Distributed formation control of non-holonomic robots without a global reference frame

In this paper we consider the problem of controlling a team of non-holonomic robots to reach a desired formation. The formation is described in terms of the desired relative positions and orientations the robots need to keep with respect to each other, and it is assumed that the robots do not have a common shared reference frame. In other words, the robots can use only on-board sensing to achieve the formation. We first consider a holonomic framework, using a well known distance-based approach to reach a formation for the positions. We then include a control law for the orientations. We further discuss the problem of mirror configurations that appear when different desired relative orientations can satisfy the same distance-based constraints through different formations. Exploiting the concept of chirality, we present a relabeling strategy to reassign the robots' roles to reach the desired pattern when a mirror configuration occurs. The distance-based holonomic control is then transformed to cope with the non-holonomic constraints using a piecewise-smooth function. Simulation results, as well as hardware experiments with five m3pi robots demonstrate the applicability of our approach.