The robots of tomorrow should be endowed with the ability to adapt to drastic and unpredicted changes in their environment and interactions with humans. Such adaptations, however, cannot be boundless: the robot must stay trustworthy. So, the adaptations should not be just a recovery into a degraded functionality. Instead, they must be true adaptations: the robot must change its behaviour while maintaining or even increasing its expected performance and staying at least as safe and robust as before. The RoboSAPIENS project will focus on autonomous robotic software adaptations and will lay the foundations for ensuring that they are carried out in an intrinsically trustworthy, safe and efficient manner, thereby reconciling open-ended self-adaptation with safety by design. RoboSAPIENS will transform these foundations into ‘first time right’-design tools and platforms and will validate and demonstrate them.