The general and constant ageing of the world population that has been observed in the last decade has led robotics researchers community to focus its aims to answer the ever-growing demand for health care, housing, care-giving, and social security. Among others, the researchers at Politecnico di Torino are developing a novel platform to enhance the performance offered by present-day issues, and to assess many others which were not even taken into consideration before they have been highlighted by the pandemic emergency currently in progress. This situation, in fact, made dramatically clear how important it is to have reliable non-human operators whom one can trust when the life of elderly or weak patients is endangered by the simple presence of other people. The platform, named Paquitop, features an innovative architecture conceived for omni-directional planar motion. The machine is designed for domestic, unstructured, and variously populated environments. Therefore, the mobile robot should be able to avoid or pass over small obstacles, passing through the capability to achieve specific person tracking tasks, and arriving to the need of operating with an high dynamic performance. Given its purpose, this work addresses the design of the suspension system which enables the platform to ensure a steady floor contact and adequate stability in every using condition. Different configurations of such system are then presented and compared through use-case simulations.