Active Disturbance Rejection Control for Shape Control of Deformable Linear Objects under Non-Quasi-Static Conditions

The manipulation of deformable linear objects (DLOs) has gained widespread attention in recent years and has some practical applications, such as cable assembly. However, the shape control of DLOs is an extremely challenging problem. On the one hand, it has a complex physical model and disturbances, making it difficult for theoretical models to fully fit the actual physical model. On the other hand, it has high degrees of freedom and is an underactuated system. Therefore, determining the mapping between a small number of control inputs and multiple state outputs has become a problem. Most current control algorithms adopt a quasi-static assumption to derive this mapping. Although under this assumption, a linear mapping relationship between control inputs and state outputs can be derived, it results in relatively long control times. To address these two issues, this paper proposes an active disturbance rejection control (ADRC) method. Firstly, a mass-spring system (MSS) model of the DLO is established, and a Proportional (P) control algorithm under the quasi-static assumption is derived. Then, an extended state observer (ESO) is utilized to estimate the nonlinear error terms between the featured point velocity and the manipulated point velocity under non-quasi-static assumptions. The nonlinear error terms are compensated in the controller, achieving disturbance rejection control under non-quasi-static conditions and speeding up the control process. Finally, the stability of the algorithm is analyzed using Lyapunov methods, and the algorithm is validated through simulation.