The trustworthiness of robots and autonomous systems (RAS) has taken a prominent position on the way towards full autonomy. This work is the first to systematically explore the key facets of human-centred AI for trustworthy RAS. We identified five key properties of a trustworthy RAS, i.e., RAS must be (i) safe in any uncertain and dynamic environment; (ii) secure, i.e., protect itself from cyber threats; (iii) healthy and fault-tolerant; (iv) trusted and easy to use to enable effective human-machine interaction (HMI); (v) compliant with the law and ethical expectations. While the applications of RAS have mainly focused on performance and productivity, not enough scientific attention has been paid to the risks posed by advanced AI in RAS. We analytically examine the challenges of implementing trustworthy RAS with respect to the five key properties and explore the role and roadmap of AI technologies in ensuring the trustworthiness of RAS in respect of safety, security, health, HMI, and ethics. A new acceptance model of RAS is provided as a framework for human-centric AI requirements and for implementing trustworthy RAS by design. This approach promotes human-level intelligence to augment human capabilities and focuses on contribution to humanity.