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This paper uses a neural network to predict where knot points should go in B-spline approximations of ODE-generated trajectories, so fewer control points are needed for a given accuracy. The learning component is central to the method, which makes it an applied ML result in control and numerical approximation rather than a general systems paper. Readers should note that the abstract reports the efficiency gain as a reduction in control points, not as a measured speedup, and that the quadrotor is the test case.
A Neural Network Approach towards Real-Time Knot Point Density Estimates for the Nonlinear Quadrotor
arXiv:2610.42027v1 Announce Type: cross Abstract: Spline representations provide a compact way to approximate continuous trajectories using a finite number of parameters. When approximating trajectories generated by dynamical systems, the efficiency of a spline representation depends strongly on the placement of knot points. Uniform knot distributions often lead to inefficient representations, requiring either unnecessary control points or producing poor approximations in regions where the trajectory varies rapidly. In this work we propose a learning-based method for adaptive knot placement in B-spline approximations of trajectories generated by ordinary differential equations. A neural network learns a mapping from the initial condition of the system to quantities that characterize the local variation of the resulting trajectory. These estimates are used to construct nonuniform knot distributions that approximately equidistribute a local error indicator, reducing the number of control points needed to meet a prescribed accuracy.
Abstract:Spline representations provide a compact way to approximate continuous trajectories using a finite number of parameters. When approximating trajectories generated by dynamical systems, the efficiency of a spline representation depends strongly on the placement of knot points. Uniform knot distributions often lead to inefficient representations, requiring either unnecessary control points or producing poor approximations in regions where the trajectory varies rapidly. In this work we propose a learning-based method for adaptive knot placement in B-spline approximations of trajectories generated by ordinary differential equations. A neural network learns a mapping from the initial condition of the system to quantities that characterize the local variation of the resulting trajectory. These estimates are used to construct nonuniform knot distributions that approximately equidistribute a local error indicator, reducing the number of control points needed to meet a prescribed accuracy.
8 pages, 5 figures. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. This work is presented at IEEE CDC 2026
Systems and Control (eess.SY); Machine Learning (cs.LG)
arXiv:2610.42027 [eess.SY]
(or arXiv:2610.42027v1 [eess.SY] for this version)
https://doi.org/10.48550/arXiv.2610.42027 arXiv-issued DOI via DataCite (pending registration)
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