Understanding how our Solar System was formed 4.5 billion years ago and how it has evolved since represents one of the major challenges of modern astrophysics. The "Extremely Large Telescope" (ELT), currently built by ESO in Chile, will be decisive for unprecedented observations of asteroids, trans-Neptunian objects, and Centaurs as it will offer very high spatial resolution and sensitivity. These small distant bodies are the most primitive of the Solar System and therefore bear witness to the conditions of its formation and evolution. The study of their physical properties and composition is decisive for proposing formation and evolution scenarii and answering questions that remain opened about our Solar System origin. In particular, trans-Neptunian objects form the original remains of the outer part of the proto-solar disk. These objects were able to bring volatile species to more internal planets like Earth, conditioning their evolution and habitability. The MICADO and HARMONI instruments of the ELT will allow in-depth studies of rocky and icy dwarf planets. MICADO will bring constrains on the physical properties (size, shape, rotation, density, mass, internal structure) of hundreds of asteroids and about twenty TNOs by direct imaging and high precision astrometry. Their composition will be mapped by narrowband imaging and slit spectroscopy. In addition, the expected high astrometric precision should make it possible to measure the dynamics of several multiple systems of asteroids and KBOs giving access to the masses and therefore to the densities of the objects. MICADO will be served by MORFEO, a multi-conjugate adaptive optics (MCAO) with several laser stars and several deformable mirrors. The use of MORFEO will be crucial to observe faint and sometimes fast objects against the sky with the best possible resolution. Members of the MORFEO team, we aim at carrying out the scientific preparation of the instrument by (i) defining AO operations for non sidereal faint objects and observation strategies based on the relative geometrical configuration between the Earth and the minor bodies (ii) simulating images and spectra with a complete set of numerical tools and laboratory reflectance data (iii) devising tools for image deconvolution, processing, and analysis. We will present this approach and the expected performances.