Mathematical Problems in Engineering

Volume 2015, Article ID 108481, 8 pages

http://dx.doi.org/10.1155/2015/108481

## Robust Hierarchical Control for Uncertain Multivariable Hexarotor Systems

^{1}State Key Laboratory of Mathematical Engineering and Advanced Computing, No. 62 Science Road, Zhengzhou 450002, China^{2}School of Astronautics, Beihang University, Beijing 100191, China

Received 12 February 2015; Accepted 29 April 2015

Academic Editor: Hiroyuki Mino

Copyright © 2015 Wei Lin and Hao Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Multirotor helicopter attracts more attention due to its increased load capacity and being highly maneuverable. However, these helicopters are uncertain multivariable systems, which pose a challenge for their robust controller design. In this paper, a robust two-loop control scheme is proposed for a hexarotor system. The resulted controller consists of a nominal controller and a robust compensator. The robust compensators are added to restrain the influences of uncertainties such as nonlinear dynamics, coupling, parametric uncertainties, and external disturbances. It is proven that the tracking errors are ultimately bounded with specified boundaries by choosing the parameters of the robust compensators. Simulation results on the hexarotor demonstrate the effectiveness of the proposed control method.

#### 1. Introduction

Unmanned aerial vehicles (UAV) have attracted great attention in scientific research area in the last two decades (see [1–5] to mention a few). These kinds of vehicles have been widely used to perform civil and military missions such as inspection, surveillance, exploration, search, and rescue. Unmanned rotorcrafts have some advantages over the fix-wing aircrafts due to their special way of thrust lift generated. The helicopters can hover and take off and land vertically. Furthermore, unmanned helicopters can enter the building and implement indoor exploration tasks as well as inspection missions.

Multirotors have received much interest in the automatic control field because they can outperform the conventional helicopters in many aspects. Firstly, the fixed-pitch rotors are used and lift thrusts can be altered by the control of motor rotational speeds without a swashplate [6]. Secondly, multiple rotors can increase payload and the maneuverability of the helicopter [7]. Thirdly, the usage of the multiple rotors guarantees that each individual rotor is smaller than the equivalent main rotor of a conventional helicopter for a given airframe size [8]. Multiple smaller rotors can be enclosed within a protective frame and thus increased safety of operators. As a result of the strong points mentioned above, intensive efforts have been devoted to the tracking control problem of multirotor helicopters. Quadrotors have gained much attention in the automatic control field (see, e.g., [9–15]). In this paper, the robust motion control problem of hexarotor helicopters is investigated. Compared with quadrotors, although hexarotor helicopters may present a weight and energy consumption augmentation due to the extra motors, they can increase load capacities. Moreover, hexarotors are highly maneuverable in respect that at least four rotors can influence the dynamics of each direction. On the other hand, it results in a more fault-tolerant mechanical system for each hexarotor helicopter.

The controller design problem of a hexarotor system shares some merits with that of the quadrotor helicopter. Both kinds of helicopters can be considered as rigid bodies and thus one can apply Lagrange approach to obtain the dynamical model of the two kinds of helicopters. However, there also exist some differences between the two kinds of helicopters. The differences result from the aerodynamic forces and torques generated by the rotors. Because of two extra rotors, the torque produced in each channel is different from the quadrotors and thus affects the dynamical response differently. In this paper, a robust hierarchical control scheme is applied based on PD control method and the robust compensation approach. For each loop, a robust controller is designed with a nominal PD controller and a robust compensator. The robust compensators are introduced to restrain the influences of the uncertainties in both loops.

Compared to previous studies on the robust motion control problem of the multirotor helicopter, the proposed robust hierarchical control scheme can restrain disturbances in both the inner and outer loops. The tracking errors of this rotorcraft are guaranteed to be bounded with specified boundaries. In addition, this control scheme results in a linear time-invariant controller which is easily to be implemented in practical applications.

The remaining parts of this paper are organized as follows. In Section 2, the nonlinear mathematic model of the helicopter is described and problem description is presented. The nominal controllers and robust compensators in the attitude and position loops are designed in Section 3. In Section 4, the robust properties of closed-loop system by the designed control laws are proven. Simulation results are shown in Section 5 and conclusions are stated in Section 6.

For and , denote thatwhere is the Laplace operator, , and indicates the Laplace transform.

#### 2. Problem Description

The schematic of the hexarotor is depicted in Figure 1. Let denote an inertial frame and is a frame attached to the helicopter body with origin in the center of the mass of the rotorcraft as shown in Figure 1. The vector indicates the position of the origin of the body-fixed frame with respect to the inertial frame . In addition, let indicate the three Euler angles: the pitch angle , the roll angle , and the yaw angle , which depends on the rotation from the inertial frame to the body-fixed frame . The mathematical model of the helicopter can be derived by the Lagrangian method as (see, e.g., [9])where is the mass of the helicopter, is the inertia matrix of the helicopter relative to the frame , is the gravity constant, is the Coriolis terms, , , and and are the external body-fixed frame force and torque respectively. and can be obtained aswhere is the distance from each motor to the center of the mass of the rotorcraft, denotes the force-to-moment scaling factor, and are the thrusts generated by the six rotors respectively. take the following forms:where is a positive constant and are the rotational speeds of the six rotors respectively. Define the control inputs asIn practical applications, there already exist many power distribution boards to distribute the four control inputs to the six rotors for the multirotors. Therefore, the power distribution problem is not further discussed here.