Hierarchical modeling and simulation of a wheeled-legged manipulator with wheel slippage using the Gibbs–Appell approach

Abstract In this research, a hierarchical dynamic and kinematic modeling framework is proposed for a wheeled-legged manipulator (WLM), explicitly incorporating wheel slip and skid effects through the Gibbs–Appell formulation. Unlike traditional Lagrangian methods that depend on constraint multipliers, the proposed approach unifies the platform and manipulator dynamics while substantially reducing computational complexity. This integration enables efficient handling of nonholonomic constraints without compromising physical fidelity and offers a clear separation between subsystems, allowing the effects of wheel-ground interactions to be analyzed independently from manipulator motions. The proposed formulation is validated through a combination of MATLAB/Webots simulations and laboratory experiments conducted under both dry and wet (soapy ceramic) surface conditions. Experimental results indicate end-effector position deviations of 8–10.5% primarily due to wheel slip and initial joint torque discrepancies of 6.5–20% that progressively diminish as steady-state motion is reached. Comparative evaluation against a conventional Lagrangian model highlights the computational advantage of the Gibbs–Appell formulation, demonstrating reduced assembly time and fewer symbolic differentiation operations. Furthermore, a sensitivity analysis on friction coefficients and slip ratios confirms the robustness of the model to variations in surface conditions. Beyond accurate dynamic prediction, the hierarchical structure enables modular real-time implementation, supporting controller design, trajectory planning, and fault detection. Overall, the results demonstrate that the Gibbs–Appell-based hierarchical modeling framework combines analytical rigor with computational efficiency, providing a robust foundation for control and optimization in advanced wheeled-legged robotic manipulators.