Star-shaped Tilted Hexarotor Maneuverability: Analysis of the Role of the Tilt Cant Angles

TL;DR

The paper addresses how the cant tilt angle $α$ of a star-shaped tilted hexarotor (STH) governs maneuverability under gravity compensation and torque decoupling. It develops a geometric framework that characterizes the feasible control-force subspaces through closed-form volumes such as $V_{\mathcal{F}_B}$ and $V_{\mathcal{F}_B^h}$, and areas like $A_{\mathcal{F}_B^h}$, all as functions of $α$ via the tilt-dependent matrices $\mathbf{F}_α$, $\mathbf{M}_α$ and the derived $\mathbf{H}_α = \mathbf{F}_α \mathbf{B}_α$. Key results include $V_{\mathcal{F}_B} = 12\sqrt{3} (c_f \bar{u})^3 cα sα^2$, $A_{\mathcal{F}_B^h}$ and $V_{\mathcal{F}_B^h}$ with case-dependent expressions, showing $α$-dependent optima (e.g., $V_{\mathcal{F}_B}$ and $A_{\mathcal{F}_B^h}$ peak around $α \approx 54{.}5^\circ$, while $V_{\mathcal{F}_B^h}$ peaks near $42^\circ$). These results reveal trade-offs between aggressive lateral actuation and hovering robustness, providing design guidelines such as preferring $α \approx 50^\circ$ for a balanced performance. The findings lay groundwork for future work on dihedral tilt angles and combined cant–dihedral optimization for STHs.

Abstract

Star-shaped Tilted Hexarotors are rapidly emerging for applications highly demanding in terms of robustness and maneuverability. To ensure improvement in such features, a careful selection of the tilt angles is mandatory. In this work, we present a rigorous analysis of how the force subspace varies with the tilt cant angles, namely the tilt angles along the vehicle arms, taking into account gravity compensation and torque decoupling to abide by the hovering condition. Novel metrics are introduced to assess the performance of existing tilted platforms, as well as to provide some guidelines for the selection of the tilt cant angle in the design phase.

Figures (12)

• Figure 1: STH model - yellow arrow represent the tilted rotors spinning axes.
• Figure 2: Investigation of $V_{\mathcal{F}_B}$: (a) value of $V_{\mathcal{F}_B}$ in function of $\alpha \in \Gamma_\alpha$, (b-c) 3D polytopes representing the zero-moment force spaces characterized by the same volume (related to the tilt angles marked in orange in Fig. \ref{['fig:V_FB_with_points']}) - the blue plane represents the hovering plane introduced in Sec. \ref{['sec:gravit_compensation_constraint']}.
• Figure 3: Value of ${A}_{\mathcal{F}_B^h}$ in function of $\alpha \in \Gamma_\alpha$, highlighting cases A-C.
• Figure 4: $\alpha = 10^{\degree}$ (case A)
• Figure 5: $\alpha = 50^{\degree}$ (case B)

Theorems & Definitions (1)

• Remark