Self-adaptive robotic systems operate autonomously in dynamic and uncertain environments, requiring robust real-time monitoring and adaptive behaviour. Unlike traditional robotic software with predefined logic, self-adaptive robots exploit artificial intelligence (AI), machine learning, and model-driven engineering to adapt continuously to changing conditions, thereby ensuring reliability, safety, and optimal performance. This paper presents a research agenda for software engineering in self-adaptive robotics, structured along two dimensions. The first concerns the software engineering lifecycle, requirements, design, development, testing, and operations, tailored to the challenges of self-adaptive robotics. The second focuses on enabling technologies such as digital twins and AI-driven adaptation, which support runtime monitoring, fault detection, and automated decision-making. We identify open challenges, including verifying adaptive behaviours under uncertainty, balancing trade-offs between adaptability, performance, and safety, and integrating self-adaptation frameworks like MAPE K/MAPLE-K. By consolidating these challenges into a roadmap toward 2030, this work contributes to the foundations of trustworthy and efficient self-adaptive robotic systems capable of meeting the complexities of real-world deployment.