Splitting monoidal stable model categories

If C is a stable model category with a monoidal product then the set of homotopy classes of self-maps of the unit forms a commutative ring, [S,S]C. An idempotent e of this ring will split the homotopy category: [X,Y]C≅e[X,Y]C⊕(1−e)[X,Y]C. We prove that provided the localised model structures exist, this splitting of the homotopy category comes from a splitting of the model category, that is, C is Quillen equivalent to LeSC×L(1−e)SC and [X,Y]LeSC≅e[X,Y]C. This Quillen equivalence is strong monoidal and is symmetric when the monoidal product of C is.

Cooperative Mapping and Exploration using Counter-rotational Potential Fields

This paper presents a novel technique for mapping and exploration using cooperating autonomous underwater vehicles. Rather than using the typical lawnmower sweep pattern to search an entire area, the proposed navigational plan involves guiding the formation directly towards each object of interest in turn, before arriving at a final goal position. This is achieved by the use of traditional artificial potential fields alongside counter-rotational potential fields. These clockwise and counter-clockwise fields are employed simultaneously by vehicles to ensure that the entire object is scanned rather than simply avoided as is the case with traditional collision avoidance techniques. The proposed methodology allows a formation to have fluid-like motion whilst a separation distance between cooperating agents (free of angular constraints) is maintained with a greater degree of flexibility than traditional formation control approaches. Owing to its nature, this technique is suited for applications such as exploration, mapping and underwater inspection to name a few. Simulation results demonstrate the efficacy of the proposed approach.