two different realizations of the differential-drive robot.
In the first realization, a desired constant translational and rotational velocity is sent to the robot (kinematic realization), while in the second realization, the robot's control actions are desired translational and rotational accelerations (second-order robot).
A total of three different datasets are provided, two for the kinematic mobile robot and one for the second-order robot.
The second, smaller dataset for the kinematic mobile robot shall indicate the data-efficiency of the EDMD approach.
For each of the three datasets, three raw data files with predecessor pose data (X_i.dat) and three raw data files of successor pose data (Y_i.dat) are provided, where the number i from the set {0,1,2} corresponds to the predecessor and successor data and indicates the applied control basis u_i.
In addition to zero control (i=0), the EDMD approach requires data for the differential-drive mobile robot for two linearly independent constant control vectors over a predefined sampling time.
Further information about the chosen control bases and the sampling times can be found in the readme files associated with the dataset directories.
Notably, the dataset for the second-order robot realization additionally contains approximative velocity data as well as the exact times at which the pose measurement of the external motion capture system has been received.
This additional time information is provided to facilitate the smoothing of the velocity data.

<h3>File Setup</h3>
The following files and directories are provided.<br>
<ul>
<li><i>kinematic_dataset1</i><br>
This directory contains raw data files containing the predecessor and successor pose data for the first sampling of the kinematic mobile robot. Each line consists of [x-position, y-position, orientation]. The chosen constant control vectors read u0=[0 m/s, 0 rad/s], u1=[0.2 m/s, 0.6 rad/s], and u2=[0.2 m/s, -0.4 rad/s] and the sampling time is 0.1 seconds.</li>

<li><i>kinematic_dataset2</i><br>
This directory contains raw data files containing the predecessor and successor pose data for the second sampling of the kinematic mobile robot. Each line consists of [x-position, y-position, orientation]. The chosen constant control vectors read u0=[0 m/s, 0 rad/s], u1=[0.2 m/s, 0.6 rad/s], and u2=[0.2 m/s, -0.4 rad/s] and the sampling time is 0.05 seconds.</li>

<li><i>secondorder_dataset</i><br>
This directory contains raw data files containing the predecessor and successor pose data for the sampling of the second-order mobile robot. Each line consists of [x-position, y-position, orientation, v (translational velocity), omega (angular velocity)]. The chosen constant control vectors read u0=[0 m/^2s, 0 rad/s^2], u1=[0.2 m/s^2, 0 rad/s^2], and u2=[0 m/s^2, 0.5 rad/s^2] and the sampling time is 0.05s. Note that additional time instances of the measured data are provided in the respective first column. This might facilitate the necessary smoothing of the translational and angular velocities.</li>

<li><i>ProcessVisualizeKinematic.m</i><br>
This is a minimal MATLAB file which can be used to process and visualize the recorded data for the kinematic mobile robot. Further information can be found in the comments of the file.</li>

<li><i>ProcessVisualizeSecondorder.m</i><br>
This is a minimal MATLAB file which can be used to process and visualize the recorded data for the second-order mobile robot. Further information can be found in the comments of the file.</li>
</ul>