Robots will revolutionise the world's economy and society over the next twenty years, 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, assistive and medical robots, offshore energy, environmental monitoring, search and rescue, defence, and support for the aging population. The robotics and autonomous systems area has been highlighted by the UK Government in 2013 as one the 8 Great Technologies that underpin the UK's Industrial Strategy for jobs and growth. The essential challenge can be characterised as how to obtain successful INTERACTIONS. Robots must interact physically with environments, requiring compliant manipulation, active sensing, world modelling and planning. Robots must interact with each other, making collaborative decisions between multiple, decentralised, heterogeneous robotic systems to achieve complex tasks. Robots must interact with people in smart spaces, taking into account human perception mechanisms, shared control, affective computing and natural multi-modal interfaces.Robots must introspect for condition monitoring, prognostics and health management, and long term persistent autonomy including validation and verification. Finally, success in all these interactions depend on engineering enablers, including architectural system design, novel embodiment, micro and nano-sensors, and embedded multi-core computing. The Edinburgh alliance in Robotics and Autonomous Systems (EDU-RAS) provides an ideal environment for a Centre for Doctoral Training (CDT) to meet these needs. Heriot Watt University and the University of Edinburgh combine internationally leading science with an outstanding track record of exploitation, and world class infrastructure enhanced by a recent £7.2M EPSRC plus industry capital equipment award (ROBOTARIUM). A critical mass of experienced supervisors cover the underpinning disciplines crucial to autonomous interaction, including robot learning, field robotics, anthropomorphic & bio-inspired designs, human robot interaction, embedded control and sensing systems, multi-agent decision making and planning, and multimodal interaction. The CDT will enable student-centred collaboration across topic boundaries, seeking new research synergies as well as developing and fielding complete robotic or autonomous systems. A CDT will create cohort of students able to support each other in making novel connections between problems and methods; with sufficient shared understanding to communicate easily, but able to draw on each other's different, developing, areas of cutting-edge expertise. The CDT will draw on a well-established program in postgraduate training to create an innovative four year PhD, with taught courses on the underpinning theory and state of the art and research training closely linked to career relevant skills in creativity, ethics and innovation. The proposed centre will have a strong participative industrial presence; thirty two user partners have committed to £9M (£2.4M direct, £6.6M in kind) support; and to involvement including Membership of External Advisory Board to direct and govern the program, scoping particular projects around specific interests, co-funding of PhD studentships, access to equipment and software, co-supervision of students, student placements, contribution to MSc taught programs, support for student robot competition entries including prize money, and industry lead training on business skills. Our vision for the Centre is as a major international force that can make a generational leap in the training of innovation-ready postgraduates who are experienced in deployment of robotic and autonomous systems in the real world.