A bio-inspired localization-free stochastic coverage algorithm with verified reachability

Dependence on constant availability to an external localization service is often unreliable and infeasible in mobile robots. In this paper, we take inspiration from a continuous fish motion model, the persistent turning Walker (PTW), to devise a strategy which is able to achieve 2D and 3D coverage in an unknown environment in the absence of a localization service, such as a global positioning system (GPS). This is achieved by converting the continuous-time dynamical system into a discrete-time Markov chain which is then shown to exhibit strongly connected properties that are verifiable through numerical methods. The aforementioned proposed framework can also be used to study the continuous-time dynamics of other biological systems and evaluate their properties. The performance of the PTW model is also compared with two existing random search strategies, simple random walks (SRW) and correlated random walks (CRW) by using analytical bounds, simulation results, and statistical tests. The simulation results show that the proposed PTW algorithm covers a given search-space at a faster rate compared to the CRW and SRW models. Hence, the PTW may be effectively used as a coverage strategy by mobile robots in underwater or underground environments where the availability of a GPS cannot be guaranteed at all times.