Rigid–Flexible Coupled Dynamics Modeling and Trajectory Compensation for Overhead Line Mobile Robots

When a mobile robot on an overhead line carries out operations, the effects of the elastic deformation and vibration of the flexible overhead line on motion performance cannot be ignored. This study proposes a method for active compensation of the robot’s trajectory, based on the force–deformation characteristics of the overhead line. Overhead line mobile robot systems show a complex nonlinear coupled vibration problem. To simplify the flexible environment, it is modeled as a single-degree-of-freedom spring–damped system. A rigid–flexible coupled dynamics model is established using the sub-bar method and the Lagrangian method. A numerical simulation is used to compare and analyze the end trajectories of mobile robots using generalized coordinates when the overhead line is rigid and flexible, respectively, revealing the coupling mechanism between the flexible overhead line and the robot. Based on the force–deformation characteristics of the overhead line, an active robot trajectory compensation method is proposed. The experimental results show that the established rigid–flexible coupling dynamics model describes the dynamic characteristics of an overhead line mobile robot, and the active robot trajectory compensation method has certain feasibility. The proposed method provides a reference basis for the control of overhead line mobile robots and has some applicability in addressing motion compensation issues in flexible environments.