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This paper proposes an uncertainty and disturbance estimator (UDE)-based controller for nonlinear systems with mismatched uncertainties and disturbances, integrating the UDE-based control and the conventional backstepping scheme. The adoption of the backstepping scheme helps to relax the structural constraint of the UDE-based control. Moreover, the reference model design in the UDE-based control offers a solution to address the “complexity explosion” problem of the backstepping approach. Furthermore, the strict-feedback form condition in the conventional backstepping approach is also relaxed by using the UDE-based control to estimate and compensate “disturbance-like” terms including nonstrict-feedback terms and intermediate system errors. The uniformly ultimate boundedness of the closed-loop system is analyzed. Both numerical and experimental studies are provided.

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Motion planning is a crucial, basic issue in robotics, which aims at driving vehicles or robots towards to a given destination with various constraints, such as obstacles and limited resource. This paper presents a new version of rapidly exploring random trees (RRT), that is, liveness-based RRT (Li-RRT), to address autonomous underwater vehicles (AUVs) motion problem. Different from typical RRT, we define an index of each node in the random searching tree, called "liveness" in this paper, to describe the potential effectiveness during the expanding process. We show that Li-RRT is provably probabilistic completeness as original RRT. In addition, the expected time of returning a valid path with Li-RRT is obviously reduced. To verify the efficiency of our algorithm, numerical experiments are carried out in this paper.