Efficient Hamel's integrator for vehicle-manipulator systems

Vehicle-manipulator systems offer versatile manipulation and mobility in challenging environments. However, conventional dynamic modeling approaches often encounter singularities and may fail to capture underlying symmetries. In addition, they typically exhibit high computational complexity, which scales cubically with the total degrees of freedom of the vehicle and manipulator. This work proposes a singularity-free formulation for vehicle-manipulator systems built on Hamel's formalism. This approach is particularly advantageous for nonholonomic systems, as applying the Lagrange–d'Alembert principle within this framework eliminates the unnecessary Lagrange multipliers associated with velocity constraints. Furthermore, we present an efficient variational integrator, augmented with a quasi-Newton algorithm, that solves the root-finding problem for the discrete Hamel's equations with linear time complexity. We demonstrate the effectiveness of the variational integrator through numerical studies of a space manipulator and a nonholonomic mobile manipulator, and verify its linear-time complexity with a dedicated performance benchmark.