In this talk, we start by giving a short Introduction on Walsh processes. We essentially start by giving the main properties of this type of processes, together with their local time at the vertex. Thereafter, we will expose my recent results, that deal with the construction of a general class of Spider's motion having a spinning measure depending on its own local time. We explain the concatenation method of probability measures used for the construction of the process and also how the weak uniqueness was obtained, with the aid of the well-posedness for the corresponding linear parabolic operator, having a new class of transmission; called: local-time Kirchhoff's boundary condition. Finally, we show how these latest results will lead to a new problem of stochastic control, called: stochastic optimal scattering (or diffraction) of Walsh processes, with optimal spinning measure selected from its own local time.