Mode-Dependent Differential-Algebraic Kinematic Modeling of a Four-Wheel Wall-Climbing Robot on Cylindrical Inner Surfaces

Multi-wheel wall-climbing robots operating on cylindrical inner surfaces are subject to configuration-dependent wheel-surface contacts and nonholonomic rolling constraints, making planar differential-drive or fixed-contact kinematic models insufficient when the active contact topology changes. This study develops a mode-dependent differential-algebraic kinematic model for a four-wheel wall-climbing robot on cylindrical inner surfaces. Given the instantaneous active contact set, the wheel-surface geometry is reconstructed from nonlinear point-on-surface and tangency constraints using an adaptive Levenberg–Marquardt method. The reconstructed contact geometry is then used to assemble normal-velocity compatibility and rolling constraints, yielding an analytical mapping from a nominal body-twist reference to active-wheel speed commands. The model is integrated into trajectory-based motion generation and assessed through multibody co-simulation incorporating contact and friction effects. For unidirectional and S-shaped motions, the axial root-mean-square errors (RMSEs) are 5.6 mm and 11.5 mm, with normalized axial errors of 0.112% and 0.096%, respectively; the circumferential-angle RMSEs are $1.{25}^{\circ }$ and $1.{32}^{\circ }$, with normalized angular errors of 1.39% and 0.73%. These results demonstrate the applicability of the model to contact-dependent geometric reconstruction and wheel-speed command generation under varying multi-wheel contact topologies on cylindrical inner surfaces, and offer an extensible approach to the kinematic modeling of multi-wheel locomotion in cylindrical environments.