Consider an angular TSP where you have a vehicle initially located at a

point $p_0$ in the Euclidean plane, oriented so that it is facing $($say$)$ point

$p_1,$ out of points $p_1,$dots,$p_n.$ The vehicle will rotate to face one of the

points $p_i($which might be $p_1,$ in which case it does not need to do any

rotation$)$ and then travel in a straight line until it arrives there. Then, it

will rotate to face one of the other points $p_j$ and then travel in a straight

line until it arrives there. The process continues until the vehicle arrives

back at $p_0$ and is facing $p_1,$ as it began. The goal is to return to the initial

configuration in the shortest possible time, which is measured as a sum of

straight$-$line travel plus time spent rotating. Formulate this problem as a

GTSP with $O(n^2)$ nodes, where $n$ is the number of nodes in the original

problem.