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

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© 2012 Maplesoft, a division of Waterloo Maple Inc. Introduction Case Studies: Quadrotor – Quanser Planetary Rover – University of Waterloo and Canadian Space Agency Challenges in Model-based design and development Maplesoft Engineering Solutions

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© 2012 Maplesoft, a division of Waterloo Maple Inc. “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…

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© 2012 Maplesoft, a division of Waterloo Maple Inc. Scalability Tasks Capacity Number of functions (Complexity)

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© 2012 Maplesoft, a division of Waterloo Maple Inc. Scalability Multi-domain Modeling Engine/ Powertrain Torque/Speed Inputs Chassis/Tire Torque/Speed Outputs Apply Load??? Driveline Tasks Capacity Number of functions (Complexity)

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© 2012 Maplesoft, a division of Waterloo Maple Inc. Scalability Multi-domain Modeling Real-time Performance Engine/ Powertrain Torque/Speed Inputs Chassis/Tire Torque/Speed Outputs Apply Load??? Driveline Tasks Capacity Number of functions (Complexity)

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© 2012 Maplesoft, a division of Waterloo Maple Inc.

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

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© 2012 Maplesoft, a division of Waterloo Maple Inc. 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.

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© 2012 Maplesoft, a division of Waterloo Maple Inc. 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 Parameter Identification Build Subsystem Prototypes for Technically Risky Subsystems Evaluate Performance Trade various Concepts *Simulink is a registered trademark of The Mathworks, Inc. Quarc is a registered trademark of Quanser Consulting, Inc.

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© 2012 Maplesoft, a division of Waterloo Maple Inc. 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 Parameter Identification Build Subsystem Prototypes for Technically Risky Subsystems Parameter Identification Prototype Full System Deploy with Sim Controller Deploy Final Product, Controllers Curriculum Evaluate Performance Trade various Concepts

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© 2012 Maplesoft, a division of Waterloo Maple Inc. Multibody Modeling

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© 2012 Maplesoft, a division of Waterloo Maple Inc. Multibody Modeling

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© 2012 Maplesoft, a division of Waterloo Maple Inc. Multibody Modeling

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© 2012 Maplesoft, a division of Waterloo Maple Inc. Multibody Modeling

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© 2012 Maplesoft, a division of Waterloo Maple Inc. Multibody Modeling

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© 2012 Maplesoft, a division of Waterloo Maple Inc. Multibody Modeling

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© 2012 Maplesoft, a division of Waterloo Maple Inc. Multibody Modeling

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© 2012 Maplesoft, a division of Waterloo Maple Inc. Multibody Modeling

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© 2012 Maplesoft, a division of Waterloo Maple Inc. MapleSim Model: Multibody Quadrotor Model + Controller

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© 2012 Maplesoft, a division of Waterloo Maple Inc. MapleSim Model: Multibody Quadrotor Model + Controller

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© 2012 Maplesoft, a division of Waterloo Maple Inc. MapleSim Model: Multibody Quadrotor Model

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© 2012 Maplesoft, a division of Waterloo Maple Inc. MOVIE #1

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© 2012 Maplesoft, a division of Waterloo Maple Inc. Generated s-function from the MapleSim plant model QUARC®/Simulink® Model *Simulink is a registered trademark of The Mathworks, Inc. Quarc is a registered trademark of Quanser Consulting, Inc.

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© 2012 Maplesoft, a division of Waterloo Maple Inc. MOVIE #2 Flight Test

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© 2012 Maplesoft, a division of Waterloo Maple Inc.

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

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© 2012 Maplesoft, a division of Waterloo Maple Inc. Visualization Environment Modeling Environment Angular velocity input Steering angle input Six-wheeled Rocker-Bogie Rover

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© 2012 Maplesoft, a division of Waterloo Maple Inc. Rigid Wheel Model

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© 2012 Maplesoft, a division of Waterloo Maple Inc. MOVIE #3 Visualization in MapleSim

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© 2012 Maplesoft, a division of Waterloo Maple Inc. Rover Kinematics

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© 2012 Maplesoft, a division of Waterloo Maple Inc. Automatic Generation of the Constraint Equations in MapleAutomatic Generation of the Constraint Equations in Maple Rover Kinematics

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© 2012 Maplesoft, a division of Waterloo Maple Inc. -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*co s(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*si n(phi)*sin(xi)*sin(eta)*sin(zeta)-1.*yBR*sin(phi)*cos(xi)*cos(zeta)... 27 Constraint Equations of 36 variables Automatic Generation of the Constraint Equations in MapleAutomatic Generation of the Constraint Equations in Maple Rover Kinematics

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© 2012 Maplesoft, a division of Waterloo Maple Inc. Differential Joint Steering Wheel/soil forces Additional Constraints and ForcesAdditional Constraints and Forces Rover Kinematics

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© 2012 Maplesoft, a division of Waterloo Maple Inc. MOVIE #4 Quasi-static Simulation using MATLAB®Quasi-static Simulation using MATLAB® Rover Kinematics *Matlab is a registered trademark of The Mathworks, Inc.

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© 2012 Maplesoft, a division of Waterloo Maple Inc. Energy OptimizationEnergy Optimization Rover Path Planning

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© 2012 Maplesoft, a division of Waterloo Maple Inc. Software Component Library Modeling Workspace Rover Component Library

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© 2012 Maplesoft, a division of Waterloo Maple Inc. Lighting System Solar Arrays Hardware Components

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© 2012 Maplesoft, a division of Waterloo Maple Inc. Battery Motor Flywheel Load simulator PXI Sensors Hardware Components

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© 2012 Maplesoft, a division of Waterloo Maple Inc. 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 HiL Implementation

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© 2012 Maplesoft, a division of Waterloo Maple Inc. HiL Implementation

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© 2012 Maplesoft, a division of Waterloo Maple Inc. HiL Implementation

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© 2012 Maplesoft, a division of Waterloo Maple Inc. 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 HiL Implementation – Sample Results

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© 2012 Maplesoft, a division of Waterloo Maple Inc. 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

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© 2012 Maplesoft, a division of Waterloo Maple Inc. 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.

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© 2012 Maplesoft, a division of Waterloo Maple Inc. Automatic Equation Generation Automatic Equation Generation Symbolic model simplification Optimized code generation Best performance ~10x faster than similar tools Advanced analysis Parameter optimization Sensitivity etc Multibody kinematics and dynamics Equation-based Model Creation Enter system equations Test/Validate model Easy component block generation Greater insight into system behavior

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© 2012 Maplesoft, a division of Waterloo Maple Inc. Plant model Analysis Controller design Equation and code generation Controller implementation (and design) Realtime management Embedded controller Data acquisition System HIL 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

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© 2012 Maplesoft, a division of Waterloo Maple Inc. 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.

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© 2012 Maplesoft, a division of Waterloo Maple Inc. Thank You! Questions? To stay connected: www.maplesoft.com/subscribe

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