Output: The minimum distance such that all points are visited.
The First Reveal: Brute Force
The general idea is to generate a complete graph from the set of points. We define a complete graph a simple undirected graph in which every pair of distinct vertices is connected by a unique edge.
What this effectively produces is a graph with complete freedom. The robot is not constrained to the path it could take, but we'll leave it to the greedy algorithm to take care of the rest. Running a MST algorithm on this graph will then generate the minimum weight of all distances, such that all nodes are linked.
Of course, we'd have to cover distance between each edge in the process.
Consider the complete graph above, with a radius of 10. We then obtain: