On consensus algorithms for double-integrator dynamics without velocity measurements and with input constraints

This note deals with consensus strategy design for double-integrator dynamics. Specifically, we consider the case where the control inputs are required to be a priori bounded and the velocity (second state) is not available for feedback. Two different design methods are proposed. First, based on the auxiliary system approach, we propose a consensus algorithm that extends some of the existing results in the literature to account for actuator saturations and the lack of velocity measurement. The proposed velocity-free control scheme, using local information exchange, achieves consensus among the team members with an a priori bounded control law, whose upper bound depends on the number of neighbors of the vehicle. Second, we propose another approach based on the use of a high order dynamic auxiliary system such that the upper bound of the control law is independent of the number of neighbors of the vehicle, and the performance of the closed loop system is improved in terms of the response damping. Finally, simulation results are provided to illustrate the effectiveness of the proposed algorithms.