Ensuring the sustainability of future space missions requires addressing the space-debris issue proactively. Space debris threatens future space missions, making the need for collision avoidance manoeuvres essential. This research explores robust methods to perform such manoeuvres, focusing on guidance and control systems, using the Starlink constellation as a reference. A robust guidance system integrating convex optimisation enables autonomous, fuel-efficient collision avoidance of space debris. Testing across diverse conditions shows suitability for various satellite characteristics. Attitude-control requirements are analysed with a linear quadratic regulator controller. Low-thrust manoeuvres with constant capabilities are optimal for this specific mission, minimising fuel usage and achieving desired miss distances. The outcomes of this research represent a significant advancement in space-debris mitigation and contribute to enhancing space sustainability.