© 2012 Maplesoft, a division of Waterloo Maple Inc. Paul Goossens, VP of Application Engineering Dr. Orang Vahid, Senior Modeling Engineer

© 2012 Maplesoft, a division of Waterloo Maple Inc.

Paul Goossens, VP of Application EngineeringDr. Orang Vahid, Senior Modeling Engineer

High-Fidelity Physical Modeling for Aerospace Mechatronics Applications


• Introduction

• Case Studies:

• Quadrotor – Quanser

• Planetary Rover – University of Waterloo and Canadian Space Agency

• Challenges in Model-based design and development

• Maplesoft Engineering Solutions

Agenda


Physical Model-based Development

“Virtual” Prototyping through Model-based Design and Development plays an increasingly key role in system design, commissioning and testing.

•Increasing adoption of MBD and simulation

• Reduce prototyping cycles and costs

• Increase end-user functionality, quality, safety and reliability

• Deterministic, repeatable testing platform

Connection to real components with virtual subsystems through Hardware-in-the-Loop (HIL) Testing is critical to this strategy

• Validation of subcomponents and/or controllers before integrating into the vehicle reduces errors and costs

• Validation of model against the real thing improves the whole process, dramatically reducing development cycles and time-to-market in the future

Greater demand for greater model fidelity…


Scalability

Task

s Capacity

Number of functions (Complexity)

Emerging Challenges...


Scalability

Multi-domain Modeling

Engine/Powertrain

Torque/SpeedInputs

Chassis/TireTorque/Speed Outputs

Apply Load???Driveline

Task

s Capacity




Scalability

Multi-domain Modeling

Real-time Performance

Engine/Powertrain

Torque/SpeedInputs

Chassis/TireTorque/Speed Outputs

Apply Load???Driveline

Task

s Capacity




Qball-X4 Development


Paper Concept for Product

Rough Feasibility Study Paper

Calculations, Low fidelity Simulations

Plant Modelin MapleSim







Export Plant to Simulink Dev RT

Controller in QUARC Include Visualization

Modify Model Structure, and Fidelity

Evaluate Performance Trade various Concepts


*Simulink is a registered trademark of The Mathworks, Inc. Quarc is a registered trademark of Quanser Consulting, Inc.









Parameter Identification

Build Subsystem Prototypes for

Technically Risky SubsystemsEvaluate Performance

Trade various Concepts












Build Subsystem Prototypes for

Technically Risky Subsystems


Prototype Full System Deploy

with Sim Controller

Deploy Final Product, Controllers

Curriculum

Evaluate Performance Trade various Concepts




Multibody Modeling



Multibody Modeling


Multibody Modeling



Multibody Modeling



Multibody Modeling



Multibody Modeling



Multibody Modeling



Multibody Modeling



MapleSim Model: Multibody Quadrotor Model + Controller



MapleSim Model: Multibody Quadrotor Model + Controller



MapleSim Model: Multibody Quadrotor Model



MOVIE #1



Generated s-function from the MapleSim plant model

QUARC®/Simulink® Model




MOVIE #2

Flight Test



Planetary Rovers


System Components

Rover dynamics

Wheels

Solar cells

Wheel motors

Battery

Power electronics

Heaters

Robotic arms, other peripherals

Terrain

Environment

Planetary Rovers

Rover Modeling: A Multi-disciplinary Approach


Visualization Environment

Modeling Environment

Angular velocity input

Stee

ring

angl

e in

put

Planetary Rovers

Six-wheeled Rocker-Bogie Rover


Planetary Rovers

Rigid Wheel Model


Planetary Rovers

MOVIE #3

Visualization in MapleSim


Planetary Rovers

Rover Kinematics


Automatic Generation of the Constraint Equations in Maple

Planetary Rovers

Rover Kinematics


-2.*l1x-1.*ySL*cos(xi)*sin(eta)*sin(zeta)+ySR*cos(xi)*sin(eta)*sin(zeta)+zSL*cos(xi)*sin(eta)*cos(zeta)-1.*zSR*cos(xi)*sin(eta)*cos(zeta)-1.*cos(xi)*cos(eta)*xSL+cos(xi)*cos(eta)*xSR-1.*ySL*sin(xi)*cos(zeta)+ySR*sin(xi)*cos(zeta)-1.*zSL*sin(xi)*sin(zeta)+zSR*sin(xi)*sin(zeta)-1.*l1y+sin(xi)*cos(eta)*xSL-1.*sin(xi)*cos(eta)*xSR-1.*ySL*cos(xi)*cos(zeta)+ySR*cos(xi)*cos(zeta)-1.*zSL*cos(xi)*sin(zeta)+zSR*cos(xi)*sin(zeta)+ySL*sin(xi)*sin(eta)*sin(zeta)-1.*ySR*sin(xi)*sin(eta)*sin(zeta)-1.*zSL*sin(xi)*sin(eta)*cos(zeta)+zSR*sin(xi)*sin(eta)*cos(zeta)+l1y*cos(phi)-1.*l1z*sin(phi)-1.*l1z+cos(eta)*sin(zeta)*ySL-1.*cos(eta)*sin(zeta)*ySR-1.*cos(eta)*cos(zeta)*zSL+cos(eta)*cos(zeta)*zSR+l1y*sin(phi)-1.*sin(eta)*xSL+sin(eta)*xSR+l1z*cos(phi)-1.*cos(xi)*cos(eta)*xSL+cos(xi)*cos(eta)*xBL-1.*ySL*cos(xi)*sin(eta)*sin(zeta)-1.*ySL*sin(xi)*cos(zeta)+yBL*cos(xi)*sin(eta)*sin(zeta)+yBL*sin(xi)*cos(zeta)+zSL*cos(xi)*sin(eta)*cos(zeta)-1.*zSL*sin(xi)*sin(zeta)-1.*zBL*cos(xi)*sin(eta)*cos(zeta)+zBL*sin(xi)*sin(zeta)-1.*l3xsin(xi)*cos(eta)*xSL-1.*sin(xi)*cos(eta)*xBL+ySL*sin(xi)*sin(eta)*sin(zeta)-1.*ySL*cos(xi)*cos(zeta)-1.*yBL*sin(xi)*sin(eta)*sin(zeta)+yBL*cos(xi)*cos(zeta)-1.*zSL*sin(xi)*sin(eta)*cos(zeta)-1.*zSL*cos(xi)*sin(zeta)+zBL*sin(xi)*sin(eta)*cos(zeta)+zBL*cos(xi)*sin(zeta)+l3y-1.*sin(eta)*xSL+sin(eta)*xBL+cos(eta)*sin(zeta)*ySL-1.*cos(eta)*sin(zeta)*yBL-1.*cos(eta)*cos(zeta)*zSL+cos(eta)*cos(zeta)*zBL+l3z-1.*cos(xi)*cos(eta)*xSR+cos(xi)*cos(eta)*xBR-1.*ySR*cos(xi)*sin(eta)*sin(zeta)-1.*ySR*sin(xi)*cos(zeta)+yBR*cos(xi)*sin(eta)*sin(zeta)+yBR*sin(xi)*cos(zeta)+zSR*cos(xi)*sin(eta)*cos(zeta)-1.*zSR*sin(xi)*sin(zeta)-1.*zBR*cos(xi)*sin(eta)*cos(zeta)+zBR*sin(xi)*sin(zeta)+l3xxSR*sin(xi)*cos(eta)*cos(phi)-1.*xSR*sin(eta)*sin(phi)-1.*xBR*sin(xi)*cos(eta)*cos(phi)+xBR*sin(eta)*sin(phi)+ySR*cos(phi)*sin(xi)*sin(eta)*sin(zeta)-1.*ySR*cos(phi)*cos(xi)*cos(zeta)+ySR*cos(eta)*sin(zeta)*sin(phi)-1.*yBR*cos(phi)*sin(xi)*sin(eta)*sin(zeta)+yBR*cos(phi)*cos(xi)*cos(zeta)-1.*yBR*cos(eta)*sin(zeta)*sin(phi)-1.*zSR*cos(phi)*sin(xi)*sin(eta)*cos(zeta)-1.*zSR*cos(phi)*cos(xi)*sin(zeta)-1.*zSR*cos(eta)*cos(zeta)*sin(phi)+zBR*cos(phi)*sin(xi)*sin(eta)*cos(zeta)+zBR*cos(phi)*cos(xi)*sin(zeta)+zBR*cos(eta)*cos(zeta)*sin(phi)+l3y-1.*xSR*sin(xi)*cos(eta)*sin(phi)-1.*xSR*sin(eta)*cos(phi)+xBR*sin(xi)*cos(eta)*sin(phi)+xBR*sin(eta)*cos(phi)-1.*ySR*sin(phi)*sin(xi)*sin(eta)*sin(zeta)+ySR*sin(phi)*cos(xi)*cos(zeta)+ySR*cos(eta)*sin(zeta)*cos(phi)+yBR*sin(phi)*sin(xi)*sin(eta)*sin(zeta)-1.*yBR*sin(phi)*cos(xi)*cos(zeta)...

27 Constraint Equations of 36 variables

Planetary Rovers

Automatic Generation of the Constraint Equations in Maple

Rover Kinematics


Differential Joint

SteeringWheel/soil forces

Planetary Rovers

Additional Constraints and Forces

Rover Kinematics


Planetary Rovers

MOVIE #4

Quasi-static Simulation using MATLAB®

Rover Kinematics

*Matlab is a registered trademark of The Mathworks, Inc.


Planetary Rovers

Energy Optimization

Rover Path Planning


Software Component Library Modeling Workspace

Planetary Rovers

Rover Component Library


Planetary Rovers

Lighting System Solar Arrays

Hardware Components


Planetary Rovers

Battery Motor Flywheel Load simulator PXI Sensors

Hardware Components


Software Hardware (Test Bench)

Lighting System

Solar Panels

Battery

Motor

Charge Controller

Inverter

Load Simulator

Flywheel

Component Modeling

Solar Panels

Battery

Motor

Irradiation Model

NI® PXI

LabVIEW™ 2009

Rover Model HiL Graphical User Interface

Planetary Rovers

HiL Implementation


Planetary Rovers

HiL Implementation


Planetary Rovers

HiL Implementation


Summer Full Load - Pure Hardware vs. Solar Panel in the Loop

Summer Full Load - Pure Hardware vs. Solar Panel, Motor, Load Simulator in the loop

Planetary Rovers

HiL Implementation – Sample Results


What is MapleSim?

MapleSim is a truly unique physical modeling tool:

• Built on a foundation of symbolic computation technology

• Handles all of the complex mathematics involved in the development of engineering models

• Multi-domain systems, plant modeling, control design

• Leverages the power of Maple to take advantage of extensive analytical tools

• Reduces model development time from months to days while producing high-fidelity, high-performance models


Maplesoft Engineering Solutions

Multi-domain physical modeling

Driveline Component Library

More Libraries

-dSPACE®-LabVIEW™-NI® VeriStand™-MATLAB® & Simulink®-B&R Automation Studio

*Simulink and MATLAB are registered trademark of The Mathworks, Inc. All other trademarks are property of their respective owners.


AutomaticEquationGeneration Symbolic model simplification

Optimized code generation

Best performance

~10x faster than similar tools

Advanced analysisParameter optimizationSensitivity etcMultibody kinematics and dynamics

Equation-based Model CreationEnter system equationsTest/Validate modelEasy component block generation

Greater insight into system behavior

The Symbolic Advantage


Hardware in the Loop Simulation

Plant modelAnalysisController design

Equation andcode generation

Controller implementation (and design)Realtime management

Embedded controllerData acquisition

SystemHIL Simulation

*Simulink and MATLAB are registered trademark of The Mathworks, Inc. All other trademarks are property of their respective owners.

-dSPACE®-LabVIEW™-NI® VeriStand™-MATLAB® & Simulink®-B&R Automation Studio


Key Takeaways...

• Physical modeling: increasingly important – and increasingly complex – in systems design, testing and integration.

• Symbolic technology: proven engineering technology that significantly improves model fidelity without sacrificing real-time performance.

• MapleSim: ideal tool for rapid development of high-fidelity physical models of mechatronics systems to help engineers achieve their design goals.


Thank You!

Questions?

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Documents

© 2012 Maplesoft, a division of Waterloo Maple Inc. Paul Goossens, VP of Application Engineering Dr. Orang Vahid, Senior Modeling Engineer