Professor Robert Mahony pioneered the application of the principles of symmetry to address practical challenges in systems theory and robotics. Identifying and solving key scientific roadblocks by leveraging the intrinsic geometry and symmetry of the problem domain, Professor Mahony spearheaded the development of advanced algorithms for state estimation and optimisation. These contributions have yielded profound societal impacts. The 'Mahony filter' was crucial to the initial wave of commercial drones and is a design cornerstone of the contemporary multi-billion dollar drone industry, delivering one of the most substantial advances in the design of inertial navigation systems witnessed in half-a-century.