Robust adaptive formation control of USVs with sensor measurement sensitivity and external disturbance under input saturation

In this work, a novel adaptive formation control scheme is designed for the formation control issue of USVs with sensor measurement sensitivity and time-varying external disturbance under input saturation. The leader-follower method is adopted to achieve formation keeping for USVs. The formation control issue is converted into several independent trajectory-tracking issues and each follower can only obtain position signal of the leader through sensor, while other information about the leader remains unknown. In the control design, sensor measurement sensitivity, external disturbance and input saturation are considered. To address external disturbance, a disturbance observer is adopted to estimate external disturbance. When the control law for each follower is designed, the estimation generated by the observer is used in place of the actual disturbance. Because the propulsion system of each follower is subject to physical limits, the designed control law encounters saturation constraints. Under input saturation, smooth Gaussian errors function is employed to soften the control law so that the control input received by the thruster stays within the maximum threshold. Moreover, the parameter adaptive method is employed to overcome the sensitivity errors existing in the sensor responsible for acquiring the position signal of the leader, the unknown term arising from the unknown sensitivity-errors coefficient is replaced with a virtual parameter, and an adaptive law is derived for the virtual parameter. It is proven that all signals of closed-loop control system of each follower are bounded by using Lyapunov theory. Besides, the availability of the control scheme is demonstrated by simulation results. • This work considers the problem that the sensor responsible for acquiring position signal of the leader on each follower suffers from sensitivity errors. Under the designed adaptive control scheme, the problem is successfully overcome. • In this work, handling the unknown sensitivity-error coefficient does not require the system to satisfy any specific condition. The position signal containing the unknown sensitivity coefficient is directly fed into the backstepping procedure. A single-parameter learning-based adaptive method is employed to overcome sensitivity errors, the unknown term caused by the unknown sensitivity-error coefficient is replaced with a virtual parameter, and an adaptive law is derived for this virtual parameter. • This work replaces the saturation function that contains sharp corners with the smooth Gaussian errors function which fits the original saturation more closely and thus gives higher approximation accuracy.