The assignment of distributed mobile autonomous robots to targets, which occurs for instance as an important task in flexible manufacturing environments, is solved by using a self-organization approach motivated by pattern formation principles in biological, chemical and physical systems. Similar to observerations in many natural systems, like ant tribes, pattern formation of coloured shells or convection patterns in the Rayleigh-Bénard problem of fluid dynamics, the selforganization principles lead to a robust and fault tolerant behaviour where the patterns or structures recover from disturbances. The considered problem is the dynamic assignment of a number of robots to given targets where the mobile robots have to move to the targets in order to perform some tasks there. Hereby, each robot uses only local information, i.e., no world coordinate system is necessary. The underlying mathematical problem of the robot-target assignment is the so-called two-index assignment problem from combinatorial optimization. The used approach guarantees always feasible solutions in the assignment of robotic units to targets. As a consequence, for scenarios with only convex obstacles with large enough distances to each other, no spurious states cause the assignment process to fail. The error resistant control method for distributed autonomous robotic systems is demonstrated by several experiments with mobile robots. These results are compared and supplemented with computer simulations.