Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Exploring a New Design Paradigm for Omnidirectional MAVs for Minimal Actuation and Internal Force Elimination: Theoretical Framework and Control

Ahmed Ali, Chiara Gabellieri, Antonio Franchi

TL;DR

This work introduces a novel omnidirectional MAV design that achieves full SE(3) control with only six inputs by coupling a main base to four propeller-bearing links through passive joints, with one propeller actively tilted. The authors derive a detailed dynamic model, identify equilibria at every base pose, and show internal forces can be eliminated (or minimized) via a Pulley-Belt-Spring (PJD) design, yielding a minimal-thrust equilibrium for all poses. A geometric, nonlinear controller is developed using dynamic extension and backstepping on SE(3), and is proven locally asymptotically stable via Lyapunov analysis; an efficient ABA-based implementation enables real-time deployment. Numerical simulations including parametric uncertainty and actuator noise validate decoupled translational and rotational motions and demonstrate near-minimal thrust at equilibrium, highlighting potential for low-actuation, fully-actuated aerial platforms. The work sets the stage for experimental validation and extensions to non-coplanar propeller layouts and more general trajectories.

Abstract

This paper presents a novel concept for achieving omnidirectionality in a multirotor aerial vehicle (MAV) that uses only 6 inputs and ensures no internal forces at the equilibria. The concept integrates a single actively-tilting propeller along with 3 pendulum-like links, each carrying a propeller, connected by passive universal joints to the main body. We show that this design ensures omnidirectionality while minimizing the internal forces and without resorting to overactuation (i.e., more than 6 inputs). A detailed dynamic model of the multi-link MAV is first developed. Afterwards, the analysis identifies the equilibrium configurations and illustrates that a forced equilibrium exists for every pose of the MAV's main platform. In order to render this equilibrium asymptotically stable for the closed-loop system, a geometric nonlinear controller is constructed using dynamic feedback linearization and backstepping techniques with the main platform configuration error being the left-trivialized error on SE(3). The stability of the closed-loop system is then investigated by employing standard Lyapunov arguments on the zero dynamics. We conclude by providing numerical simulations validating the proposed approach. They demonstrate the MAV capability to perform decoupled attitude and translational motions under non-zero initial conditions, parametric uncertainty, and actuators noise.

Exploring a New Design Paradigm for Omnidirectional MAVs for Minimal Actuation and Internal Force Elimination: Theoretical Framework and Control

TL;DR

This work introduces a novel omnidirectional MAV design that achieves full SE(3) control with only six inputs by coupling a main base to four propeller-bearing links through passive joints, with one propeller actively tilted. The authors derive a detailed dynamic model, identify equilibria at every base pose, and show internal forces can be eliminated (or minimized) via a Pulley-Belt-Spring (PJD) design, yielding a minimal-thrust equilibrium for all poses. A geometric, nonlinear controller is developed using dynamic extension and backstepping on SE(3), and is proven locally asymptotically stable via Lyapunov analysis; an efficient ABA-based implementation enables real-time deployment. Numerical simulations including parametric uncertainty and actuator noise validate decoupled translational and rotational motions and demonstrate near-minimal thrust at equilibrium, highlighting potential for low-actuation, fully-actuated aerial platforms. The work sets the stage for experimental validation and extensions to non-coplanar propeller layouts and more general trajectories.

Abstract

This paper presents a novel concept for achieving omnidirectionality in a multirotor aerial vehicle (MAV) that uses only 6 inputs and ensures no internal forces at the equilibria. The concept integrates a single actively-tilting propeller along with 3 pendulum-like links, each carrying a propeller, connected by passive universal joints to the main body. We show that this design ensures omnidirectionality while minimizing the internal forces and without resorting to overactuation (i.e., more than 6 inputs). A detailed dynamic model of the multi-link MAV is first developed. Afterwards, the analysis identifies the equilibrium configurations and illustrates that a forced equilibrium exists for every pose of the MAV's main platform. In order to render this equilibrium asymptotically stable for the closed-loop system, a geometric nonlinear controller is constructed using dynamic feedback linearization and backstepping techniques with the main platform configuration error being the left-trivialized error on SE(3). The stability of the closed-loop system is then investigated by employing standard Lyapunov arguments on the zero dynamics. We conclude by providing numerical simulations validating the proposed approach. They demonstrate the MAV capability to perform decoupled attitude and translational motions under non-zero initial conditions, parametric uncertainty, and actuators noise.
Paper Structure (30 sections, 4 theorems, 104 equations, 7 figures, 2 tables)

This paper contains 30 sections, 4 theorems, 104 equations, 7 figures, 2 tables.

Table of Contents

  1. introduction
  2. Research Problems and Related Work
  3. Contributions
  4. Motivations Behind the Design Idea
  5. Outline
  6. Proposed Design and Dynamical Model
  7. Mechanical Design Idea
  8. Equations of Motion
  9. Study of Attainable Equilibria and Internal Forces at each Equilibrium
  10. Effect of the Aerodynamic Drag Torque at the Equilibrium
  11. Minimal Thrust at Equilibrium vs Presence of Internal Forces
  12. Stabilization of the Equilibria
  13. Informal Outline of the Solution
  14. Main Results
  15. Efficient Implementation of the Controller
  16. ...and 15 more sections

Key Result

Lemma 1

Consider a vehicle with a thrust magnitudes vector $f=col(f_i)$$\in \mathbb{R}_{\geq 0}^l$ with the corresponding propellers configurations $C^0_{i}(C^0_{1},\alpha_i)\in SE(3)$, relative to a right-handed inertial frame whose z-axis direction opposes the axis along which the gravitational force is a

Figures (7)

  • Figure 1: Conceptual representation of the proposed MAV idea. The origins of the frames $\mathcal{F}_b$ and $\mathcal{F}_{p_2}$ are attached to CoMs of the base $B_1$ and the propeller link $B_2$, respectively. The shown configuration is when $\mathcal{F}_b$ coincides with $\mathcal{F}_w$ and all the frames of the links have the same orientation as $\mathcal{F}_w$. The joint $q_{j1}$ and $q_{j2}$ positions are zero when $\mathcal{F}_{p_j}$ has the same orientation as $\mathcal{F}_b$, $j=\{2,\ldots,5\}$. The link $B_5$ is attached to $B_1$ through an active joint, unlike the the rest of the joints which are passive.
  • Figure 2: The connection between $B_j$ ($j=2,3,4$) and the base $B_1$ in PJD$_2$ consists of universal passive joint with a Pulley-Belt-Spring module. $\bar{B}_j$ is the intermediate link connecting $B_1$ to $B_j$. $b$, $p$ and $s$ denote the belt, pulley and a torsion spring, respectively. $\tau_{sj}$ is the torsion spring torque around the rotation axis of $q_{j1}$, i.e. $e_{j1}$.
  • Figure 3: Time evolutions of the state and input for a common simulation are presented for two designs: (a) PJD$_1$ and (b) PJD$_2$. The simulation comprises two phases. First (0-60s), a step reference of 1m along the inertial $y_w$ axis is commanded for the base position, with the initial attitude held constant. Second (60-130s, gray-shaded), a step reference demands a $60^\circ$ rotation about the inertial $y_w$ axis for the attitude, while the position at $t=60$s is maintained. Imperfections such as large initial errors, uncertainty, and noise contribute to the angular velocity and attitude errors during both the initial position maneuver and the subsequent attitude maneuver
  • Figure 4: Time evolution of the zero dynamics states showing convergence.
  • Figure 5: Comparison of the total thrust evolution between PJD$_1$ and PJD$_2$ for the same scenario in Fig. \ref{['Sim1']}. In steady state, PJD$_2$ thrust magnitudes sum up to exactly the minimal value \ref{['minDefinition_Fmin']}, unlike its PJD$_1$ counterpart, which is about 2% higher (still much better compared to the internal forces required by state of the art designs).
  • ...and 2 more figures

Theorems & Definitions (12)

  • Definition 1
  • Lemma 1
  • proof
  • Proposition 1
  • proof
  • Remark 1
  • Theorem 1
  • proof
  • Proposition 2
  • proof
  • ...and 2 more