Wa `alaykum As-Salamu waRahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
Since a robot has no mind or heart, it is inconceivable of it to perform acts of worship on behalf of humans.
Answering your question, Sheikh Ahmad Kutty, a Senior Lecturer and an Islamic Scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
Pilgrimage, like all other acts of worship in Islam, requires intention and presence of mind/heart as a precondition for its validity. Since a robot has no mind or heart, it is inconceivable of it to perform acts of worship on behalf of humans. Acts of worship are valid only if done by humans who are conscious of their actions.
That is why neither a child nor a person who is not in full of senses can be expected to perform Hajj on behalf of another; since taklif (legal responsibility) is lifted from them.
This in no way means to suggest that humans cannot use robots for performing mechanical services that require no mental deliberation or conscious will. They can be used for essential chores or services as we use other devices or instruments.
Almighty Allah knows best.