Almost Global Asymptotic Trajectory Tracking for Fully-Actuated Mechanical Systems on Homogeneous Riemannian Manifolds Article Swipe
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1109/lcsys.2024.3396565
· OA: W4392677623
In this work, we address the design of tracking controllers that drive a\nmechanical system's state asymptotically towards a reference trajectory.\nMotivated by aerospace and robotics applications, we consider fully-actuated\nsystems evolving on the broad class of homogeneous spaces (encompassing all\nvector spaces, Lie groups, and spheres of any finite dimension). In this\nsetting, the transitive action of a Lie group on the configuration manifold\nenables an intrinsic description of the tracking error as an element of the\nstate space, even in the absence of a group structure on the configuration\nmanifold itself (e.g., for $\\mathbb{S}^2$). Such an error state facilitates the\ndesign of a generalized control policy depending smoothly on state and time,\nwhich drives the geometric tracking error to a designated origin from almost\nevery initial condition, thereby guaranteeing almost global convergence to the\nreference trajectory. Moreover, the proposed controller simplifies elegantly\nwhen specialized to a Lie group or the n-sphere. In summary, we propose a\nunified, intrinsic controller guaranteeing almost global asymptotic trajectory\ntracking for fully-actuated mechanical systems evolving on a broad class of\nmanifolds. We apply the method to an axisymmetric satellite and an\nomnidirectional aerial robot.\n
