Optimization of robust formation tracking control for traffic cone robots with matching and mismatching uncertainties: A fuzzy-set theory-based approach

A formation tracking control problem for uncertainty traffic cone robots (TCRs) is considered. In this paper, the TCRs can not only perform formation behaviors but also track placement targets under environmental constraints (i.e., the position constraints in the y-direction.). To deal with the environmental constraints, a differential homeomorphism transformation is selected to eliminate the constraints. Moreover, the uncertainty of the TCRs is bounded, including matching portions and mismatching portions. For the matching uncertainty, a series of adaptive parameters are introduced to estimate the real-time information of the uncertainty. The mismatching uncertainty is tackled by a geometric decomposition, which is orthogonal to the range space of the formation. At the same time, a fuzzy uncertainty optimization design problem is presented. The global solution to the resulting optimization problem always exists and is unique. Using adaptive robust control, TCRs' performance is deterministically and fuzzy-optimized. The system performance is demonstrated by a range of numerical simulations and real experiments with three TCRs.