High-level spatial Dubins airplane-based reference smoothing with low-level geometric tracking for quadrotor control

Jul 16, 2026

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A quadrotor control method combines a high-level reference smoothing stage with a low-level geometric tracking stage. The high-level stage uses a spatial Dubins airplane model to reduce dimensionality and computational burden while exploiting the model structure to decouple spatial modeling and pose a small linear program. The low-level stage applies a geometric tracking controller grounded in the full quadrotor dynamics. The approach tracks references under lateral path constraints, exemplified by obstacle-contour reference tracking, using two deployment setups: offline high-level planning or receding-horizon closed-loop planning over a finite spatial horizon.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages7

Reading Time18 min

Introduction

Problem Formulation

Problem Solution

High-level reference smoothing

High-level spatial Dubins airplane-based reference smoothing with low-level geometric tracking for quadrotor control Mogens Plessen* arXiv :2607 . 11724v1 [ cs .RO] 13 Jul 2026 Abstract—A method for the control of quadrotors is presented. It is composed of a high-level reference smoothing step and a low-level reference tracking step. The high-level step leverages the Dubins airplane model for dimensionality reduction and reduced computational complexity, and exploits its structure for decoupling, spatial modeling and the formulation of a small linear program. The low-level step leverages a geometric tracking controller, which is based on the full quadrotor model. The method is designed for the tracking of references subject to lateral constraints along the path. An example is the tracking of references along obstacle contours. It is differentiated between two different setups. Either the high-level planning step is conducted once and offline, or, alternatively, the high-level planning step is conducted recedingly online in closed-loop over a limited spatial prediction horizon. Index Terms—Quadrotor control, Dubins airplane model, geometric tracking control, linear programming. I. INTRODUCTION The literature for quadrotor or in general multirotor control is very rich [1], [2] . This underlines both relevance as well as complexity. Examples are given for illustration. First, in [3] a fast nonlinear model predictive control method is proposed for reference tracking. However, to reduce computational complexity on-board their prediction horizon is only 50ms. Furthermore, their objective function requires the selection of two positive semi-definite matrices, a non-negative scalar and one positive definite matrix as hyperparameters, all in different units. Numerical values are not stated to evaluate required tuning effort. Similarly, in [4] the objective function of their optimal control problem, which is solved off-board, consists of 6 different weighted terms, the prediction span is 0.8s, and a hermitian spline fit is used as centerline for tracking. Second, in the smoothing step of [5], B-spline optimization is used, requiring the selection of control points, the degree of the spline, an objective function with 3 hyperparameters weighting smoothness, collision cost, soft limits on velocity and acceleration, multiple threshold parameters, and a nonlinear optimization solver. Third, in [6] a spatiotemporal safe flight corridor generation method is proposed based on cubic Bzier curves. However, Bzier curves, and similarly other spline-based methods, are not suitable for every application as Fig. 10(a) demonstrates. A research gap is identified that remains open, and which provides the motivation for this article. Methods are desired that (i) hierarchically reduce complexity from low-level tracking to high-level planning for computational efficiency, while (ii) maintaining trajectory shaping ability, in particular, not just at control points but along the entire trajectory, and (iii) reduce the number of hyperparameters to a minimum. The proposal of such a method is the contribution of this article. Three ideas are combined: (i) high-level path planning based on the lower-dimensional Dubins airplane model [8], [9], (ii) a spatial modeling approach [10]–[13], and (iii) a layered *[pmogens@proton.me](pmogens@proton.me), Findklein GmbH, Switzerland (a) Counterexample 1: different spline methods [7] are used for smoothing of an edgy 4-waypoint reference. (b) Counterexample 2: a low-level controller is used for closed-loop tracking of a 3-waypoint reference. Fig. 1. Problem visualization by counterexamples: it is wished to (i) closely track an edgy sparse waypoints reference, (ii) while laterally staying on a specific side of the reference (e.g., avoiding the obstacle area left of the reference) . Three spline-based fits fails condition (i) by staying far from the reference, while the method of directly tracking the

FAQs

What are the two main stages of the proposed quadrotor control method?

The method has a high-level reference smoothing step and a low-level reference tracking step.

How does the high-level stage reduce computational complexity?

It leverages the spatial Dubins airplane model for dimensionality reduction and uses the structure to formulate a small linear program for reference smoothing.

What kinds of constraints and scenarios does the method target for tracking?

It tracks references subject to lateral constraints along the path, such as tracking references along obstacle contours while staying on a specified side of the reference.

Jul 16, 2026

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