Robots and autonomous systems (RAS) will revolutionise the world's economy and society for the foreseeable future, working for us, beside us and interacting with us. The UK urgently needs graduates with the technical skills and industry awareness to create an innovation pipeline from academic research to global markets. Key application areas include manufacturing, construction, transport, offshore energy, defence, and health and well-being. The recent Industrial Strategy Review set out four Grand Challenges that address the potential impact of RAS on the economy and society at large. Meeting these challenges requires the next generation of graduates to be trained in key enabling techniques and underpinning theories in RAS and AI and be able to work effectively in cross-disciplinary projects. The proposed overarching theme of the CDT-RAS can be characterised as 'safe interactions'. Firstly, robots must safely interact physically with environments, requiring compliant manipulation, active sensing, world modelling and planning. Secondly, robots must interact safely with people either in face-to-face natural dialogue or through advanced, multimodal interfaces. Thirdly, key to safe interactions is the ability for introspective condition monitoring, prognostics and health management. Finally, success in all these interactions depends on foundational interaction enablers such as techniques for vision and machine learning. The Edinburgh Centre for Robotics (ECR) combines Heriot-Watt University and the University of Edinburgh and has shown to be an effective venue for a CDT. ECR combines internationally leading science with an outstanding track record of exploitation, and world class infrastructure with approximately £100M in investment from government and industry including the National ROBOTARIUM. A critical mass of over 50 experienced supervisors cover the underpinning disciplines crucial to RAS safe interaction. With regards facilities, ECR is transformational in the range of robots and spaces that can be experimentally configured to study both the physical interaction through robot embodiment, as well as, in-field remote operations and human-robot teaming. This, combined with supportive staff and access to Project Partners, provides an integrated capability unique in the world for exploring collaborative interaction between humans, robots and their environments. The reputation of ECR is evidenced by the additional support garnered from 31 industry Project Partners, providing an additional 23 studentships and overall additional support of approximately £11M. The CDT-RAS training programme will align with and further develop the highly successful, well-established CDT-RAS four-year PhD programme, with taught courses on the underpinning theory and state of the art and research training, closely linked to career relevant skills in creativity, RI and innovation. The CDT-RAS will provide cohort-based training with three graduate hallmarks: i) advanced technical training with ii) a foundation international experience, and iii) innovation training. Students will develop an assessed learning portfolio, tailored to individual interests and needs, with access to industry and end-users as required. Recruitment efforts will focus on attracting cohorts of diverse, high calibre students, who have the hunger to learn. The single-city location of Edinburgh enables stimulating, cohort-wide activities that build commercial awareness, cross-disciplinary teamwork, public outreach, and ethical understanding, so that Centre graduates will be equipped to guide and benefit from the disruptions in technology and commerce. Our vision for the CDT-RAS is to build on the current success and ensure the CDT-RAS continues to be a major international force that can make a generational leap in the training of innovation-ready postgraduates, who will lead in the safe deployment of robotic and autonomous systems in the real world.