The experiments were performed in a 150 cm x 45 cm x 45 cm acrylic box (Figure \ref{525014}) filled with commercially available Quikrete 1962 Eglin silica sand that has a mean particle diameter of 0.8-1.8 mm \cite{Nardelli_2017}. Quikrete is a very common granular media to perform mobility experiments in and this is a legacy test bed from past experiments \cite{Thoesen_2020,Thoesen_2020a,Thoesen_2019a,Thoesen_2020b}. Quikrete silica sand was added to the test bed such that there was 20 cm of depth in order to prevent any wall effects from occurring between the screws and the bottom of the test bed.
Prior to each trial, the sand was reset manually using a modified thatch rake using a strictly consistent procedure. This was done to minimize the variance in measured quantities due to a buildup of plastic deformation in the sand. It has been shown that inconsistent soil conditions cause variability in the interactions of the mobility system and the granular media \cite{Heverly_2013}, which increases variance in the measured performance parameters. First, the craft would be removed from the soil. Next, the tines of the thatch rake would be drawn in longitudinal and transverse directions repeatedly until the sand was no longer compacted. Finally, the sand level was checked to make sure that the volume fraction of the sand remained constant between trials.
Once the sand was reset, the craft was replaced at the end of the test bed, and the ramp angle was set using a digital angle gauge and manual inputs to the craft's control system. After this process, the camera was set to record and the control script was launched at the command line to start the run. The craft was then allowed to traverse forwards until the ramp had deposited two discrete scoops into the collection bin, thus concluding the run. Two scoops were chosen because this is the maximum amount of scoops possible in this length of a test track at the highest screw angular velocity of 40 RPM with the longest load time of 6 seconds. Finally, the collection bin was removed and weighed using a digital scale and the resulting value was recorded. After recording the mass, the process was repeated for a multiplicity of five trials per experimental configuration.
The RPM, voltage, and current data vectors for each of the five motors were analyzed in MATLAB. For each trial, the current and voltages of each motor were multiplied together to obtain the electrical power supplied to the DC motors. Next, the time average of the power curves were taken across the temporal range where the craft had reached steady state, as indicated by the RPM versus time curve. The time-average power values for all five trials were recorded, and the ensemble average of these values was taken to determine the average power consumption for that specific set of experimental parameters.
Next, the videos of each run were analyzed using a color tracking MATLAB script. The camera was calibrated by taking several images of the checkerboard, including ones planar to the green color tracking target, and analyzing them in MATLAB to get the camera's intrinsic and extrinsic parameters. This enabled the pixel coordinates to be converted into world coordinates. The script analyzed each video frame by frame, finding the location of the center of the green target and thus, giving distance over time and therefore velocity. The average velocity was then calculated by taking the time-average of the velocity over the duration where the craft was considered in steady state. The values for all five trials were taken and averaged together to get an average velocity for that specific set of experimental parameters. A video exhibiting the operation of the excavation system during the experimental process is shown in Figure \ref{680769}.