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

arXiv: https://arxiv.org/abs/2403.04900 · HTML: https://mlsanity.com/paper/2403.04900/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Mar 2024.

## Built on by (most cited first, 1 of 1)

- [Leveraging Symmetry to Accelerate Learning of Trajectory Tracking Controllers for Free-Flying Robotic Systems](https://mlsanity.com/paper/2409.11238/) (2024)

## Abstract (arXiv)

In this work, we address the design of tracking controllers that drive a mechanical system's state asymptotically towards a reference trajectory. Motivated by aerospace and robotics applications, we consider fully-actuated systems evolving on the broad class of homogeneous spaces (encompassing all vector spaces, Lie groups, and spheres of any finite dimension). In this setting, the transitive action of a Lie group on the configuration manifold enables an intrinsic description of the tracking error as an element of the state space, even in the absence of a group structure on the configuration manifold itself (e.g., for mathbbS2). Such an error state facilitates the design of a generalized control policy depending smoothly on state and time, which drives the geometric tracking error to a designated origin from almost every initial condition, thereby guaranteeing almost global convergence to the reference trajectory. Moreover, the proposed controller simplifies elegantly when specialized to a Lie group or the n-sphere. In summary, we propose a unified, intrinsic controller guaranteeing almost global asymptotic trajectory tracking for fully-actuated mechanical systems evolving on a broad class of manifolds. We apply the method to an axisymmetric satellite and an omnidirectional aerial robot.