Tracking of a Moving Target on a Hyperboloid and its Extension to Leader-follower Formation Controller
Abstract
This paper proposes a novel controller for a double-integrator agent to track a moving target with bounded velocity on a hyperboloid ℍn. The control law uses the intrinsic Riemannian structure of the hyperboloid, including the logarithm map, covariant derivative, and parallel transport, to make all its terms coordinate-free. Such formulation eases the implementation of the proposed tracking controller in the ambient Minkowski space without doing any additional chart computations. We use Barbalat's lemma for the hyperboloid to establish the convergence proof. Later, the proposed tracking controller is extended to a leader-follower formation control, where each agent reaches at a desired position around a moving leader in ℍn. We validate the results with numerical simulations considering two different target trajectories, geodesic and spiral, as examples.
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BibTeX
@misc{shukla2026tracking,
title = {{Tracking of a Moving Target on a Hyperboloid and its Extension to Leader-follower Formation Controller}},
author = {Ashish Shukla and Sanad Shaha and Kashyap Rajeevsarathy and Arijit Sen},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.09261},
eprint = {2611.09261},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.09261},
}
RIS
TY - UNPB
TI - Tracking of a Moving Target on a Hyperboloid and its Extension to Leader-follower Formation Controller
AU - Ashish Shukla
AU - Sanad Shaha
AU - Kashyap Rajeevsarathy
AU - Arijit Sen
PY - 2026
DA - 2026/11/06
PB - arXiv
DO - 10.48550/arxiv.2611.09261
UR - https://arxiv.org/abs/2611.09261
AB - This paper proposes a novel controller for a double-integrator agent to track a moving target with bounded velocity on a hyperboloid ℍ^n. The control law uses the intrinsic Riemannian structure of the hyperboloid, including the logarithm map, covariant derivative, and parallel transport, to make all its terms coordinate-free. Such formulation eases the implementation of the proposed tracking controller in the ambient Minkowski space without doing any additional chart computations. We use Barbalat's lemma for the hyperboloid to establish the convergence proof. Later, the proposed tracking controller is extended to a leader-follower formation control, where each agent reaches at a desired position around a moving leader in ℍ^n. We validate the results with numerical simulations considering two different target trajectories, geodesic and spiral, as examples.
ER -