Title: Almost Global Asymptotic Trajectory Tracking for Fully-Actuated Mechanical Systems on Homogeneous Riemannian Manifolds 

Abstract: Many robotic systems (or subsystems thereof) can be modeled as mechanical (i.e., Lagrangian) systems with a homogeneous Riemannian manifold as their configuration space and the applied external force as their control input. In this talk, we consider the design of trajectory tracking controllers in this setting, seeking a globally valid, time-and-state-feedback control policy that drives the system’s state asymptotically towards a chosen reference trajectory. In the special case of systems evolving on Lie groups, it is already well-understood that the tracking control problem can be solved via the stabilization of the so-called “error dynamics” arising directly from the group structure, reducing the “tracking problem” to the “regulation problem". In our work, we show that a similar approach can also be adopted in a more general setting, even on homogeneous spaces that do not admit a Lie group structure (e.g., on spheres of any dimension other than 0, 1, 3). We apply the method to synthesize tracking controllers for several example systems, guaranteeing exactly zero probability of failing to converge from a randomly-selected initial state. These results also have broader implications as building blocks in the synthesis of tracking controllers for underactuated mechanical systems.

Bio:  Dr. Jake Welde is an Assistant Professor in the Sibley School of Mechanical and Aerospace Engineering at Cornell University. His research explores the role of differential geometry and dynamical systems theory in control synthesis and design for robotic systems, exploiting structural properties to explainably synthesize efficient controllers, accelerate learning algorithms, and develop more capable robot morphologies. Prior to joining MAE at Cornell in 2025, Jake spent a decade at the University of Pennsylvania, where he completed his undergraduate and doctoral degrees in Mechanical Engineering and Applied Mechanics and his Masters in Robotics, working in the General Robotics, Automation, Sensing, and Perception (GRASP) Laboratory.