Visibility maintenance via controlled invariance for leader-follower vehicle formations

The paper studies the visibility maintenance problem (VMP) for a leader-follower pair of Dubins-like vehicles with input constraints, and proposes an original solution based on the notion of controlled invariance. The nonlinear model describing the relative dynamics of the vehicles is interpreted as linear uncertain system, with the leader robot acting as an external disturbance. The VMP is then reformulated as a linear constrained regulation problem with additive disturbances (DLCRP). New positive D-invariance conditions for linear uncertain systems with parametric disturbance matrix are introduced and used to solve the VMP when box bounds on the state, control input and disturbance are considered. The proposed design procedure is shown to be easily adaptable to more general working scenarios. Extensive simulation results are provided to illustrate the theory and show the effectiveness of our approach.