1. IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM): Model-based Off-line Compensation of Path Deviation for Industrial Robots in Milling Applications E. Abele, J. Bauer, M. Pischan Institute for Production Management, Technology and Machine Tools, (PTW) Technische Universität Darmstadt M. Friedmann, C. Reinl, O. von Stryk Simulation, Systems Optimization and Robotics Group, (SIM) Technische Universität Darmstadt

2. E. Abele J. Bauer M. Pischan Model-based Off-line Compensation of Path Deviation for Industrial Robots in Milling Applications M. Friedmann C. Reinl O. von Stryk Simulation, Systems Optimization, and Robotics IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM) 2011

3. Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 2 Presentation Outline 1.Introduction 2.Model of Robot Dynamics and Milling Force 3.Analysis and Model Calibration 4.Model-based Compensation of Deviation 5.Conlusion

4. Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 3 Potential Application Areas Area of milling operation with IR Accuracy Cutting Volume Deburring, grinding and milling aluminum and cast parts for foundry industry © Audi© Trimet Milling and Drilling of aluminum and steal parts for the automotive industry © BMW Milling Prototyping- application © DELCAM Trimming/ Milling of fibre- reinforced plastics for aerospace und automotive industries © Fehrer Milling and Drilling of integral parts for the aerospace industry © EADS Milling and finishing of molds for the mold and die production industry © Röders

5. Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 4 1. Static deflection:  Reason: High compliance of the robot structure 2. Low frequency oscillation:  Reason: Excitation of the system‘s eigen frequencies 3. High frequency oscillation:  Reason: Excitation of higher system‘s eigen frequencies (spindle, tool) Challenges during milling applications with robots  Adaption of the robot‘s tool path

6. Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 5 Interaction: Robot Structure  Milling Process InteractionStructureMilling Process Displacement Δx,y,z Force F Process FxFx FyFy FzFz Multibody Robot ModelProcess Force Model Milling Force Model coupling Offline Compensation

7. Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 6 1.Introduction 2.Model of Robot Dynamics and Milling Force 3.Analysis and Model Calibration 4.Model-based Compensation of Deviation 5.Conlusion Presentation Outline

8. Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 7 Modeling robot dynamics: kinematic structure rigid link with rotational joint: q i joint position; d i, z i a i DH-parameter arbitrary positioning of joint axis along z-axis by transition p i : extension by virtual rotational axes by virtual axes: q x,i q y,i : virtual joint positions Covers arbitrary tilting effects at actuated joints

9. Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 8 Modeling robot dynamics: multi-body dynamics and drivetrain Prarametrization of dynamics for each rigid body i : mass m i intertia tensor I i center of mass com i Newton-Euler algorithm for setting up Torque in jonts: drivetrain an elasticity:  i : desired joint position K i : stiffness D i : damping s i : backlash Coverd effects: Backlash of gears Friction in joints Dyanmic tilting at actuated and virtual axes M(q) : Inertia matrix : Coriolis + centrifugal forces G(q) : Gravitational forces : Joints Foces + Torques

10. Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 9 Efficient, object-oriented, modular Implementation in C++ Modeling entities used here: base, rigid body, variable/fixed rotation Further available: variable translations (  prismatic joints), forks (  tree-shaped structures beyond the kinematic chain) Equations of motion General form: Is obtained by recursive method evaluating robot structure during runtime  MBS can be changed without changing program: Invers dynamics: recursive Newton-Euler-algorithm Forward dynamics: Composite Rigid Body Algorithm, Articulated Body Algorithm Optional: Calculation of derivatives Automated derivation based on ADOL-C-library [Walther‘06] Precise derivatives of equations of motion with respect to any state variable and modeling parameter  interface to numerical sensitivity analysis, parameter estimation and trajectory optimization Modeling robot dynamics: Implementation „MBSLIB“

11. Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 10 Process Force Calculation 2. Calculation of the chip geometry - Tool moves in discrete time steps - Chip subdivided into disks of the height ∆z, ∆φ - Calculation of the chip thickness h for each section 1. Representation of the work piece - Multi dexel discretisation - Dexel representation as a line segment  - To receive a sufficient accuracy the discretisation should be: 3. Process force calculation - Calculation of the force per tooth F rta for each disk - Summation over all teeth and disks - Transformation into the tool coordinate system T(φ)

12. Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 11 Experimental validation cutting force calculation 4. Experimental validation - Test independent of a robot model - Test conducted on a robot with gantry machine structure - Milling forces are measured - Low pass filtering of the forces  static deviation is in the focus - Results show a good correlation but the dipping operation cannot be simulated

13. Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 12 1.Introduction 2.Model of Robot Dynamics and Milling Force 3.Analysis and Model Calibration 4.Model-based Compensation of Deviation 5.Conlusion Presentation Outline

14. Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 13 Prediction of Path Deviation by Coupled Simulation Simulation loop 1.Calculate pose and velocity of TCP depending on current state of robot 2.Calculate external forces resulting from process force model 3.Calculate forces in joints resulting from drives 4.Solve equations of motion for acceleration of joints 5.Integrate for next time-step 6.For each time-step: go to 1. FxFx FyFy FzFz +

15. Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 14 Prediction Path deviation Multibody Robot Model FxFx FyFy FzFz Process Force Model Milling Force +

16. Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 15 Example 2): Calculation of sensitivities simulataneously to simulation automated derivative calculation of integration step Optimal Design of Experiment and Sensitivity-Analysis Example 1): Find optimal position to determine a certain parameter ( e.g. mass m 6 ) by measurements. consider bounded working volume solve constraint non-linear problem Derivatives w.r.t. q and m 6 are available with ADOL-C Solution by interior-point- method IPOPT [Wächter‘06] subject to sensitivities in actuated joints robot path Key feature to deepest possible understanding of interaction between parameters dynamics

17. Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 16 1.Introduction 2.Model of Robot Dynamics and Milling Force 3.Analysis and Model Calibration 4.Model-based Offline Compensation of Deviation 5.Conlusion Presentation Outline

18. Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 17 Compensation of the TCP displacement (1) Reference solution Simulation run with an ideal robot and reference trajectory: Recording of joint positions Calculation external forces at TCP  Low pass filtering Filtered ideal forces Simulation of ideal robot work piece tool path

19. Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 18 Compensational points : Compensation of the TCP displacement (2) Determination of compensating trajectories Reference: forces and joint position from first simulation run filtering Ideal trajectories select interpolating points invers dynamics calculation Torques at interpolating points. assume Model-based approach considers milling forces and robot dynamics Off-line method does not require access to internal robot control Efficient calulation of compensational path

20. Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 19 Compensation of the TCP displacement (3) Experimental Validation Experimantal set-up: 1. First run with low feed rate 1.5 mm/s and milling depth 0.5 mm  process forces neglectable  no deviation 2. Milling with feed rate 50 mm/s and milling depth 1.5 mm a) without compensation b) with compensation Result:  Signifikant error reduction: root mean square error from e rms,1 =0.7 mm to e rms,2 =0.57 mm

21. Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 20 1.Introduction 2.Model of Robot Dynamics and Milling Force 3.Analysis and Model Calibration 4.Model-based Compensation of Deviation 5.Conlusion Presentation Outline

22. Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 21 Conclusion High speed cutting in hard materials with industrial robots: strong interaction of mechanical robot structure and removal process Prediction of static and dynamic TCP-deviations by coupled efficient simulation of milling process and of robot motion dynamics: Modular implementation for multi-body-system dynamics Covers causal effects for path deviation: tilting, elasticities and backlash of gears Applicable to any robot with tree structure Automated precise calculation of derivatives with respect to any model parameter. efficient model-based off-line compensation strategy Significant improvements to the processing accuracy Neither a modification of the robot nor access to the robot’s internal control is necessary: the users standard access possibilities are met Enabling advanced analysis, design of experiments, numerical parameter estimation and trajectory optimization  Cost-saving expansion the scope of machining applications of industrial robots

23. Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 22 Thank you for your attention! E. Abele J. Bauer M. Pischan {abele, bauer, pischan}@ptw.tu-darmstadt.de M. Friedmann C. Reinl O. von Stryk {friedmann, reinl, stryk}@sim.tu-darmstadt.de Simulation, Systems Optimization, and Robotics