Nonlinear Dynamic Modeling and Receding-Horizon NMPC of an Electric Unicycle on a Tensioned Cable

Traversing flexible slender structures involves strong bidirectional coupling between vehicle motion and structural vibration caused by a moving contact point. This paper presents a nonlinear modeling-and-control framework for an electric unicycle traversing a tensioned flexible cable. The cable is modeled using a tension-dominated finite-element formulation retaining vertical and lateral transverse dynamics, and is coupled to the unicycle roll and pitch dynamics through moving-contact kinematics. A modal truncation yields a control-oriented reduced-order model that preserves the nonlinear vehicle--cable coupling. Based on this model, a constrained nonlinear model predictive controller is formulated to regulate traversal, balance, actuator limits, and cable-span constraints. To reduce the computational burden associated with moving-contact interpolation, a frozen spatial contact-point interpolation strategy is introduced for the NMPC prediction model. Numerical studies under nominal, disturbed, constrained, and model-mismatch scenarios show accurate traversal, roll and pitch stabilization, attenuation of cable vibrations, and constraint-consistent closed-loop behavior. The frozen-interpolation formulation reduces and regularizes NMPC computation times relative to the non-frozen formulation, supporting its use as a computationally tractable approach for finite-element-based moving-contact vehicle--structure interaction systems.