Distributed trajectory tracking and formation control without velocity measurements by the notion of prior bounded local neighborhood synchronization error
Boxian Lin, Te Zhang, Bo Zhu, Kaiyu Qin · Measurement and Control · 2020
This paper investigates the robust consensus tracking and formation control problems of multiple second-order systems having exogenous disturbances and no velocity measurements. To account for the input saturation constraint in controller design, a novel notion of local neighborhood synchronization error is proposed, which is obtained using generalized saturation functions and can be regarded as a nonlinear variation of the well-known linear local neighborhood synchronization error. An important property of the notion is proved and then a continuous distributed controller is designed using it. To improve the robustness of the controller with respect to exogenous disturbance, a disturbance estimator–based design and a simple parameter mapping for parameter tuning are proposed. The resulting error system is proven to be small-signal [Formula: see text] stable and input-to-output stable. In particular, the synchronization errors and tracking errors converge asymptotically to zero if the disturbances converge to some constants. By the parameter mapping, the steady-state synchronization errors and tracking errors can be made arbitrarily small. The control scheme is finally modified to adapt to formation control applications by adding the desired position deviation from the leader’s trajectory. The performance of the scheme is demonstrated by the simulation results.