Reaction–Diffusion Controllers for Robots

Excitable systems, particularly spatially extended media, exhibit a wide variety of travelling patterns and different modes of interaction. The Belousov—Zhabo-tinsky [1] (BZ) reaction is the most well known and extensively studied example of non-linear chemical system exhibiting complex behaviour. The BZ reaction is well known to exhibit spontaneous oscillatory behaviour. The mechanistic details are complex but involve a fine balance between an auto-catalytic oxidation process and an inhibitor of the autocatalytic reaction. If the chemical conditions are altered beyond the point where the reaction exhibits spontaneous oscillatory behaviour, then the BZ reaction exhibits a property known as excitability. An excitable system has a steady state and is stable to small perturbations; however, if the perturbations exceed a critical threshold, then the system responds with an excitation event. In the case of a thin layer architecture, this results in a circular wave travelling from the source of the perturbation. Parts of the wave front annihilate when they reach the boundaries or collide with other fronts; however, other parts will propagate across the whole free area of the reactor. Because the BZ system is excitable and due to the properties of wave propagation, it can be considered as a uniform locally connected primitive neural network (a type of neural network similar to that in Protozoa). The information processing capabilities of BZ media are relatively well studied in the framework of reaction—diffusion computing [2, 3]. A reaction—diffusion processor is the term used to describe an experimental chemical reactor which computes by sensibly, purposefully and predictably transforming the initial local disturbances in the chemical concentration profiles — the data pattern — into dynamical structures such as travelling excitation waves, or stationary output such as a spatial distribution of precipitate — result patterns — in these processors the computation is implemented via the interaction of either diffusive or phase waves in the chemical system [2, 3]. Reaction—diffusion processors of this general type possess an amorphous structure (absence of any type of rigid hardware-like architecture in the processor's liquid phase) and massive parallelism (a thin layer Petri dish may contain thousands of elementary computing micro-volumes).