Prof. Robert Mahony from the Australian National University visited CDSL on September 1, 2026, and gave a seminar entitled “Equivariant Systems Theory.” Prof. Mahony leads the Systems Theory and Robotics Group at ANU, where his research focuses on nonlinear systems and control with applications to robotics and computer vision. He is widely
known for his contributions to geometric observer design, state estimation, and aerial robotics.
In his seminar, Prof. Mahony introduced equivariant systems theory, a framework for studying nonlinear dynamical systems by exploiting their underlying symmetries. Many systems arising in robotics and navigation possess natural geometric structures associated with rotations, rigid-body motions, or other symmetry transformations. Rather than treating such systems as arbitrary nonlinear models, equivariant systems theory uses these symmetries to obtain more structured representations of the dynamics and to facilitate the design of state estimators and controllers. Prof. Mahony discussed how this viewpoint leads to tools such as the equivariant filter for state estimation and the equivariant regulator for control, as well as a broader classification of nonlinear systems according to their symmetry structures.
The seminar was closely related to CDSLʼs research interests in nonlinear systems, observer design, and state estimation. CDSL has studied a variety of estimation problems for nonlinear and networked dynamical systems, including nonlinear observers, resilient state estimation, and distributed observers. Prof. Mahonyʼs symmetry-based perspective provided a valuable opportunity to explore how geometric structure can be systematically exploited in the analysis and design of nonlinear estimation and control systems. Prof. Mahonyʼs seminar gave CDSL members a different way to think about nonlinear estimation and control, especially through the use of symmetry and geometric structure. The discussion after the seminar also helped us relate these ideas to problems that we are currently studying. It was a pleasure to have Prof. Mahony visit CDSL, and we hope to have more chances to exchange ideas in the future.