In the above article, an error in [1, Th. 2].

This paper presents a balance control technique for a novel wheel-legged robot. We first derive a dynamic model of the robot and then apply a linear feedback controller based on output regulation and linear quadratic regulator (LQR) methods to maintain the standing of the robot on the ground without moving backward and forward mightily. To take into account nonlinearities of the model and obtain a large domain of stability, a nonlinear controller based on the interconnection and damping assignment - passivity-based control (IDA-PBC) method is exploited to control the robot in more general scenarios. Physical experiments are performed with various control tasks. Experimental results demonstrate that the proposed linear output regulator can maintain the standing of the robot, while the proposed nonlinear controller can balance the robot under an initial starting angle far away from the equilibrium point, or under a changing robot height.

This article proposes a novel image-based visual servoing for a flexible aerial refueling boom with an eye-in-hand camera. The dynamic model of the flexible refueling boom is established by absolute nodal coordinate formulation (ANCF), after which the dynamic model is decomposed into a slow subsystem and a fast subsystem based on the singular perturbation approach. With respect to slow subsystem, the image feedback is used to control the flexible refueling boom so that the projection of the point marker on the back of the receiver converges to the desired position. With respect to fast subsystem, linear quadratic regulator (LQR) is applied to stabilize the vibration of the flexible refueling boom. The asymptotic convergence of the image error to zero is verified based on the Lyapunov theory. Simulation is used to demonstrate the effectiveness of the proposed method.

In this paper, nonlinear control techniques are exploited to balance an unmanned bicycle with enlarged stability domain. We consider two cases. For the first case when the autonomous bicycle is balanced by the flywheel, the steering angle is set to zero, and the torque of the flywheel is used as the control input. The controller is designed based on the Interconnection and Damping Assignment Passivity Based Control (IDA-PBC) method. For the second case when the bicycle is balanced by the handlebar, the bicycle's velocity is high, and the flywheel is turned off. The angular velocity of the handlebar is used as the control input and the balance controller is designed based on feedback linearization. In these cases, the global stability of the closed-loop unmanned bicycle is theoretically proved based on Lyapunov theory. The experiments are conducted to validate the efficacy of the proposed nonlinear balance controllers.

In this paper, the gain scheduling technique is applied to design a balance controller for an autonomous bicycle with an inertia wheel. Previously, two different balance controllers are needed depending on whether the bicycle is stationary or dynamic. The switch between the two different controllers may cause the instability of the autonomous bicycle. Our proposed gain scheduled controller can balance the autonomous bicycle in both stationary and dynamic cases. A physical system is built and experiments are carried out to demonstrate the effectiveness of the gain scheduled controller.