Experimental Flight Testing of a Fault-Tolerant Adaptive Autopilot for Fixed-Wing Aircraft Joonghyun Lee John Spencer Siyuan Shao Juan Augusto Paredes Dennis S. Bernstein Ankit Goel

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Experimental Flight Testing of a

Fault-Tolerant Adaptive Autopilot for Fixed-Wing Aircraft

Joonghyun Lee, John Spencer, Siyuan Shao, Juan Augusto Paredes, Dennis S. Bernstein, Ankit Goel

Abstract— This paper presents an adaptive autopilot for

ﬁxed-wing aircraft and compares its performance with a ﬁxed-

gain autopilot. The adaptive autopilot is constructed by aug-

menting the autopilot architecture with adaptive control laws

that are updated using retrospective cost adaptive control. In

order to investigate the performance of the adaptive autopilot,

the default gains of the ﬁxed-gain autopilot are scaled to

degrade its performance. This scenario provides a venue for

determining the ability of the adaptive autopilot to compensate

for the degraded ﬁxed-gain autopilot. Next, the performance

of the adaptive autopilot is examined under failure conditions

by simulating a scenario where one of the control surfaces

is assumed to be stuck at an unknown angle. The adaptive

autopilot is also tested in physical ﬂight experiments under

degraded-nominal conditions, and the resulting performance

improvement is examined.

I. INTRODUCTION

Autonomous ﬂight control of an aircraft under rapidly

changing conditions requires an autopilot that can control the

aircraft in uncertain environments and without detailed mod-

els. An autopilot for a ﬁxed-wing aircraft typically consists

of a set of trim commands along with low-level controllers

to follow intermediate commands. The trim conditions for

an aircraft can be computed by solving nonlinear algebraic

equations for trim equilibria [1], but a detailed model of

the aircraft aerodynamics is required. Moreover, for low-

cost aircraft that are usually repaired or modiﬁed onsite, the

true aerodynamic properties may be different from nominal

aerodynamics. Consequently, a ﬁxed-gain autopilot may not

be able to maintain performance in a rapidly changing envi-

ronment or under failure conditions such as damaged wings

or faulty actuators. In this scenario, an adaptive autopilot may

be able to compensate for the lost performance by updating

the autopilot gains accordingly. With these motivations in

mind, this paper explores the use of an in situ learning

technique to modify the autopilot during the ﬂight.

Various adaptive control techniques have been investigated

for ﬁxed-wing aircraft control [2]. A sliding mode fault-

tolerant tracking control scheme was used for control of

a ﬁxed-wing UAV under actuator saturation and state con-

straints in [3], [4]. A backstepping algorithm was used in

[5] to design a nonlinear ﬂight controller for a ﬁxed-wing

UAV with thrust vectoring. An MRAC-based technique was

This research was supported in part by the Ofﬁce of Naval Research

under grant N00014-19-1-2273.

Joonghyun Lee, John Spencer, Siyuan Shao, Juan Augusto Paredes, and

Dennis S. Bernstein are with the Department of Aerospace Engineering,

University of Michigan, Ann Arbor, MI 48109. joonghle, spjohn,

shaosy, jparedes, dsbaero@umich.edu

Ankit Goel is with the Department of Mechanical Engineering, University

of Maryland, Baltimore County, MD 21250. ankgoel@umbc.edu

used to augment the control system to improve the dynamic

performance of a ﬁxed-wing aircraft in [6]. However, these

techniques rely on the availability of a sufﬁciently detailed

model for the control system synthesis.

In contrast, the present paper uses the retrospective cost

adaptive control (RCAC) algorithm to learn the autopilot

gains from the measured data in situ. RCAC is a digital

adaptive control technique that is applicable to stabilization,

command following, and disturbance rejection. Instead of

relying on a model of the system, RCAC uses the past mea-

sured data and past applied input to recursively optimize the

controller gains. RCAC is described in [7], and its extension

to digital PID control is given in [8]. The application of

RCAC for a multicopter autopilot are described in [9], [10].

The contribution of this paper is the development of an

adaptive autopilot for ﬁxed-wing aircraft, and a comparison

of its performance with a well-tuned ﬁxed-gain autopi-

lot under nominal conditions, performance recovery of a

degraded-nominal autopilot, and performance improvement

under actuator failure. In particular, this paper presents the

potential advantages of an adaptive autopilot by investigating

two scenarios. In the ﬁrst scenario, a well-tuned ﬁxed-gain

controller is degraded by scaling all of the gains by a

small factor, and it is shown that the adaptive autopilot

is able to compensate for the degraded gains by learning

the necessary gains. This scenario is investigated both in

simulation and in physical ﬂight experiments. In the second

scenario, the aircraft is simulated with a faulty aileron, thus

emulating an actuator failure condition, and it is shown, in

simulation experiments, that the adaptive autopilot improves

the trajectory-tracking performance.

The paper is organized as follows: Section II deﬁnes the

notation used in this paper, Section III reviews the autopilot

architecture implemented in the PX4 ﬂight stack, Section IV

presents the adaptive augmentation of autopilot, Section V

presents the simulation ﬂight tests, and Section Vpresents

the outdoor ﬂight tests. Finally, Section VII concludes the

paper with a summary and future research directions.

II. NOTATION

Let FEdenote an Earth-ﬁxed frame such that ˆ

kEis

aligned with the acceleration due to gravity *

g . Let FAC

denote an aircraft-ﬁxed frame such that ˆıAC is aligned with

the fuselage, ˆAC is along the wing, and ˆ

kAC is chosen

to complete the right-handed frame. Note that ˆ

kAC points

vertically down. Next, let cdenote the center of mass of

the aircraft, and let wbe an point ﬁxed on Earth. The

coordinates of the aircraft relative to win the Earth frame are

arXiv:2210.13621v1 [eess.SY] 24 Oct 2022

denoted by r4

rc/w

E∈R3.The velocity of the aircraft

relative to win the Earth frame is v4

vc/w/E

E∈R3.

Let Ψ,Θ,and Φdenote the 3-2-1 azimuthal, elevation,

and bank Euler angles of the aircraft. The angular velocity

of FAC relative to FEin the aircraft-ﬁxed frame is given

by ω4

ωAC/E

AC ∈R3.The angular acceleration of

FAC relative to FEin the aircraft-ﬁxed frame is given by

α4

αAC/E

AC ∈R3.The measurement of the variable xis

denoted by xm, and the setpoint for the variable xis denoted

by xs.Finally, let e3

=001T.

The angles Ψ,Θ,and Φcomprise a 3-2-1 sequence of

Euler angles that parameterize the orientation of FAC relative

to FE.The components of ωare the yaw rate, pitch rate, and

roll rate, which are different from the azimuth rate, elevation

rate, and bank rate. Hence, integrating the components of

ωdoes not yield the azimuthal, elevation, and bank Euler

angles. In fact, the relation between the Euler-angle rates

and the components of ωis given by (4) in the following

section.

III. FLIGHT CONTROL ARCHITECTURE

In this work, we consider the ﬂight control architecture

implemented in the PX4 ﬂight stack. The control system

consists of a mission planner and two cascaded controllers

in nested loops as shown in Figure 1. The mission planner

generates position setpoints based on user-deﬁned waypoints.

Mission

Planner

Position

Controller

Attitude

Controller

Fixed-Wing

Aircraft

rs, VT,s

Φs,

Θs

αs

rm, VT, VG

Φm,Θm, VT, VI, ωm

Fig. 1. Autopilot architecture.

The outer loop, also called the position controller, consists

of two decoupled controllers for the longitudinal and lateral

motion of the aircraft, as shown in Figure 2. The longitudinal

controller is based on the total energy control system (TECS)

described in [11]–[14], and the lateral controller is based on

the guidance law described in [15]. The inputs to the position

controller are the true airspeed setpoint VT,s,the position

setpoint rs,the true airspeed VT,the position measurement

rm,and the ground velocity VG.The TECS input includes

the altitude setpoint hs

=eT

3rsand the altitude measurement

=eT

3rm.The longitudinal controller generates the thrust

and the elevation setpoint, and the lateral controller generates

the bank setpoint. The output of the position controller is thus

the thrust setpoint Tsand the attitude setpoint Ψs,Θs,Φs.

The inner loop, also called the attitude controller, consists

of two cascaded controllers, as shown in Figure 3. The

Longitudinal

Controller

(TECS)

Lateral

Controller

VT,s

Θs

Φs

Fig. 2. Position controller architecture.

ﬁrst controller uses the elevation and bank errors and a

proportional control law to generate the elevation-rate and

bank-rate setpoints. In particular, the elevation-rate setpoint

Θsand the bank-rate setpoint ˙

Φsare given by

Θs=kθ(Θs−Θm),(1)

Φs=kφ(Φs−Φm),(2)

where kθ, kφare the scalar gains. The azimuthal-rate is

algebraically given by

Ψs=gtan Φscos Θs

(3)

to ensure coordinated turn. Finally, the body-ﬁxed angular-

velocity setpoint ωsis given by

ωs=S(Θm,Φm)



Φs

Θs

Ψs



,(4)

where

S(Θm,Φm)4

=



1 0 sin Θm

0 cos Φmsin Φmcos Θm

0−sin Φmcos Φmcos Θm



.(5)

Next, a feedforward and a PI control law generates the

angular-acceleration setpoint αs. In particular, αsis given

αs=VT,0

Gω,ﬀωs+VI,0

VI2

Gω,PI(q) (ωs−ωm),(6)

where Gω,ﬀ=kω,ﬀis a proportional control law,

Gω,PI(q) = kω,P+kω,I

q−1is a PI control law, VIis the

indicated airspeed, and VT,0and VI,0are the true airspeed

and the indicated airspeed at trim conditions respectively,

which are aircraft parameters. Note that qis the forward-shift

operator, kω,ﬀ, kω,P,and kω,Iare 3×3diagonal matrices,

and are thus parameterized by 9 scalar gains. Finally, using

the angular-acceleration setpoint, the actuator deﬂections are

computed using control allocation methods.

The ﬁxed-wing autopilot thus consists of 11 gains. In

practice, these 11 gains are tuned manually, which requires

considerable expertise. We assume that the default gains

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ExperimentalFlightTestingofaFault-TolerantAdaptiveAutopilotforFixed-WingAircraftJoonghyunLee,JohnSpencer,SiyuanShao,JuanAugustoParedes,DennisS.Bernstein,AnkitGoelAbstractThispaperpresentsanadaptiveautopilotforxed-wingaircraftandcomparesitsperformancewithaxed-gainautopilot.Theadaptiveautopilotisco...

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Experimental Flight Testing of a Fault-Tolerant Adaptive Autopilot for Fixed-Wing Aircraft Joonghyun Lee John Spencer Siyuan Shao Juan Augusto Paredes Dennis S. Bernstein Ankit Goel

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