On visibility maintenance via controlled invariance for leader-follower Dubins-like vehicles

The paper studies the visibility maintenance problem (VMP) for a leader-follower pair of robots modelled as first-order dynamic systems 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 can then be 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 can be easily adapted to provide the control with UBB disturbances rejection capabilities. As an extension, the paper addresses the VMP on a circle. Simulation experiments show the effectiveness of the proposed designs.