This study investigates the robust finite-time stabilization of an autonomous underwater vehicle (AUV) with disturbance rejection, where the finite-time can be predetermined. The AUV is modeled as a rigid body moving within fluids, and the systems dynamics involves uncertain parameters arising from the hydrodynamic coupling between the AUV and fluid, along with unknown external disturbances. Direct compensation for the system’s dynamics, a common approach in controller design, is ineffective for AUVs with uncertainties. Therefore, a robust anti-disturbance control method without compensating for unknown dynamics is proposed. To begin, a time rescaling method is introduced to convert the specified finite-time stabilization of the system into an asymptotic stabilization for a time rescaling system. Then, an exponential PID controller is designed for the time rescaling system to handle unknown constant disturbances while a high-gain control strategy is used to suppress the uncertain dynamics, which also enhances the robustness against the uncertain dynamics. The specified finite-time stabilization control law is ultimately derived from the designed exponential control law of the time rescaling system. Numerical simulations are conducted to verify the results.

This article investigates the roto-translation invariant (RTI) formation of multiple underactuated planar rigid bodies, which are established under the framework of matrix Lie groups. The main contribution is that we define the RTI and pseudo RTI (P-RTI) formation of planar rigid bodies. Different from the common formation given in the earth-fixed frame, the RTI formation is defined in the body-fixed frame so that it possesses a rigid-body motion obtained by composing rotation and translation simultaneously. Moreover, regarding fully actuated planar rigid bodies, we propose the velocity and force requirements to maintain the RTI formation, which are derived based on the kinematic and dynamic model, respectively. Another contribution of this article is that the RTI formation feasibility is investigated for underactuated planar rigid bodies subject to nonholonomic constraints on velocities and accelerations. To be more specific, we study the occasions when wheeled mobile robots and underactuated surface vessels can maintain the RTI or P-RTI formation. Finally, the results of the simulation and experiment are presented so as to exhibit the RTI and P-RTI formation intuitively.

This article investigates the moving-target circular formation control problem for multiple nonholonomic vehicles under a directed graph. First, a novel moving-target enclosing control scheme is proposed by using the feedback linearization approach, in which the design procedure of the cooperative controller is more straightforward. Compared with the existing literature, the designed controller relaxes some existing constraints and the corresponding stability analysis is more concise. Second, based on the distance measurements, the observers, including sliding-mode observer and relative position observer, are designed to estimate the relative position so that the global position measurements are not required. Therefore, the observer-based controller becomes more suitable for practical application. Numerical simulations are conducted to illustrate the effectiveness of the proposed controllers.

In this paper, the problems of specified finite-time distributed attitude estimation and velocity-free attitude synchronization are studied for rigid bodies on special orthogonal group SO(3). Using the geometric convexity on SO(3), the exponential distributed observers are proposed for each rigid body to estimate the common time-varying reference states which are only available to a part of followers. Then, the specified finite-time distributed observers are proposed by using the time-rescaling approach, where the finite terminal time can be specified in advance according to the task requirements. The advantage of time-rescaling method is that the asymptotic, exponential, or finite-time distributed observers can be converted to the specified finite-time distributed observers via choosing an appropriate continuously differentiable scaling function that satisfies some required properties to rescale time. Based on the distributed observers, the velocity-free attitude synchronization control torques are designed by virtue of observer-like systems. The performances of the specified finitetime distributed observers and the velocity-free attitude synchronization with distributed observers are illustrated through numerical/SimMechanics simulations.

In this paper, the adaptive consensus disturbance rejection problem is considered for the liner multi-agent systems under directed graphs. Based on the relative state information of the neighboring agents, the consensus protocols, including a state observer and a disturbance observer, are designed to guarantee that the consensus error goes to zero with the complete disturbance rejection. Furthermore, the state observer is designed in a fully distributed fashion with adaptive coupling gain, which has the advantage that the consensus protocol design is independent of the Laplacian matrix associated with the communication network. Finally, an example is given to verify the effectiveness of the theoretical results.