Journal of Advanced Transportation

Volume 2018, Article ID 1467040, 20 pages

https://doi.org/10.1155/2018/1467040

## A Load Transportation Nonlinear Control Strategy Using a Tilt-Rotor UAV

^{1}Department of Electronic Engineering, Universidade Federal de Minas Gerais, 31270-901 Belo Horizonte, MG, Brazil^{2}Department of Aerospace Engineering, University of Texas at Austin, Austin, TX 78712, USA

Correspondence should be addressed to Guilherme V. Raffo; rb.gmfu@offar

Received 28 August 2017; Revised 22 November 2017; Accepted 17 December 2017; Published 27 June 2018

Academic Editor: Andrea Monteriù

Copyright © 2018 Guilherme V. Raffo and Marcelino M. de Almeida. 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

This paper proposes a nonlinear control strategy to solve the trajectory tracking problem of a tilt-rotor Unmanned Aerial Vehicle (UAV) when transporting a suspended load. For the present study, the aim of the control system is to track a desired trajectory of the aircraft with load’s swing-free, even in the presence of external disturbances, parametric uncertainties, unmodeled dynamics, and noisy position measurements with lower sampling frequency than the controller. The whole system modeling is obtained through the Euler-Lagrange formulation considering the dynamics of the tilt-rotor UAV coupled to the suspended load. As for the nonlinear control strategy, an inner-loop control is designed based on input-output feedback linearization combined with the dynamic extension approach to stabilize the attitude and altitude of the UAV assuming nonlinearities, while an outer-loop control law is designed for guiding the aircraft with reduced load swing. The linearized dynamics are controlled using linear mixed controllers with pole placement constraints. The solution is compared to two simpler control systems: the first one considers the load as a disturbance to the system but does not avoid its swing; the second one is a previous academic result with a three-level cascade strategy. Finally, in order to deal with the problem of position estimation in presence of unknown disturbances and noisy measurements with low sampling frequency, a Linear Kalman Filter with Unknown Inputs is designed for estimating both the aircraft’s translational position and translational disturbances. Simulation results are carried out to corroborate the proposed control strategy.

#### 1. Introduction

Research in Unmanned Aerial Vehicles (UAVs) has gained much attention in the last years, mainly for its variety of applications. Some examples of uses for UAVs might be listed as cargo transportation and delivery, surveillance, field recognition, cave exploration, cinematographic filming, military purposes, 3D mapping, search and rescue, and wildlife research, among many others. The present work focuses on studying the problem of suspended load transportation. This kind of task is extremely important in some missions such as search and rescue, surface exploration, military applications, and personal assistance, among others. Piloted aircraft usually require an experienced pilot to transport suspended payloads to a destination while avoiding any accident with the load and the aircraft itself. Fully autonomous UAVs, on the other hand, are required to use more sophisticated control laws so as to achieve similar (or even better) performances.

The most common UAVs that are studied in academia are helicopters, quadrotors, and fixed-wing airplanes. On one hand, rotorcrafts have the advantage over airplanes for performing Vertical Take-Off and Landing (VTOL), while on the other hand, airplanes are able to obtain higher forward flights with greater range and autonomy. Aiming to combine the advantages of both kinds of aircraft, present research on UAVs is increasingly interested in the tilt-rotor UAV, a hybrid copter-plane aircraft. The tilt-rotor is a type of aircraft that combines the vertical lift capacity of helicopters with the range, autonomy, and speeds of fixed-wing airplanes. For missions of search and rescue, for example, tilt-rotors might stand out since it can reach disaster zones faster than rotorcrafts, while also being able to hover over some position of interest.

This work proposes a robust nonlinear control strategy for the tilt-rotor UAV in the helicopter flight-mode with the further requirement that it should track a desired trajectory carrying a suspended load. Furthermore, the control system should maintain both the aircraft and the load stable even in the presence of external disturbances, parametric uncertainties, unmodeled dynamics, and noisy position measurements with lower sampling frequency than the controller.

The most notorious research works assessing control of tilt-rotor UAVs started being published after 2005. In [1] a back-stepping strategy was applied to a tilt-rotor with two degrees of freedom on each rotor. The use of two degrees of freedom was later abandoned due to difficulties on practical implementation. Reference [2] was able to experimentally maintain a tilt-rotor in hovering using nonlinear control in the vicinity of the equilibrium point. In [3] an adaptation to the previous solution was performed by including coupling gyroscopic body effects on the system’s model used for control design. Reference [4] explored the use of gain-scheduling to control a tilt-rotor’s roll and pitch by choosing a vast number of linearization points, with results being presented in [5]. A nonlinear control of a tilt-rotor UAV was proposed in [6] by means of cascade control using feedback linearization over a numerical model of the aircraft obtained on wind-tunnel tests. The work of [7] presented an approach to control a tilt-rotor UAV using Fuzzy Logic Control. In [8], a Model Predictive Control (MPC) was designed for the attitude of the aircraft. Reference [9] derived a simplified Euler-Lagrange model for the tilt-rotor UAV and used it to design a back-stepping control strategy. In [10], linear and mixed controllers were designed based on LMI (Linear Matrix Inequality) approach for trajectory tracking of a tilt-rotor UAV in helicopter flight-mode. In order to cover a large range of forward velocity of a tilt-rotor UAV, a robust adaptive mixing control strategy was proposed in [11].

Regarding the load transportation control problem, many research works are found in the literature. Nonlinear controllers were introduced in [12, 13] for stabilization of suspended loads in crane operations. Quadrotor UAV was used in [14] to transport a suspended load from one desired point to another applying a machine learning approach to avoid load swing. Reference [15] also used a quadrotor UAV to stabilize the swing of a suspended load with unknown mass by combining a Proportional-Derivative controller with Retrospective Cost Adaptive Control. In [16], trajectories are generated to a quadrotor UAV so that a suspended load passes through a desired trajectory.

Some works also address the problem of load transportation using a tilt-rotor UAV. In [17, 18], MPC strategies based on linearized models around desired trajectories were proposed for trajectory tracking of a tilt-rotor UAV with reduced load’s swing. In [19], the trajectory tracking problem of the suspended load was solved through the design of control and state estimation strategies based on linearized, time-invariant state-space equations but did not allow yaw angle tracking, or the occurrence of changes in the load’s mass and rope’s length. This latter work was improved in [20], where an MPC based on a linear time-varying model was designed to perform trajectory tracking of the suspended load with stabilization of the tilt-rotor UAV when parametric uncertainties and external disturbances affect the load, the rope’s length and total system mass vary during taking-off and landing, and the desired yaw angle changes throughout the trajectory. Nevertheless, the above control strategies, developed to solve the load transportation problem using a tilt-rotor UAV, are based on linearized models, which limit the domain of attraction of the closed-loop control system. In order to improve that, a nonlinear cascade control strategy was proposed in [21, 22] for trajectory tracking of a tilt-rotor UAV with load’s swing-free. Although this control strategy enlarged the domain of attraction, this nonlinear solution used a three-level cascade strategy, which might not be very attractive from the control point of view, since outer-loops are capable of destabilizing inner-loops if the design is not properly tuned.

This paper improves the results presented in [21, 22], in which the position of the aircraft was assumed to be perfectly known, by proposing a two-level cascade strategy, reducing computational costs and attaining a solution whose nonlinear controllers are simpler to tune due to lower number of cascaded loops. Each level of the cascade system executes a control law through the method of input-output feedback linearization (IOFL), which constantly linearizes the system so that linear control design techniques can be applied. In summary, the work in [21, 22] uses two loops to control altitude and attitude, while this work achieves the same in a single loop by using a dynamic extension approach for controlling these variables by actuating on their snaps. The external loop presented in this paper performs trajectory tracking for translational motion while reducing the load’s swing. Besides, the proposed control strategy is designed based on a detailed whole-body dynamic model of the tilt-rotor UAV using the Euler-Lagrange formulation.

Some model simplifications are assumed in the control design, neglecting some dynamic cross coupling between generalized coordinates. These assumptions can be close to reality if the system’s angular velocities and generalized acceleration are not very high, which is acceptable when the tilt-rotor UAV operates in the helicopter flight-mode. In order to deal with those neglected terms, mixed controllers with pole placement constraints are designed based on the linearized dynamics with the addition of integral terms, featuring robustness against unmodeled dynamics and constant disturbance rejection, while guaranteeing satisfactory time response.

In order to solve the problem of position and speed estimation in presence of unknown disturbances and noisy measurements with low sampling frequency, a Linear Kalman Filter with Unknown Inputs (LKFUI) is designed for estimating the aircraft’s translational position and speed and the corresponding disturbances. It assumes that the position is actually measured by a positioning system (e.g., GPS, vision system) equipment with sampling time , where is the controller sampling time. The estimator evaluates the position of the aircraft when no new measurements are available from the sensor, also taking into account its measurement uncertainty. The estimator also considers that the aircraft’s motion may be affected by disturbances (e.g., wind), which are not usually measured. The designed estimator is based on the formulation proposed by [23], which presents a generalized approach to Kalman Filters called* Gain-Constrained Kalman Filtering* in which both LKFUI and LKF are particular solutions.

The proposed control system performance is evaluated through simulation results and compared to a simpler controller, whose design considers the load as a disturbance to the system but does not avoid its swing, and to the three-level cascade strategy proposed in [22].

The remainder of the paper is structured as follows: Section 2 presents the whole-body modeling of the tilt-rotor UAV with suspended load; Section 3 presents the proposed control structure describing the design of the aforementioned nonlinear control system with the linear mixed controllers. In addition, an estimation model for the system is presented in order to develop the LKFUI algorithm; Section 4 shows simulation results; and, finally, Section 5 concludes this paper and provides suggestions of future works.

*Notation*. Let , , be the unit vectors in the direction of the -, -, and -axes, respectively, of a proper reference frame ; represents the rotation matrix from frame to frame ; expresses the rotation matrix of an angle around axis ; the vector denotes an angular velocity of frame with respect to frame represented in frame ; is the skew symmetric matrix related to the vector . Let denote the relative degree of a system’s output ; is the Lie derivative operation. Let the state vectors , denote the value of the states at sampling instant , being their estimated values; contains the values measured at instant , while represents the estimation of the same vector; denotes the fact that at instant has been predicted using measured information up to instant . Let and be two different sampling times with and an integer; () denotes the estimated states of the system seconds after the instant given at , where index represents increments in the controller’s cycles, while index represents sampling instants of sensors. A complementary list of nomenclature is provided in the Section “Nomenclature.”

#### 2. Tilt-Rotor UAV with Suspended Load Modeling

This section presents the whole-body dynamic modeling of the tilt-rotor UAV with suspended load using the Euler-Lagrange formulation. The multibody system is composed of four rigid bodies (see Figure 1): the main body (carbon-fiber structure, landing gear, battery, and electronic devices); two thrusters groups, one on each side of the aircraft (tiltable mechanisms with rotors), connected to the main body by a revolute joint; and the suspended load, which is assumed to be attached to the main body via a rigid rod with negligible mass. The following coordinate frames used in the system modeling are defined as (see Figure 1) a fixed inertial frame , a moving frame rigidly attached to the main body, a frame rigidly attached to the main body’s center of mass, frames and rigidly attached to the rotation axes of the right and left tiltable mechanisms, respectively, and a frame rigidly attached to the suspended load’s center of mass.