Almost Global Asymptotic Trajectory Tracking for Fully-Actuated Mechanical Systems on Homogeneous Riemannian Manifolds
<|reference_start|>Almost Global Asymptotic Trajectory Tracking for Fully-Actuated Mechanical Systems on Homogeneous Riemannian Manifolds: 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 $\mathbb{S}^2$). 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.<|reference_end|>
@article{welde2024almost,
    title={Almost Global Asymptotic Trajectory Tracking for Fully-Actuated
  Mechanical Systems on Homogeneous Riemannian Manifolds},
    author={Jake Welde and Vijay Kumar},
    journal={arXiv preprint arXiv:2403.04900},
    year={2024},
    doi={10.1109/LCSYS.2024.3396565},
    archivePrefix={arXiv},
    eprint={2403.04900},
    primaryClass={eess.SY cs.RO cs.SY math.OC}
}