Confinement Control of Double Integrators using Partially Periodic Leader Trajectories
This work provides a theoretical framework for confinement control in multi-agent systems, relevant for robotics and swarm applications, though it is an incremental extension of existing averaging and input-to-state stability methods.
The paper addresses multi-agent confinement control using a leader with repulsive effects on double-integrator followers. It shows that by decomposing leader inputs into periodic and aperiodic components, followers can be confined about a time-dependent trajectory, with tracking error made arbitrarily small for a single follower.
We consider a multi-agent confinement control problem in which a single leader has a purely repulsive effect on follower agents with double-integrator dynamics. By decomposing the leader's control inputs into periodic and aperiodic components, we show that the leader can be driven so as to guarantee confinement of the followers about a time-dependent trajectory in the plane. We use tools from averaging theory and an input-to-state stability type argument to derive conditions on the model parameters that guarantee confinement of the followers about the trajectory. For the case of a single follower, we show that if the follower starts at the origin, then the error in trajectory tracking can be made arbitrarily small depending on the frequency of the periodic control components and the rate of change of the trajectory. We validate our approach using simulations and experiments with a small mobile robot.