Control of wheeled mobile robots singularly perturbed by using the slipping and skidding variations: curvilinear coordinates approach (Part I)**The authors would like to thank Instituto Federal de Educação, Ciência e Tecnologia da Bahia (IFBA) and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), all of them of Brazil, for the research grant, financial support and study fellowship.

Geometric Modelling and Control of Slow-Fast Realization of Nonholonomic Mechanical Systems

“…To facilitate the development of practical autonomous wheeled mobile robotic (WMR) systems, it is essential to capture the physical nature of slip violations of the nonholonomic constraints, before losing traction. Previous singularly perturbed methods for WMR systems [8][9][10][11], have paid very little attention to the geometric structure of the underlying mechanical system. For this reason, these approaches result in a complex representation of the slow-fast dynamics and consequently, pose challenges in the approximation of the slip dynamics in practical WMR systems.…”

“…Hamerlain et al, construct higher-order sliding-mode controllers to mitigate the sliding effects, first applied to a unicycle [154] and later to a car-like robot [155]. Fernández et al, use SPT to model the dynamics of WMR systems, they design a trajectory tracking control law for the zero-order (nonholonomic) dynamics and propose a robust auxiliary controller to mitigate the sliding effects [9]. The relationship between the Bakker-Pacejka formula and the RDF coefficients is discussed in [11].…”

“…Moreover, the output linearization approach in [8] requires the invariance condition and the structure of the PD control law to be approximated simultaneously. The WMR equations of motion in [8][9][10][11] have complex coupling between the slow and fast dynamics making the approximation of the associated invariant manifold highly nontrivial. All of these approaches form the equations of motion using the Lagrangian formalism, and very few make use of the intrinsic geometry structures underlying mechanical systems resulting in complex equations.…”