In this article, we consider the trajectory tracking and vibration suppression of a flexible-link flexible-joint manipulator under uncertainties and external time-varying unknown disturbances. The coupled ordinary differential equation and partial differential equation model dynamic of the system is presented by employing the Hamilton principle. Using the singular perturbation theory, the dynamic is decomposed into a no-underactuated slow ordinary differential equation and fast partial differential equation subsystem, which solves the problem of the underactuated ordinary differential equation subsystem of the ordinary differential equation and partial differential equation cascade and reduces the analytical complexity. For the slow subsystem, to guarantee the trajectory tracking of the joint, an adaptive global sliding mode controller without gain overestimation is designed, which can guarantee the global stability of the slow system and reduce the chattering of the sliding mode control. For the fast subsystem, an adaptive boundary controller is developed to suppress the elastic vibration of the flexible link during the trajectory tracking. The stability of the whole closed-loop system is rigorously proved via the Lyapunov analysis method. Simulation results show the effectiveness of the proposed controller.

The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/adem.202101767.

Trajectory tracking is a key step for a free-floating space robot (FFSR) system to complete a space operation. However, the flexibility of links and deadzone in joint input torque decrease the system's trajectory tracking accuracy. The angle tracking for the multi-flexible-link FFSR was discussed to suppress the vibrations of the flexible links and prevent the influence of the deadzone. First, the dynamic equation of the FFSR system was derived. Second, the FFSR system was decomposed into the slow and fast subsystems. Then, for the slow subsystem, a robust control method based on a nominal model and a deadzone estimation compensator were proposed. For the fast subsystem, a linear quadratic regulator optimal method was used to actively suppress vibrations. Finally, experiments were carried out to verify that the FFSR is capable of effectively tracking the desired trajectory. The simulation results show the robustness of the control scheme. It effectively suppressed the vibrations as the vibration modes of the links convergent to zero. This study provides a control scheme for improving the trajectory tracking accuracy of FFSR, which is of practical importance.

A comprehensive three-dimensional dynamic model of a multi-cable double-drum winding hoister with flexible guides is presented, as the existing models cannot deal with the three-dimensional eccentricity of the cage and out-of-plane excitation generated by rotational drums. The entire system consists of three subsystems: cable subsystem, cage subsystem, and guide subsystem, respectively. Displacement and force boundary conditions are employed to couple those subsystems, and the interaction between cage and guides is considered as bidirectional coupling. The dynamic models of the three subsystems are established by Hamilton principle and Newton-Euler equation in a three-dimensional space independently. The dynamic model is discretized and solved by the Galerkin method and Runge–Kutta method. The three-dimensional displacement excitations and three-dimensional eccentricity can be handled in this dynamic model. The differences between two-dimensional dynamic model and three-dimensional dynamic model are discussed and the mechanism of entire system vibration are also analyzed by numerical simulation with typical unbalance factors, the cage eccentricity. The results show that the proposed three-dimensional dynamic model is more accurate in some realistic cases, existing out-of-plane excitation or three-dimensional eccentricity of the cage.

Nonlinear dynamic of a flexible slender truss-structure mounted manipulator for on-orbit assembly, which can be simplified as a beam-rotating link interaction system, is theoretically investigated. The governing partial differential equations (PDEs) of beam with time-varying coefficients is established by using the D'Alembert principle incorporated with the moment balance method where the beam is of a Euler-Bernoulli type and the influence of slope is considered. Such system is a typical parametrically excited system. The multiple scales method is used to determine the approximate solution and the conditions of the primary resonance (ω 1 ≈ ω ref ) and sub-harmonic resonance (ω 1 ≈ 2ω ref , ω 1 ≈ 3ω ref and ω 1 ≈ 4ω ref ) are obtained. In addition, the nonlinear response, stability and bifurcations for primary and sub-harmonic resonance conditions have also been investigated by varying system parameters. Moreover, the results of some specific conditions by the perturbation analysis are compared with the numerical solution and are found to be in good agreement. This work has certain guiding significance for autonomous on-orbit assembly task and the method can be extended to the more general three-dimensional case.INDEX TERMS On-orbit assembly, flexible slender truss-structure mounted manipulator, parametric excitation, method of multiple scales, primary resonance, sub-harmonic resonance.