# LCNS Positioning of a Lunar Surface Rover Using a DEM-Based Altitude Constraint
## 2 Lunar Surface Rover Mission Profile  
The rover traverse selected for this paper is based on the literature [22] and circum-navigates the de Gerlache crater in an anti-clockwise direction (see Figure 1). With a total length of 320 km, expected to be covered in about 11 days by a pressurized rover with an average speed of 5 km/h (operated by humans) [22], this traverse has been chosen to cover areas of scientific interest and present two major technical advantages: first, the slopes encountered in the traverse are manageable by the actual rovers (i.e., lower than 25 degrees), and second, the traverse is covered by high-resolution DEMs. This paper only considers a small portion of this traverse, which coincides with one of the high-resolution lunar DEMs [26]. The portion of the traverse considered in this publication is highlighted in Figure 1 with a black square. From this point forward, the term \"traverse\" is used to refer to this small portion of the overall traverse proposed in [22].  
A remotely operated rover was chosen for this study, with a maximum speed of 0.36 km/h [22] (which is representative of tele-robotic operation), contrary to the 5 km/h which was considered by [22] for a small pressurized rover (SPR), leading to a completion of the traverse portion (as bounded by the black squared in Figure 1) in about 3 days. The two-dimensional traverse was converted to a three-dimensional traverse sampled at a rate of 1 Hz by considering a maximum horizontal velocity of 0.36 km/h using the following steps:  
1. Loading the 2D traverse [22] provided in a replaced[id=fm]geographic information systemGeographic Information System (GIS) shapefile;
2. Time tagging the points along the traverse such that the horizontal velocity equals 0.36 km/h;
3. Interpolating the horizontal traverse at the requested time-step (1 s);
4. Interpolating the DEM to get the rover position in polar stereographic reference frame (including the height). As the velocity is horizontally constrained, the actual velocity in three dimensions will be slightly larger than 0.36 km/h;
5. Converting the polar stereographic coordinates to a selenodetic reference frame.  
Figure 2 shows the elevation and slope along the traverse with the time in days covering a distance of approximately 27 km and a height ascent of 1300 m. The maximum slope encountered is 21.2 degrees, while the average slope is 8.2 degrees. The traverse was loaded into the ESA lunar navigation simulator [28,29] to acquire the link data with the LCNS satellites. The simulation environment used in the publication also considered the terrain data provided on the NASA PDS archive and generated by LOLA [27]. In this way, the simulation also accounts for the local topography and related signal occultations (see Figure 3a for the implementation of the traverse in the simulation environment).  
Figure 1: Lunar South Pole traverse shown on top of a low resolution DEM (100 m/pixel) available at the LOLA Planetary Data System (PDS) archive [27], while the small square indicates the region for which a high resolution DEM at 5 m/pixel is available. Projection is polar stereographic where \((0,0)\) denotes the South Pole.  
Figure 2: Rover altitude profile within the coverage of the high-resolution DEM. **(a)** shows the rover height above the Selenoid, while **(b)** shows the slope given by the DEM.