Flexible-joint manipulators (FJMs) have been widely used in the fields of industry, agriculture, medical service, aerospace, etc. However, the FJMs in practical applications inevitably encounter various uncertainties including matched and mismatched disturbances. In this paper, we consider the high precision tracking control problem of FJMs in the presence of unknown lumped matched and mismatched disturbances. An efficient model-assisted composite control approach is proposed by integrating two reduced-order extended state observers (RESOs), a second-order command filtered backstepping (SCFB) technique and an error compensation dynamic system. Unlike some existing methods, the RESOs constructed with partial known model information are capable of estimating and compensating the matched and mismatched disturbances simultaneously. In addition, by employing the SCFB with an error compensation system, the proposed approach can not only overcome the problem of “explosion of complexity” inherent in backstepping, but also reduce the filtering errors arising from the command filters. The stability of the resulting control system and the convergence of error signals are guaranteed by Lyapunov stability theory. Comparative simulations are conducted for a single-link FJM with both matched and mismatched disturbances, and the results show that the proposed approach achieves a better tracking performance, i.e., compared with conventional backstepping method and adaptive fuzzy command filtered control method, the tracking accuracy is improved by 99.5% and 99.2%, respectively.

The horizontal translational oscillator with a rotational actuator (TORA) is a typical underactuated mechanical system, whose control problem is still open and theoretically challenging. At present, the existing control methods are structurally complicated and require an exact knowledge of the system parameters. Moreover, few works have considered the output feedback stabilization of the TORA system subject to practical constraints of input saturation and angular velocity unmeasurement. To address these problems, this paper proposes a novel model-free amplitude-limited control approach to stabilize the TORA system at the origin using only angle feedback. Firstly, the passivity of the horizontal TORA system is analyzed, based on which a novel Lyapunov function augmented with an auxiliary signal is constructed by taking the input saturation into account. Then, an amplitude-limited control law is derived in a straightforward manner. In order to make the control law independent of velocity feedback, the auxiliary signal is designed in terms of the ball rotational angle and an output of a dynamic system. The asymptotic stability of the entire control system is rigorously guaranteed by utilizing Lyapunov theory and LaSalle’s invariance principle. Finally, simulation results with comparisons to existing methods demonstrate the effectiveness and superiority of the proposed control approach.

To achieve precise end-effector control from the initial position to the target position of a planar three-link PAA (passive-active-active) system with underactuated first joint, a position control strategy based on the same angular velocity constraint and neural networks is proposed. The dynamic model of the system is established using the Euler-Lagrange equation, and the constraint equations of underactuated joints are analyzed to obtain the angular velocity relationships among the system links. Next, under the same angular velocity constraint for the active links, a Lyapunov-based controller is constructed. A simulation platform is constructed to collect angular data of both active and passive links. The collected data are augmented using a generative adversarial network (GAN), and the mapping between passive and active link angles is established through a deep neural network (DNN). Considering the geometric constraints among link angles, the target angles for all system links corresponding to the end-effector position are optimized using a genetic algorithm, the desired end-effector position are optimized using a genetic algorithm. Based on the Lyapunov function, the designed controller synchronously stabilizes the second and third links to their target angles while achieving passive link angle control. Consequently, the position control objective of the system end-effector is realized through a non-switching control strategy. Simulation results show that, compared with the switching control method, the system end-point under the non-switching control strategy converges to (-0.698 0, 1.003 0) within 8 s, with shorter convergence time and smaller errors, avoiding complex integration processes. The non-switching control strategy achieves precise control of the system end-point from the initial position to the target position.