Formation Control via Orientation and Position Estimation

Abstract

In the previous chapter, the orientation angles $\theta _i$ are estimated or controlled such that $\hat{\theta }_i - \hat{\theta }_j = \theta _i - \theta _j$. Then, after the orientation alignment, the agents with aligned orientation could be controlled in a displacement-based setup. That is, given a desired configuration $p^*$, the formation control has been achieved up to rotation and translation in the sense of $p_j - p_i \rightarrow p_j^*- p_i^*$ with respect to a common coordinate frame. Thus, the relative displacements between neighboring agents have been controlled. But, if we could estimate the positions of agents and the estimated positions are used to control the motions of agents, then the desired formation might be achieved more rapidly. In this chapter, we would like to estimate the positions of agents, up to a common offset in positions, using only relative measurements.