In Odoo, you can use the "user_id" field in the "res.users" model to get the currently connected user. You can then use this field to update the signature field in your desired model.

Here's an example of how you can do this in a form view:

1. In your form view, create a new field for the signature, and set its "related" attribute to "user_id.signature"

2. In your form's "save" method, write a code to update the signature field with the current user's signature:

   def save(self):
   current_user = self.env.user
   self.signature = current_user.signature
   return super(YourModel, self).save()

This way when the form is saved the user's signature will be added to the signature field.