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We describe a trajectory planning method for heterogeneous mobile robot teams in known environments. We consider two core problems that arise with heterogeneous robot teams: asymmetric inter-robot collision constraints and varying dynamic limits. Asymmetric collision constraints are important for close-proximity flight of rotorcraft due to the downwash effect, which complicates spatial coordination. Varying dynamic limits complicate temporal coordination between robots and must be taken into account during planning. Our method builds upon a hybrid planner that combines graph-planning techniques with trajectory optimization and scales well to large homogeneous robot teams. We extend the hybrid planning approach to include the additional spatial and temporal coordination to support heterogeneous teams. Our method scales well with the number of robots and robot types and we demonstrate our approach on a team of 15 physical robots of 4 different types, including quadrotors and differential drive robots.

Discriminative base motifs within DNA templates for fluorescent silver clusters are identified using methods that combine large experimental data sets with machine learning tools for pattern recognition. Combining the discovery of certain multibase motifs important for determining fluorescence brightness with a generative algorithm, the probability of selecting DNA templates that stabilize fluorescent silver clusters is increased by a factor of >3.

DNA-stabilized silver clusters are remarkable for the selection of fluorescence color by the sequence of the stabilizing DNA oligomer. Yet despite a growing number of applications that exploit this property, no large-scale studies have probed origins of cluster color or whether certain colors occur more frequently than others. Here we employ a set of 684 randomly chosen 10-base oligomers to address these questions. Rather than a flat distribution, we find that specific color bands dominate. Cluster size data indicate that these "magic colors" originate from the existence of magic numbers for DNA-stabilized silver clusters, which differ from those of spheroidal gold clusters stabilized by small-molecule ligands. Elongated cluster structures, enforced by multiple base ligands along the DNA, can account for both magic number sizes and color variation around peak wavelength populations.

Fluorescent DNA-stabilized silver nanoclusters contain both cationic and neutral silver atoms. The absorbance spectra of compositionally pure solutions follow the trend expected for rod-shaped silver clusters, consistent with the polarized emission measured from individual nanoclusters. The data suggest a rod-like assembly of silver atoms, with silver cations mediating attachment to the bases.