Force Polytope-Based Cant-Angle Selection for Tilting Hexarotor UAVs

Alberto Piccina; Massimiliano Bertoni; Angelo Cenedese; Giulia Michieletto

cs.ROApr 7, 2026

Force Polytope-Based Cant-Angle Selection for Tilting Hexarotor UAVs

Authors: Alberto Piccina, Massimiliano Bertoni, Angelo Cenedese, Giulia Michieletto

Organizations: Department of Management and Engineering, University of Padova, Vicenza, Italy · Department of Information Engineering, University of Padova, Padova, Italy · Department of Industrial Engineering, University of Padova, Padova, Italy

Abstract

From a maneuverability perspective, the main advantage of tilting multirotor UAVs lies in the dynamic variability of the feasible executable wrench, which represents a key asset for physical interaction tasks. Accordingly, cant-angle selection should be optimized to ensure high performance while avoiding abrupt variations and preserving real-world feasibility. In this context, this work proposes a lightweight control framework for star-shaped interdependent cant-tilting hexarotor UAVs performing interaction tasks. The method uses an offline-computed look-up table of zero-moment force polytopes to identify feasible cant angles for a desired control force and select the optimal one by balancing efficiency and smoothness. The framework is integrated with a geometric full-pose controller and validated through Monte Carlo simulations in MATLAB/Simulink and compared against a baseline strategy. The results show a significant reduction in computation time, together with improved pose-tracking performance and competitive actuation efficiency. A final physics-based simulation of a complete wall inspection task in Simscape further confirms the feasibility of the proposed strategy in interacting scenarios.

Figures & tables

Fig. 1: Schematic representation of a star-shaped interdependent cant-tilting hexarotor. Each propeller spinning axes can be online reoriented by selecting the cant angle

\alpha

, thus enabling reconfiguration of the achievable wrench space.

$m$	$[$ \mathrm{kg} $]$	$3.500$
$\mathbf{J}$	$[$ \mathrm{kg}\text{,}{\mathrm{m}}^{2} $]$	$\;\mathrm{diag}\left(\scalebox{.9}{$ \begin{bmatrix}0.147;0.155;0.251\end{bmatrix} $}\right)$
$\ell$	$[$ \mathrm{m} $]$	$0.385$
$c_{f}$	$[$ \mathrm{N} $]$	$1.500\times 10^{-3}$
$c_{\tau}$	$[$ \mathrm{N}\text{,}\mathrm{m} $]$	$4.590\times 10^{-5}$
$\bar{\omega}$	$[$ \mathrm{Hz} $]$	$108.00$
$\tau_{\alpha}$	$[$ \mathrm{s} $]$	$5\times 10^{-3}$

TABLE I: Parameters of the

\alpha

-TingH platform case study

Fig. 2: 3D representation of the zero-moment control force polytope for

\alpha=25^{\circ}

Fig. 3: Overall control architecture of the proposed framework. The geometric full-pose controller generates the desired wrench, while an offline-computed LUT is exploited to select a feasible and efficient tilt angle

\alpha

prior to control allocation.

MoCap	$\boldsymbol{\Sigma}_{p}$	[ ${\mathrm{m}}^{2}$ ]	$10^{-7}\cdot\;\mathrm{diag}\left(\scalebox{.9}{$ \begin{bmatrix}4.099;2.838;0.211\end{bmatrix} $}\right)$
	$\boldsymbol{\Sigma}_{R}$	[ $\deg\mathrm{{}^{2}}$ ]	$\mathrm{diag}\left(\scalebox{.9}{$ \begin{bmatrix}0.0012;0.0011;0.0011\end{bmatrix} $}\right)$
	$\boldsymbol{\Sigma}_{v}$	[m 2 /s 2 ]	$10^{-6}\cdot\;\mathrm{diag}\left(\scalebox{.9}{$ \begin{bmatrix}2.050;1.419;0.105\end{bmatrix} $}\right)$
	$\boldsymbol{\Sigma}_{\omega}$	[deg 2 /s 2 ]	$\;\mathrm{diag}\left(\scalebox{.9}{$ \begin{bmatrix}0.0024;0.0022;0.0022\end{bmatrix} $}\right)$
Force Sensor	$\boldsymbol{\Sigma}_{f}$	[ ${\mathrm{N}}^{2}$ ]	$10^{-3}\cdot\;\mathrm{diag}\left(\scalebox{.9}{$ \begin{bmatrix}2.5;2.5;2.5\end{bmatrix} $}\right)$
Force Sensor	$\mathbf{m}_{f}$	[ $\mathrm{N}$ ]	$\left[0.1\;0.1\;0.1\right]^{\top}$

TABLE II: Model Parameters of MoCap and Force Sensor

\displaystyle(\alpha^{\ast},\mathbf{u}^{\ast})=(\alpha(t^{+}),\mathbf{u}(t^{+}))=\text{argmin}_{\begin{subarray}{c}\alpha(t^{+})\in\Gamma_{\alpha}\\ \mathbf{u}(t^{+})\in\bar{\mathcal{U}}\end{subarray}}\left(\left\|\mathbf{C}_{\alpha(t^{+})}\mathbf{u}(t^{+})-\scalebox{.9}{

\begin{bmatrix}\mathbf{f}{c}^{\ast}\ \boldsymbol{\tau}{c}^{\ast}\end{bmatrix}

}\right\|^{2}+J(\alpha(t^{+}),\alpha(t))\right)

(25)

Table 6

$\mathbf{K}_{pp}$	$\mathrm{diag}\left(\left[30\;30\;70\right]\right)$	$\mathbf{K}_{op}$	$\mathrm{diag}\left(\left[20\;20\;5\right]\right)$
$\mathbf{K}_{pd}$	$\mathrm{diag}\left(\left[10\;10\;10\right]\right)$	$\mathbf{K}_{od}$	$\mathrm{diag}\left(\left[10\;10\;10\right]\right)$
$\mathbf{K}_{pi}$	$\mathrm{diag}\left(\left[30\;30\;40\right]\right)$	$\mathbf{K}_{oi}$	$\mathrm{diag}\left(\left[0.1\;0.1\;1\right]\right)$
$r^{\ast}\left[$ \mathrm{N} $\right]$	$1$	$c_{r}\left[-\right]$	$\frac{1}{3}$
$\mathcal{T}_{w}$ [s]	$\{0,20,38,60,80\}$
$\mathcal{F}_{w}$ [N]	$\left\{\scalebox{.9}{$ \begin{bmatrix}0\ 0\ 0\end{bmatrix} $},\scalebox{.9}{$ \begin{bmatrix}0\ 0\ 0\end{bmatrix} $},\scalebox{.9}{$ \begin{bmatrix}0\ -8\ 10\end{bmatrix} $},\scalebox{.9}{$ \begin{bmatrix}-10\ 7\ 2\end{bmatrix} $},\scalebox{.9}{$ \begin{bmatrix}-6\ -8\ 0\end{bmatrix} $}\right\}$

TABLE III: Numerical Simulation Parameters: Controller Gains, Cant-Angle Selection, and Force Profile

Fig. 4: Validation of the influence of the weight coefficients

c_{1}

and

c_{2}

on the cant-angle selection, with identical force profile and radius

r^{\ast}

Fig. 5: Cant-angle trajectory $\alpha(t)$ and corresponding zero-moment force polytope sections at four selected instants on the hovering plane, together with the applied (red dashed) and instantaneous required (red marker) forces, confirming that the geometric containment condition is satisfied throughout the maneuver.

		baseline	proposed controller
			$r^{\ast}=0.5$ N	$r^{\ast}=1$ N	$r^{\ast}=3$ N	$r^{\ast}=5$ N
$\bar{t}_{c}$	$\left[$ \mathrm{ms} $\right]$	$0.5792$	$0.0565$	$0.0545$	$0.0536$	$\mathbf{0.0521}$
$\\|\bar{\mathbf{e}}_{p}\\|$	$\left[$ \mathrm{m} $\right]$	$0.0422$	$\mathbf{0.0192}$	$\mathbf{0.0192}$	$0.0202$	$0.0223$
$\mathrm{RMS}_{\mathbf{e}_{p}}$	$\left[$ \mathrm{m} $\right]$	$0.0352$	$\mathbf{0.0282}$	$0.0280$	$0.0291$	$0.0313$
$\\|\bar{\mathbf{e}}_{R}\\|$	$\left[$ \mathrm{rad} $\right]$	$0.0028$	$\mathbf{0.0004}$	$0.0005$	$0.0008$	$0.0014$
$\mathrm{RMS}_{\mathbf{e}_{R}}$	$\left[$ \mathrm{rad} $\right]$	$0.0046$	$\mathbf{0.0005}$	$\mathbf{0.0005}$	$0.0009$	$0.0013$

TABLE IV:

\mathrm{MC}

KPIs for the baseline and proposed controller.

$m\left[$ \mathrm{kg} $\right]$		$3.8$
$\mathbf{J}\left[$ \mathrm{kg}\text{,}{\mathrm{m}}^{2} $\right]$		$\mathrm{diag}\left([0.107\;0.103\;0.205]\right)$
$\mathbf{K}_{pp}$	$\mathrm{diag}\left(\left[6\;6\;15\right]\right)$	$\mathbf{K}_{op}$	$\mathrm{diag}\left(\left[10\;10\;10\right]\right)$
$\mathbf{K}_{pd}$	$\mathrm{diag}\left(\left[10\;10\;20\right]\right)$	$\mathbf{K}_{od}$	$\mathrm{diag}\left(\left[1\;2\;2\right]\right)$
$\mathbf{K}_{pi}$	$\mathrm{diag}\left(\left[1\;1\;1\right]\right)$	$\mathbf{K}_{oi}$	$\mathrm{diag}\left(\left[0.1\;0.01\;0.1\right]\right)$
$r^{\ast}\left[$ \mathrm{N} $\right]$	$1$	$c_{r}\left[-\right]$	$\frac{1}{3}$
$\bar{t}_{c}\;[$ \mathrm{ms} $]$	$0.0798$	$\\|\bar{\mathbf{e}}_{p}\\|\;[$ \mathrm{m} $]$	$0.1340$

TABLE V: Simscape Physics-Based Simulation: Parameters, Controller Gains, Cant-Angle Selection, and KPIs.

Panel of Figure 12 — Fig. 6: Snapshots of the Simscape simulation (video in the supplementary material), showing the variation of the cant angle as the platform interacts with the wall.

Aerial Robotics

Aerial robotics studies the design, perception, control, and coordination of flying robots for navigation, inspection, transport, and physical interaction.

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Apr 7, 2026J/K move · Enter open · S save

Dynamic Control Allocation for Dual-Tilt UAV Platforms

Marcello Sorge, Federico Ciresola, Giulia Michieletto, Angelo Cenedese

Department of Information Engineering University of Padova Padova, Italy · Department of Management and Engineering, University of Padova Padova, Italy · Department of Industrial Engineering, University of Padova, Padova, Italy

Aerial Robotics Feedback Control

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This paper focuses on dynamic control allocation for a hexarotor UAV platform, considering a trajectory tracking task as as case study. It is assumed that the platform is dual-tilting, meaning that it is able to tilt each propeller independently during flight, along two orthogonal axis. We present a hierarchical control structure composed of a high-level controller generating the required wrench for the tracking task, and a control allocation law ensuring that the actuators produce such wrench. The allocator imposes desired first-order dynamics on the actuators set, and exploits system redundancy to optimize the actuators state with respect to a given objective function. Unlike other studies on the subject, we explicitly model actuator saturation and provide theoretical insights on its effect on control performances. We also investigate the role of propeller tilt angles, by imposing asymmetric shapes in the objective function. Numerical simulations are presented to validate the allocation strategy.

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