Modelling and linear stability analysis of highly mobile nonholonomic multibody systems

• Autores: Alfonso García-Agúndez Blanco
• Directores de la Tesis: Emilio Freire Macías (dir. tes.), Daniel García Vallejo (dir. tes.)
• Lectura: En la Universidad de Sevilla ( España ) en 2023
• Idioma: inglés
• Número de páginas: 355
• Enlaces
  • Tesis en acceso abierto en: Idus
• Resumen

  • This PhD thesis aims to develop a methodology that contributes to the modelling of nonholonomic multibody systems, the study of their linear stability and the design of linear feedback controllers. The ultimate objective is on single-person nonholonomic vehicles, particularly in terms of safety in urban transportation. By understanding how critical design parameters affect stability, it will be possible to carry out design modifications that result in safer vehicles and reduce accidents. These modifications will also cater to a wider range of potential users, including elderly and physically impaired individuals.

    From a regulatory perspective, understanding stability conditions will play a crucial role in formulating rules for the use of these vehicles within cities. Moreover, advancements focused on enhancing safety will promote the adoption of electric single-person vehicles, leading to a reduction in environmental degradation and aiding in the accomplishment of pollution reduction objectives.

    The methodology consists of the following phases. First, multibody models of a class of nonholonomic systems are developed. Subsequently, in order to carry out the linear stability analyses of these multibody systems, efficient and accurate linearization approaches are required. To this end, novel linearization procedures, for multibody systems with holonomic and nonholonomic constraints, are proposed. The correctness of the linearization approaches is validated with the linear stability results of a well-acknowledged bicycle benchmark. The results show that the procedures are completely accurate, efficient, valid for any multibody system (regardless of its complexity) and powerful, obtaining the linearized equations of motion along an arbitrary reference solution as a function of the design parameters of the multibody system. Next, by varying these parameters over a wide range of values, a detailed sensitivity analysis of the eigenvalues can be performed to assess the linear stability of the multibody system. Lastly, linear feedback controllers can be designed by using the linearized equations of motion.

    These linearization approaches are applied to study the linear stability of several nonholonomic systems. First, linear time-invariant (LTI) systems are addressed. In particular, the linear stability of the steady forward motions of classical nonholonomic systems, as the skateboard or the rolling hoop, and highly mobile nonholonomic multibody systems, such as the bicycle, the waveboard and the electric kickscooter, is assessed. Next, the case of periodic linear time-varying (LTV) systems is studied, including a detailed linear stability analysis of the circular steady motion of the rolling toroidal wheel. Another application is the use of the linearization procedures in multiphysics scenarios, and, in particular, with hydraulically actuated multibody systems. Finally, the approaches are applied in the design of linear feedback controllers for nonholonomic multibody systems. As an example of application, the optimal control of the well-known ball-plate system, using a Linear-Quadratic Regulator (LQR), is shown.