We develop here a novel hypothesis that may generate a general research framework of how autonomous robots may act as a future contingency to counteract the ongoing ecological mass extinction process. We showcase several research projects that have undertaken first steps to generate the required prerequisites for such a technology-based conservation biology approach. Our main idea is to stabilise and support broken ecosystems by introducing artificial members, robots, that are able to blend into the ecosystem's regulatory feedback loops and can modulate natural organisms' local densities through participation in those feedback loops. These robots are able to inject information that can be gathered using technology and to help the system in processing available information with technology. In order to understand the key principles of how these robots are capable of modulating the behaviour of large populations of living organisms based on interacting with just a few individuals, we develop novel mathematical models that focus on important behavioural feedback loops. These loops produce relevant group-level effects, allowing for robotic modulation of collective decision making in social organisms. A general understanding of such systems through mathematical models is necessary for designing future organism-interacting robots in an informed and structured way, which maximises the desired output from a minimum of intervention. Such models also help to unveil the commonalities and specificities of the individual implementations and allow predicting the outcomes of microscopic behavioural mechanisms on the ultimate macroscopic-level effects. We found that very similar models of interaction can be successfully used in multiple very different organism groups and behaviour types (honeybee aggregation, fish shoaling, and plant growth). Here we also report experimental data from biohybrid systems of robots and living organisms. Our mathematical models serve as building blocks for a deep understanding of these biohybrid systems. Only if the effects of autonomous robots onto the environment can be sufficiently well predicted can such robotic systems leave the safe space of the lab and can be applied in the wild to be able to unfold their ecosystem-stabilising potential.