Distributed trajectory tracking and formation control without velocity measurements by the notion of prior bounded local neighborhood synchronization error

Boxian Lin,Bo Zhu,Kaiyu Qin,Te Zhang

doi:10.1177/0020294019877501

Abstract

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.

Highlights

In recent years, distributed coordination of multivehicle systems (MVSs) has attracted much attention due to its practical significance
If all the conditions of Lemma 3–5 are satisfied and (~ri, r~_i, zi)T viewed as state and output, the small-signal L‘ stable and locally input-to-state stable (LISS) are both achieved for the system (equation [46])
It is seen that the uncertainty and disturbance estimator (UDE) reject the disturbances effectively and the position tracking objective is achieved

Summary

Introduction

In recent years, distributed coordination of multivehicle systems (MVSs) has attracted much attention due to its practical significance. The synchronized trajectory tracking and formation control under a given input constraint without using velocity measurements have not received much attention. 2. Using the notion of prior bounded LNSEs, a robust control scheme for synchronized trajectory tracking of multiple second-order systems without velocity measurements is designed.

Results

Conclusion