Collective decision-making is an important problem in swarm robotics arising in many different contexts and applications. The Weighted Voter Model has been proposed to collectively solve the best-of- problem, and analysed in the thermodynamic limit. We present an exact finite-population analysis of the best-of-two model on complete as well as regular network topologies. We also present a novel analysis of this model when agent evaluations of options suffer from measurement error. Our analytical results allow us to predict the expected outcome of best-of-two decision-making on a swarm system without having to do extensive simulations or numerical computations. We show that the error probability of reaching consensus on a suboptimal solution is bounded away from 1 even if only a single agent is initialised with the better option, irrespective of the total number of agents. Moreover, the error probability tends to zero if the number of agents initialised with the best solution tends to infinity, however slowly compared to the total number of agents. Finally, we present bounds and approximations for the best-of- problem.

Programmable and self-assembled magnetic pillars are essential to expanding the application domain of magnetic microparticle collectives. Typically, the collective behavior of self-assembled magnetic pillars is carried out by generating uniform and time-varying magnetic fields. However, magnetic field-shaping capabilities employing non-uniform fields have not been explored for magnetic pillars. In this study, we generate non-uniform magnetic fields using a nine-coil electromagnetic system to achieve object manipulation, upstream/downstream locomotion, and independent actuation. We begin analyzing the static magnetic self-assembly of reduced iron microparticles and experimentally derive the average dimensions (height and diameter) of the resulting pillars. Subsequently, we delve into the collective dynamic response under non-uniform and time-varying magnetic fields, unveiling four distinct modalities. In order to demonstrate the versatility of our approach, we extend our study to the two-dimensional manipulation of a millimeter-sized glass bead using a precessing magnetic field describing a Lissajous curve. Moreover, we showcase the ability of magnetic pillars to adapt to confined and dynamic conditions within fluidic tubes. We finally present a noteworthy case where the nine-coil electromagnetic system independently actuates two clusters of magnetic pillars. Our study shows the potential of using non-uniform magnetic fields to actuate self-assembled magnetic pillars, enabling morphology reconfiguration capabilities, object manipulation, locomotion, and independent actuation.