https://mygita.com how about something like a Gita Mini which is a follow bot? It is for paved outdoors as well as indoors. You can lock it from your phone and can follow the elderly person.
I think there are might be some tweaks to make it suit your purpose. But it is worth looking into how it can help senior care as a follow bot.
P.S: I did a ton of research for small farm robotics and met very interesting startup founders in the healthcare/robotics area on the way. If anyone wants to brainstorm or even simply chat about senior healthcare and robotics, please reach out. This is something that is very close to my heart and if I can help make connections even if I can’t help in any technical/material way, it would make me very glad.