MEAM Seminar: “Hierarchical Methods for Geometric Control of Underactuated, Free-Flying Robotic Systems”

Free-flying robotic systems (such as multibody aerial and space vehicles) evolve on high-dimensional non-Euclidean manifolds subject to nonlinear, underactuated dynamics. Because such systems can rely only on the severely limited computational resources available onboard, the design of general-purpose controllers capable of dynamic and reliable real-time performance remains a formidable challenge. To mitigate these obstacles and achieve the stated goals across a broad class of systems, we seek geometric insight into structural properties that transcend individual robot morphologies, developing systematic methods of controller synthesis by leveraging these features. First, we exploit the Noetherian symmetry and Riemannian structure inherent to their dynamics, revealing a class of systems that admits a certain hierarchical decomposition. In such a representation, the motion of the system’s internal degrees of freedom is completely determined by the bulk motion through its symmetry group (e.g. its position and orientation). Examples of such systems include aerial manipulators consisting of an underactuated vehicle equipped with a robotic arm. Second, in order to design and certify hierarchical controllers that leverage this structure, we prove new basic results on the stability of cascades whose subsystems are only almost globally asymptotically stable, the best possible property for smooth vector fields on general manifolds. Lastly, in our ongoing work we apply these theoretical insights to inform mechanical design and controller implementation in pursuit of a small and agile aerial manipulator capable of precise, dynamic operation.