In this letter, a novel dynamic model of a cable-driven continuum robot is established based on the principle of virtual power, in which the dynamically centralized length of the driving cable is used to simulate the driving process. This loading model implicitly represents the driving loads and explicitly describes the geometrical constraint of cables on the system. The distribution law for friction forces of actuated cables is demonstrated, which can be handily represented by the derived relationship between the tension of the cables and the Lagrange multiplier. This dynamic model is applicable for continuum robots with a single/multi-tandem arm driven by any number of cables. Furthermore, an average stress strategy is developed so that the high-frequency components of the dynamic model can be reasonably controlled in a simple but effective manner, which can strikingly reduce the stiffness of the differential equations. Simulation results show that this strategy significantly improves the simulation efficiency with sound and reasonable precision. A comparison of the results from the numerical simulations and experiments for a cable-driven continuum structure verifies the validity of the proposed model, and the average percentage error for the trajectory between the simulation and experimental results is 1.92%. Moreover, the numerical simulations for the dynamic equations of the cable-driven continuum robot with twenty segments can be run in real-time.

The operation and control of the cable-driven continuum robot (CDCR) is directly determined by the actuation of cables, and the relationship between the driving length and the tension as well as the morphology of the CDCR has not been deeply researched in previous literature. In this article, a novel methodology for perceiving the morphology, tension, and driving state of the robot is proposed, which can be calculated only by the dynamic driving length/speed of cables without using shape sensors and tension sensors. First, a model of the tension distribution along with the cable path is deduced, which takes into account the influence of the sliding friction. Second, a rigid-flexible coupling dynamic model considering the strain of the cable is established. Then, a nonlinear complementary model between the driving state and the tensions of cables is constructed based on the mechanism of cable actuation, and an efficient solution algorithm is presented. Experiments of a single arm driven by two cables and a three-tandem arm driven by multiple cables were conducted to validate the proposed method. The average errors of the perceiving morphology and tension are 1.85% and 7.26%, respectively, and the transaction between the slack and tensional state of the driving cable is accurately captured. In addition, the hysteresis behavior of the cable actuation is also perceived.

Intelligent Internet of Things and its diverse application domains are transforming industry significantly. In an industry assembly task of a multi-robot system, multi-agent system (MAS) coordinate control used in intelligent industry 5.0 systems is a critical foundation of robot control for enhanced safety and stability, increased electricity economy. MAS consensus control encounters difficult problems such as external disturbances and unknown dynamics. To overcome these deficiencies, a predefined-time adaptive consensus control scheme for a class of nonlinear multi-agent systems with unknown dynamics and external disturbances is proposed in this paper. First, two specific time-varying functions and the corresponding transformation form are constructed. Next, a predefined-time adaptive distributed controller is designed based on the backstepping method. Furthermore, an adaptive neural network is developed to handle the external disturbances and the unknown dynamics to improve the robustness of the controller. Additionally, it is proven that the errors can converge to a small neighborhood of zero using the Lyapunov stability theorem. Finally, the simulation results show that the proposed control scheme has a shorter settling time and smaller tracking errors at predefined time.

This paper presents a novel quasi-three-dimensional shear deformation theory called the spectral displacement formulation (SDF) for analyzing the free vibration of functionally graded plates. The SDF expresses the unknown displacement field as a unique form of the Chebyshev series in the thickness direction. By increasing the truncation number in the Chebyshev series, the bending analysis results can approach the three-dimensional elasticity solution and satisfy the traction-free boundary conditions without requiring a shear correction factor. The SDF is an extension of the classical plate theory, thereby naturally avoiding the shear-locking phenomenon. These characteristics enable the SDF to apply to plates of arbitrary thickness while maintaining accuracy. The nonuniform rational B-spline-based isogeometric approach is employed to enhance the applicability of this theory to free vibration analysis of functionally graded plates with complex geometries and different boundary conditions. Numerical examples are presented to demonstrate the accuracy and reliability of the proposed method in analyzing the free vibration of functionally graded plates.

A new quasi-three-dimensional (3D) shear deformation theory, called the spectral displacement formulation (SDF), is proposed for high-precision static bending analyses of functionally graded plates. The main idea is to expand unknown displacement fields into Chebyshev series of a unique form in the thickness direction; the truncation numbers are set to be adjustable to meet various application requirements. Specifically, 3D elasticity solutions and traction-free boundary conditions can be approached by increasing the number of Chebyshev bases. The SDF is also an extension of the classical plate theory and naturally avoids the shear locking problem, making it versatile for functionally graded material (FGM) plates of arbitrary thicknesses. The C1 continuity requirement for the discretization of the generalized displacements is conveniently fulfilled by the nonuniform rational B-splines (NURBS)-based isogeometric method. Numerical examples demonstrate the excellent performance of the proposed method for the displacement and stress analyses of functionally graded plates. The high precision and versatility of the present method have manifested its great potential applications in strain-based or stress-based reliability analysis, optimization design, fatigue analysis, and fracture analysis of FGM plates, and other related fields.