Autonomous Space Robotics and Mechatronics Laboratory (ASRoM-Lab) is a graduate research laboratory in the Department of Mechanical and Aerospace Engineering, Carleton University, whose primary focus is the development of advanced guidance, navigation and control strategies for next-generation space robotic and mechatronic systems. Algorithms and methodologies based on geometric mechanics and control are deployed as a promising approach to particularly study the response of space systems in the presence of off-nominal conditions appearing in space missions. Geometry-based frameworks are advantageous, since they offer synergistic integration of mechanical, electrical and computer subsystems, high-fidelity modelling, alongside effective controllers to remediate off-nominal conditions and help with the long-term autonomy of future space systems operating in hostile and uncertain outer space environments.