vdm-based navigation for small uavs · • as old as gps (>30 years) • on most uavs today...

A New Paradigm forIntegrated Navigation of UAVsBased on Vehicle Dynamic Model

Mehran Khaghani & Jan Skaloud

2Introduction

NavigationDetermination of Position, Velocity, and Attitude

X

Y

Z

Position

Velocity

Attitude

• As old as GPS (>30 years)• On most UAVs today (outdoor)

3Introduction

Integrated Inertial and Satellite Navigation (INS-GNSS)

INS: Inertial Navigation SystemGNSS: Global Navigation Satellite SystemGPS: Global Positioning System (American GNSS)UAV: Unmanned Aerial VehicleIMU: Inertial Measurement UnitPVA: Position, Velocity, AttitudePVT: Position, Velocity, TimeMEMS: Micro-Electro-Mechanical Systems

MEMS Tactical Navigatione e e>

Problem 1: GNSS outagePVA solution will drift over time

Problem 2: IMU failureNothing will work!

IMU

GNSS

Filter

∫ PVA+

( )PVA∆

PVT

,f ω PVA−

4Method

Our Proposition

Aerodynamic

Model

Navigation States

Wind velocity

UAV parameters

Control commands

Rigid Body Dynamics

Linear accelerationForcesMoments Rotational acceleration

Vehicle Dynamic Model (VDM)

Using VDM in navigation

5Method

From INS-based to VDM-based Navigation

VDM

GNSS

Filter

∫ PVA+

( )PVA∆

PVT

,f ω

,f ω PVA−

IMU

GNSS

Filter

∫ PVA+

( )PVA∆

PVT

,f ω PVA−

• VDM in process model• Physical constraints• No IMU data integration• Sensor setup• Self calibration• Platform dependence• Higher computational cost

(PC: 1.7 to 2.7 times)

• Platform independence• Low computational cost• Sensor (IMU) in process model

• IMU failure• Physical constraints

+−−

U

∫*nX

++ˆ

nX ˆ nX

ˆ wX

ˆ eX

ˆ pX++ˆ

pX

++

ˆwX

++ˆ

eX

IMUIMUZ

*eXIMU error

model (X )e

*pXParameters

model (X )p

*wXWind

model (X )w

+−

*nX

modelIMUZ

modelGNSSZ

Vehicledynamic

model (X )n nXδ

pXδ

wXδ

eXδ

Sensors(GNSS,Baro, ...)

SensorZ

Filter(e.g., EKF)

6Method

Some Other Architectures

IMU

VDM

Filter

∫

∫

( , )b bib∆ f ω ( )VA∆

( )VA∆

PVA∫

∫

( , )b bib∆ f ω

PVA

( , )b bib∆ f ω

Bryson 2004

IMU

VDM

Filter

∫

∫

PVA

( )PVA∆

PVA

Koifman 1999

Current research StillINS-based…

Common issues:• No wind• No self calibration• Partial VDM• No significant improvement

in experiments

PixHawk PCLOG

IMU

EKFVDM

Matlab Script

Sensors

GPSAir

Speed BaroGecko 4 Nav

via diff. interfaces

USB/WiFi

On line

Off line

TOPOPlane 2

7Method

Experimental Setup

Payload capacity 0.8 kgFlight endurance 45 minutes

Nominal airspeed 15 m/s

Aircraft & Sensors Connections

• Waypoints from real flight• 3D wind velocity from real data• Error statistics of real sensors• Flight simulation Sensor data Reference data

• 100 Monte-Carlo runs

8Results

GNSS Outage: Emulation Scenario

MEMS IMUStandalone GNSS

9Results

GNSS Outage: Experimental Scenario

VDM parameters calibration:• On a separate flight:• Start with nominal values in

simulations• IMU and cm-level GNSS data fused• Navigation states as observations• VDM parameters estimated

MEMS IMUStandalone GNSS

Emulation

GNSS Outage: Emulation vs Experimental Scenario

10Results

Experiment

53 m

2076 m

38 m

681 m

11Results

GNSS Outage: Experimental Scenario

• Waypoints from real flight• 3D wind velocity from real data• Error statistics of real sensors• Flight simulation Sensor data Reference data

• 100 Monte-Carlo runs

12Results

IMU failure: Emulation Scenario

MEMS IMUStandalone GNSS

13Results

IMU failure: Emulation Scenario100 Monte-Carlo runs

14Results

IMU failure: Experimental Scenario

VDM parameters calibration:• On a separate flight:• Start with nominal values in

simulations• IMU and cm-level GNSS data fused• Navigation states as observations• VDM parameters estimated

MEMS IMUStandalone GNSS

15Results

IMU failure: Experimental Scenario

The main suspect: Residual error in VDM parameters estimationSolution: Absolute attitude reference via photogrammetry (TBD)

Realization matters!• Estimation architecture,

VDM/IMU priors & on-linere-fining

• Platform, actuators, IMU + mount + models, time-stamping

GNSS outage, 2.2 kg fixed-wing MAV• Emulation: up to 100x better

without additional sensor • Experiment: 20-40x better

(e.g., @3min: 50 m vs 2 km)

Attitude estimation• Emulation:

<1° for roll & pitch, <2° for yaw• Experiment:

Mean ~5°, Max ~20-40° => Need to improve VDM calibration

Outlook• Attitude reference from

photogrammetry• Redundant IMUs• Direct actuation measurements• Online implementation

16Conclusion

Conclusion & Outlook

Acknowledgements: DDPS – CTI (Innosuisse)

17Publications

Selected Publications

Thank you for your attention• Concept / Monte-Carlo simulation

[Navigation, 2016] Autonomous Vehicle Dynamic Model-Based Navigation for Small UAVs

• Enhanced modeling / Experiments[Robotics and Autonomous Systems, 2018] Assessment of VDM-based Autonomous Navigation of a UAV under Operational Conditions

• Mapping[ISPRS Archives, 2016] Application of Vehicle Dynamic Modeling in UAVs for Precise Determination of Exterior Orientation

• Wind effects[ION GNSS+, 2016] Evaluation of Wind Effects on UAV Autonomous Navigation Based on Vehicle Dynamic Model

• Sensitivity Analysis[IEEE Transactions TAES, 2018 (under review)] Global Sensitivity Analysis ofVDM-based Navigation for UAVs