Search Deviation Analysis

A major challenge with the Sample Return Robot (SRR) competition is knowing the location and bearing of the robot, generally refereed to as pose. The reason is there is no absolute reference available when the rover starts. It know generally that it is on the starting platform somewhere in a 10 meter circle. It also knows that it is facing ±60 degrees of the reference point, i.e. generally to the west. Once it leaves the platform the only guidance is provided by visual landmarks throughout the park.

The rover's pose is critical for three reasons. Once the rover leaves the platform it needs to know how to return with samples. In Phase 1 the rover needs to know how to locate the pre-cached sample. Throughout Phase 2 the pose is needed to assure the entire park area is searched.

I am a bit of a contrarian because I do not feel many of the problems in robotics, of the SRR nature, are solved by chasing decimal points. My approach is to find a close enough response and refine as needed. For example, as long as a rover knows the starting platform is somewhere in "that' direction it can proceed. As it gets closer landmarks, like the big white band shell, will help it refine the path.

This approach is suitable for locating the pre-cached sample and the starting platform. If one assumes the search pattern performed in Phase 2 requires following very straight lines there is a requirement for a few decimal points. Such a search requires the rover to proceed in a straight line, make two 90 degree turns while offsetting from the previous path, and then return in another straight line parallel to the first. The straight line paths have to neither overlap the previously searched line very much nor leave gaps that might miss samples. Say the rover cannot deviate more than 0.5 m over a 100 m path. That requires a deviation less than $\arctan \left ( \frac{0.5}{100.0} \right )$ 0.67°. 

Another question is how close is acceptable when making a 90° turn? Those turns set the basis for the next straight path. Any deviation from 90° reduces the deviation allowed in the straight path. In other words, the total deviation for the turns and the straight path can be no more than 0.67°. 

(comment here about the 0.5 meaing the rover starts 0.25 m inside the previous search area,...)

Backing up a bit, is the 0.5 m deviation valid? The search analysis determined that a rover needs to scan a 2 m deep by 3 m wide area every two seconds. The deviation reduces the the 3 m width of the scan area. The analysis is based on a single rover searching the park. It would be absurd to assume that the search area could be reduced by one third, to 2 m by 1 m, although that would allow a 2 m deviation.