The general guiding theme and vision of the new Empa Laboratory of Sustainability Robotics is to develop novel soft robotic systems for infrastructure maintenance and environmental monitoring. The main research method of the Centre is Physical Artificial Intelligence (PAI). The work uses a bio-inspired robot development methodology and focuses on integrating advanced materials with machine-learning-based controllers and multi-sensor perception. The centre is based on an institutional partnership between Imperial College London and the Swiss Federal Laboratories for Materials Science and Technology. Research thrusts include aerial robotics platform development, soft robotics, material science and digital infrastructure systems. The initiative benefits from advanced facilities in robot manufacturing and testing, including the NEST experimental robot testing space at Empa  and a Vicon equipped flight arena at Imperial College London.