# Design and Implementation of a Fully-Actuated Integrated Aerial Platform Based on Geometric Model Predictive Control

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## Abstract

**:**

## 1. Introduction

#### Motivation and Background

- A control scheme is carefully designed such that it is singularity-free and can deal with the non-Euclidean configuration space, state and input constraints, hence is suitable for the IAP system. The control scheme is designed based on model predictive control and the dynamics of the IAP.
- The stability of the IAP under the control of the proposed MPC-based controller along with the existing flight controller of each individual sub-UAV is proved. This provides theoretical basis for the development of the IAP.
- By developing the hardware and the software system of the IAP, the proposed control scheme is successfully implemented in a prototype of IAP. To the best of the authors’ knowledge, this is the first time that the geometric model predictive control-based control scheme was successfully implemented in the real IAP prototype. The advantage of the proposed control scheme is shown through the comparison.

## 2. Configuration and Dynamic Modeling of IAP

## 3. Controller Design and Analysis

#### 3.1. Overall Architecture

#### 3.2. Outer Loop of the MPC Controller

#### 3.2.1. Terminal Set Constraints and Terminal Control of Attitude Motion

**Proposition**

**1.**

- (1)
- ${\Omega}_{r}$ is invariant,
- (2)
- ${\dot{V}}_{r}+{N}_{r}({\xi}_{r},{\tau}_{0})\le 0$, where$$\begin{array}{c}{N}_{r}={\zeta}_{r}^{T}{A}_{r}^{T}\left(\right)open="["\; close="]">\begin{array}{cc}{q}_{11}I& 0\\ 0& {q}_{12}I\end{array}{A}_{r}{\zeta}_{r}+{\tau}_{0}^{T}{r}_{1}{\tau}_{0}\hfill \end{array}$$where ${q}_{11}$, ${q}_{12}$, and r are all positive constants.
- (3)
- ${\tau}_{0}\in {S}_{6}$ holds for all ${\zeta}_{r}\in {\Omega}_{r}$.

#### 3.2.2. Terminal Set Constraints and Terminal Control of Position Motion

**Proposition**

**2.**

- (1)
- ${\Omega}_{t}$ is invariant.
- (2)
- ${\dot{V}}_{t}+{N}_{t}\le 0$, where$$\begin{array}{c}{N}_{t}={\zeta}_{t}^{T}{A}_{t}^{T}\left(\right)open="["\; close="]">\begin{array}{cc}{q}_{21}I& 0\\ 0& {q}_{22}I\end{array}{A}_{t}{\zeta}_{t}+\hfill \end{array}$$where ${q}_{21}$, ${q}_{22}$, and ${r}_{21}$ are all positive constants.
- (3)
- ${F}_{0}\in {S}_{5}$ holds for all ${\zeta}_{t}\in {\Omega}_{t}$.

#### 3.3. Solvability and Stability of the Closed Loop IAP

**Theorem**

**1.**

**Proof.**

**Remark**

**1.**

**Remark**

**2.**

## 4. Simulation and Real-World Tests

#### 4.1. Simulation System Construction

#### 4.2. Simulation Results

#### 4.3. Development of an IAP Prototype Consisting of Software and Hardware Systems

#### 4.4. Real-World Test Results

**Remark**

**3.**

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**The configuration path of the mission-platform. (the x-, y-, and z-axes are shown in yellow, green, and blue, respectively).

**Figure 9.**Position and attitude profiles tracked during real-world flight test. Note the big initial error here. A typical PID is difficult to stabilize the IAP in such condition as the controller may output large action which violates the input boundedness. In contrast, our proposed control scheme successfully stabilizes the system as it can deal with the state and input constraints.

Mass (kg) | Payload Capacity (kg) | Computing Unit | |
---|---|---|---|

Sub-UAV | 1.58 | 1.5 | PX4 open-source FCB |

IAP | 6.24 | 3.02 | Nvidia nano OBC and PX4 open-source FCB |

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**MDPI and ACS Style**

Shi, C.; Yu, Y.
Design and Implementation of a Fully-Actuated Integrated Aerial Platform Based on Geometric Model Predictive Control. *Micromachines* **2022**, *13*, 1822.
https://doi.org/10.3390/mi13111822

**AMA Style**

Shi C, Yu Y.
Design and Implementation of a Fully-Actuated Integrated Aerial Platform Based on Geometric Model Predictive Control. *Micromachines*. 2022; 13(11):1822.
https://doi.org/10.3390/mi13111822

**Chicago/Turabian Style**

Shi, Chuanbeibei, and Yushu Yu.
2022. "Design and Implementation of a Fully-Actuated Integrated Aerial Platform Based on Geometric Model Predictive Control" *Micromachines* 13, no. 11: 1822.
https://doi.org/10.3390/mi13111822