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Model-based Off-line Compensation of Path Deviation for Industrial Robots in Milling Applications M. Friedmann C. Reinl O. von Stryk E. Abele J. Bauer M. Pischan Simulation, Systems Optimization, and Robotics IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM) 2011 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 Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 2 Potential Application Areas Cutting Volume © EADS © DELCAM Milling and Drilling of integral parts for the aerospace industry Milling Prototypingapplication Area of milling operation with IR © Trimet © Audi © BMW Milling and Drilling of aluminum and steal parts © Fehrer Deburring, grinding and milling for the automotive industry Trimming/ Milling of fibrealuminum and cast parts reinforced plastics for for foundry industry aerospace und automotive industries © Röders Milling and finishing of molds for the mold and die production industry Accuracy Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 3 Challenges during milling applications with robots 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) Static Offset Low frequency oscillation Work piece holder Work Werkst piece ücktisch holder IR IR y yy xx statischer Versatz 1mm Static offset Desired Path Sollbahn x RealePath Bahn Real Desired path Desired Path Sollbahn Real Path yy xx Real path yy y x x Cross section z x Adaption of the robot‘s tool path Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 4 Interaction: Robot Structure Milling Process Structure Interaction Milling Process Displacement Δx,y,z Force FProcess Multibody Robot Model Process Force Model Model coupling Fx Fy Milling Force Fz M (q) q C(q, q ) G(q) J c' Fxyz ,tool Frta, j ,e K c h j ( , z )z K e z Offline Compensation Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 5 Ne N Z Fxyz ,tool T j ( ) Frta, j ,e e 1 j 1 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 Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 6 Modeling robot dynamics: kinematic structure • rigid link with rotational joint: linkdh,i Rot ( z; qi )·Trans(0, 0, di )·Trans(0, 0, ai )·Rot ( x; i ) qi joint position; di, zi ai DH-parameter • arbitrary positioning of joint axis along z-axis by transition pi: linkwrep,i Trans(0,0, pi )·Rot ( z; qi )·Trans(0,0, di pi )· Trans(0,0, ai )·Rot ( x;i ). • extension by virtual rotational axes by virtual axes: linkext ,i Trans (0, 0, pi )·Rot ( z; qi )·Rot ( x; q x ,i )· ·Rot ( y; q y ,i )·Trans (0, 0, di pi ) ·Trans (0, 0, ai )·Rot ( x; i ) qx,i qy,i : virtual joint positions Covers arbitrary tilting effects at actuated joints Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 7 Modeling robot dynamics: multi-body dynamics and drivetrain • Prarametrization of dynamics for each rigid body i: • mass mi • intertia tensor Ii • center of mass comi • Newton-Euler algorithm for setting up M(q): Inertia matrix C ( q, q ) : Coriolis + centrifugal forces G(q): Gravitational forces : Joints Foces + Torques C (q, q ) G(q) J c' Fxyz ,tool M (q) q i • Torque in jonts: drivetrain an elasticity: ((qi si ) qi ) , if (qi qi ) si i Di ·(qi qi ) Ki ·((qi si ) qi ) , if (qi qi ) si , else 0 qi: desired joint position Ki: stiffness Di: damping si: backlash si Coverd effects: Backlash of gears Friction in joints Dyanmic tilting at actuated and virtual axes Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 8 si qi qi Modeling robot dynamics: Implementation „MBSLIB“ 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 C(q, q ) G(q) J c' Fxyz ,tool •General form: M (q) q • 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 Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 9 Process Force Calculation 1. Representation of the work piece - Multi dexel discretisation - Dexel representation as a line segment p dt s - To receive a sufficient accuracy the discretisation should be: x y z kd ; ; 0.05 R R R z 2. Calculation of the chip geometry - Tool moves in discrete time steps y ap ∆z - Chip subdivided into disks of the height ∆z, ∆φ x - Calculation of the chip thickness h for each section 3. Process force calculation - Calculation of the force per tooth Frta for each disk - Summation over all teeth and disks - Transformation into the tool coordinate system Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 10 T(φ) 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 Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 12 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. Fx Fy Fz + Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 13 Optimal Design of Experiment and Sensitivity-Analysis Example 1): Find optimal position to determine a certain parameter ( e.g. mass m6) by measurements. Example 2): Calculation of sensitivities simulataneously to simulation • consider bounded working volume • solve constraint non-linear problem • automated derivative calculation of integration step n min q i (q; m6 ) m6 j 1 M i 1 subject to robot path forward _ kinematics(q) Vxyz sensitivities in actuated joints qi (q (t ); m6 ) m6 • Derivatives w.r.t. q and m6 are • available with ADOL-C Solution by interior-pointmethod IPOPT [Wächter‘06] Key feature to deepest possible understanding of interaction between parameters dynamics Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 15 Presentation Outline 1. Introduction 2. Model of Robot Dynamics and Milling Force 3. Analysis and Model Calibration 4. Model-based Offline Compensation of Deviation 5. Conlusion Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 16 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 Simulation of ideal robot Filtered ideal forces tool path work piece Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 17 Compensation of the TCP displacement (2) Determination of compensating trajectories Reference: forces and joint position from first simulation run • filtering Ideal trajectories qideal (t ), qideal (t ), qideal (t ), Fext (t ) • select interpolating points • invers dynamics calculation Torques at interpolating points ideal. • assume qcomp qideal 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 Compensational points qcomp : Ki1 ( iideal (tl ) si ) , if iideal 0 qicomp (tl ) qiideal (tl ) Ki1 ( iideal (tl ) si ) , if iideal 0 ideal 0 , i f 0 i Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 18 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 erms,1=0.7 mm to erms,2=0.57 mm Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 19 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 Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 20 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 Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 21 Thank you for your attention! M. Friedmann C. Reinl O. von Stryk E. Abele J. Bauer M. Pischan Simulation, Systems Optimization, and Robotics {friedmann, reinl, stryk}@sim.tu-darmstadt.de {abele, bauer, pischan}@ptw.tu-darmstadt.de Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 22