Optimal automated path planning for infinitesimal and real-sized particle assemblies

Abstract

The present article introduces an algorithm for path planning and assembly of infinitesimal and real-sized particles by using a distance and path based permutation algorithm. The main objective is to define non-overlapping particle paths subject to minimal total path length during particles positioning and assembly. Thus, a local minimum is sought with a low computational cost. For this reason, an assignment problem, to be specific Euclidean bipartite matching problem, is presented, where the particles in the initial (random selection) and final (particle assembly) configurations are in one-to-one correspondence. The cost function for particle paths is defined through Euclidean distance of each particle between the initial and final configurations. Principally, a cost flow problem is formed and solved by determining an optimal permutation subject to the total Euclidean distance of the particles and their non-overlapping paths. Monte Carlo simulations are carried out for non-overlapping paths; thus, non-colliding particles, and then total path distances of the obtained sets are minimized, resulting in an optimal solution which may not be necessarily the global optimum. Case studies on basic and complex shaped infinitesimal and real-sized particle assemblies are shown with their total costs, i.e., path lengths. It is believed that the present study contributes to the current efforts in optical trapping automation for particle assemblies with possible applications, e.g., in the areas of micro-manufacturing, microfluidics, regenerative medicine and biotechnology.