High-Fidelity Physical Modeling for Aerospace Mechatronics Applications Paul Goossens, VP of Application Engineering Dr. Orang Vahid, Senior Modeling Engineer

Agenda Introduction Case Studies: Quadrotor – Quanser Planetary Rover – University of Waterloo and Canadian Space Agency Challenges in Model-based design and development Maplesoft Engineering Solutions

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…

Emerging Challenges... Scalability Capacity Tasks Number of functions (Complexity)

Emerging Challenges... Scalability Multi-domain Modeling Capacity Tasks Capacity Number of functions (Complexity) Engine/ Powertrain Torque/Speed Inputs Chassis/Tire Outputs Apply Load??? Driveline

Emerging Challenges... Scalability Multi-domain Modeling Real-time Performance Tasks Capacity Number of functions (Complexity) Engine/ Powertrain Torque/Speed Inputs Chassis/Tire Outputs Apply Load??? Driveline

Qball-X4 Development

Qball-X4 Development Plant Model in MapleSim Paper Concept for Product Rough Feasibility Study Paper Calculations, Low fidelity Simulations Plant Model in MapleSim

Qball-X4 Development Plant Model in MapleSim Paper Concept for Product Rough Feasibility Study Paper Calculations, Low fidelity Simulations Plant Model in 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.

Qball-X4 Development Plant Model in MapleSim Paper Concept for Product Rough Feasibility Study Paper Calculations, Low fidelity Simulations Plant Model in MapleSim Export Plant to Simulink Dev RT Controller in QUARC Include Visualization Modify Model Structure, and Fidelity Build Subsystem Prototypes for Technically Risky Subsystems Evaluate Performance Trade various Concepts Parameter Identification *Simulink is a registered trademark of The Mathworks, Inc. Quarc is a registered trademark of Quanser Consulting, Inc.

Qball-X4 Development Plant Model in MapleSim Paper Concept for Product Rough Feasibility Study Paper Calculations, Low fidelity Simulations Plant Model in MapleSim Export Plant to Simulink Dev RT Controller in QUARC Include Visualization Modify Model Structure, and Fidelity Build Subsystem Prototypes for Technically Risky Subsystems Evaluate Performance Trade various Concepts Prototype Full System Deploy with Sim Controller Parameter Identification Parameter Identification Deploy Final Product, Controllers Curriculum

Qball-X4 Development Multibody Modeling

Qball-X4 Development Multibody Modeling

Qball-X4 Development Multibody Modeling

Qball-X4 Development Multibody Modeling

Qball-X4 Development Multibody Modeling

Qball-X4 Development Multibody Modeling

Qball-X4 Development Multibody Modeling

Qball-X4 Development Multibody Modeling

Qball-X4 Development MapleSim Model: Multibody Quadrotor Model + Controller

Qball-X4 Development MapleSim Model: Multibody Quadrotor Model + Controller

Qball-X4 Development MapleSim Model: Multibody Quadrotor Model

Qball-X4 Development MOVIE #1

Qball-X4 Development QUARC®/Simulink® Model Generated s-function from the MapleSim plant model Physical plant imported into Quarc model Rapid control prototyping can begin Fidelity of model improved in Quarc Sysid techniques used to get accurate model of actuator dynamics Limitations and sensors, electronics, and computation considered now. Processor fundamental sample time Sensor resolution, bandwidth, etc Non linearities Cad Model visualization used to aid in understanding *Simulink is a registered trademark of The Mathworks, Inc. Quarc is a registered trademark of Quanser Consulting, Inc.

Qball-X4 Development Flight Test MOVIE #2

Planetary Rovers

Planetary Rovers Rover Modeling: A Multi-disciplinary Approach System Components Rover dynamics Wheels Solar cells Wheel motors Battery Power electronics Heaters Robotic arms, other peripherals Terrain Environment

Angular velocity input Planetary Rovers Six-wheeled Rocker-Bogie Rover Modeling Environment Angular velocity input Steering angle input Visualization Environment

Planetary Rovers Rigid Wheel Model

Planetary Rovers Visualization in MapleSim MOVIE #3

Planetary Rovers Rover Kinematics

Planetary Rovers Rover Kinematics Automatic Generation of the Constraint Equations in Maple

27 Constraint Equations of 36 variables Planetary Rovers Rover Kinematics Automatic Generation of the Constraint Equations in Maple -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.*l3x sin(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)+l3x xSR*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 Rover Kinematics Additional Constraints and Forces Differential Joint Steering Wheel/soil forces

Planetary Rovers MOVIE #4 Rover Kinematics Quasi-static Simulation using MATLAB® MOVIE #4 *Matlab is a registered trademark of The Mathworks, Inc.

Planetary Rovers Rover Path Planning Energy Optimization

Planetary Rovers Rover Component Library Software Component Library Modeling Workspace

Planetary Rovers Hardware Components Lighting System Solar Arrays

Planetary Rovers Hardware Components Battery Motor Flywheel Load simulator PXI Sensors Rover weight? 200 kg Equivalent kinetic energy representation

Planetary Rovers HiL Implementation NI® PXI Software Hardware (Test Bench) Component Modeling Solar Panels Battery Motor Irradiation Model Lighting System Solar Panels Charge Controller NI® PXI Battery Inverter Load Simulator LabVIEW™ 2009 Rover Model HiL Graphical User Interface Motor Flywheel

Planetary Rovers HiL Implementation

Planetary Rovers HiL Implementation

Planetary Rovers HiL Implementation – Sample Results Summer Full Load - Pure Hardware vs. Solar Panel, Motor, Load Simulator in the loop Summer Full Load - Pure Hardware vs. Solar Panel in the Loop

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 -dSPACE® -LabVIEW™ -NI® VeriStand™ -MATLAB® & Simulink® -B&R Automation Studio Driveline Component Library More Libraries *Simulink and MATLAB are registered trademark of The Mathworks, Inc. All other trademarks are property of their respective owners.

The Symbolic Advantage Automatic Equation Generation Advanced analysis Parameter optimization Sensitivity etc Multibody kinematics and dynamics Greater insight into system behavior Symbolic model simplification Optimized code generation Best performance ~10x faster than similar tools Equation-based Model Creation Enter system equations Test/Validate model Easy component block generation

Hardware in the Loop Simulation Equation and code generation Controller implementation (and design) Realtime management Embedded controller Data acquisition Plant model Analysis Controller design -dSPACE® -LabVIEW™ -NI® VeriStand™ -MATLAB® & Simulink® -B&R Automation Studio System HIL Simulation *Simulink and MATLAB are registered trademark of The Mathworks, Inc. All other trademarks are property of their respective owners.

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. With the drive for greater fuel efficiency, quality and safety, physical modeling is becoming increasingly important – and increasingly complex – in automotive systems design, testing and integration Symbolic technology is a proven engineering technology that significantly helps to improve model fidelity without sacrificing real-time performance MapleSim is the ideal tool for rapid development of high-fidelity physical models of automotive systems to help engineers achieve their design goals...

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