IEEE - Aerospace and Electronic Systems - May 2022 - Tutorial XV - 7

Saavedra-Ruiz et al.
Figure 5.
Proposed control strategy attached to the native FCU controllers. The PID controllers block outputs the control signal Ut with _xa; _ya;
whereas the altitude controller outputs uzt
to control the descent of the vehicle.
CONTROL SYSTEM
This section describes the PID-based controller used to
autonomously land our rotorcraft. The IBVS controller
uses the 2D output of the estimation module as a reference
to compute position-velocity control signals to land the
vehicle. These signals are sent to the native positionvelocity
loops implemented in the PX4 flight-stack, which
transforms the positions into speeds and then converts
them into thrust commands for the vehicle's engines, to
guarantee correct control of the aircraft.
PID-BASED CONTROLLER
In order to ensure that the aircraft moves toward the landing
platform and lands on it, a control strategy is required.
Autonomous landing of the vehicle is accomplished by
feeding the position estimates of the template from the
Kalman filter to a set of three PID-based controllers.
The IBVS PIDs will perform all the calculations in the
current image frame. Setting a 2D image-based reference
for the controller, and thus avoiding the need for expensive
3D reconstructions, increases the computational
speed in on-board computers, allowing for real-time control
over the approaches of the vehicle to the landing
pad [15]. High-rate controllers tend to be robust against
sudden image changes, and with the Kalman filter output
as the reference for control, the system is capable of tracking
the landing platform even if it is abruptly moved out
of the camera's field of view.
Our approach uses a set of three PID-based controllers
attached in a cascade in an outer loop, with the two native
controllers already implemented in the Pixhawk flight
stack. The controllers of the flight stack have a standard
cascaded position-velocity loop, in which the outer position
loop transforms the position inputs to velocity outputs
and the velocity outputs are converted in the inner loop
into thrust commands for the vehicle's propellers. The
idea is to transform pixel coordinate errors into velocity
MAY 2022
c_ ,
Algorithm 1. Landing Platform Detector and Tracker
1: Inputs:
H 2 R33 Homography matrix
T 2 R2 Dimensions of the template
2: Initialization of the Kalman Filter:
A 2 R1010, R 2 R55, P 2 R1010,
Q 2 R1010, K 2 R55, S 2 R1010,
H 2 R510, Y 2 R5, X 2 R10
3: Outputs:
X 2 R10 State vector
4: Variables:
Pc 2 R5 Corners and centroid of the template
Z 2 R5 Observations of the template
Ow Width of the template in the image frame
Oh Height of the template in the image frame
u Estimated angle w.r.t X axis
5: for each frame do
6:
7:
for 1; .. . ; 5 do
Pc t computePoint(HH;T; point ¼ i)
8: end for
9: Pc t sortCorners(Pc t)
10: Ow;Oh computeObjectDims(Pct)
11:
12:
13:
14:
u computeAngle(Pc t)
if u > 90 then
unew u=90
u u unew 90
15: end if
16: Z fPc
ði¼5Þ
t ;Ow;Oh; ug
17: // KF Prediction step
18:
Xt AtXt1
19: Pt AtPt1AT
if detection is valid then
20:
21:
22:
23:
26:
// KF Correction step
Yt ZtHtXt
St HtPtHT
24: Kt PtHT
25:
27: end if
28: Xt ^Xt
29:
30: end for
IEEE A&E SYSTEMS MAGAZINE
7
X^tXt þKtYt
Pt ðI10x10KtHtÞ Pt
return Xt
t þQt
t S1
t þRt
t
IEEE - Aerospace and Electronic Systems - May 2022 - Tutorial XV

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