Recent times have seen the development of novel engineering approaches that takes inspiration from a wider range of biological processes and structures. One of the advantage, relevant in this presentation, stems from the ability of biological entities to be autonomous and self-organize. As an example of this bio-inspiration I will show how studying the emergence of territorial patterns in an animal population has motivated the development of an algorithm of spatial coverage for a robot swarm. I will first present recent findings of a collective movement model of territorial formation whereby scent-marking animals are modelled as random walkers that interact by avoiding the marks left by others. This interaction mechanism is often referred to as stigmergy. Depending on the time for which the marks remain active on the terrain it can be shown that the animal population can be in a gas, liquid or solid phase. I will further discuss why in a robot swarm it is more convenient to abandon stigmergic interactions in favour of direct interactions inspired by bird chirping. The key idea is that when two robots meet, they detect each other (in birds, this is done by chirping a challenge which is then countered), then remember the location of the encounter and treat it as a border landmark. Results on coverage times as function of the robot memory and the degree of correlation of the walk will be shown.