: A Fast Symbolic, Dynamic Simulator interfaced with
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1 18/11/2014 : A Fast Symbolic, Dynamic Simulator interfaced with Timothée Habra (Université catholique de Louvain) Houman Dallali (Instituto Italiano di Technologia) 1
2 Introduction Robots model complexity (#dof, soft actuation, ) Model-based control (model predictive control, optimal feedback control, ) 2
3 Introduction Robots model complexity (#dof, soft actuation, ) Model-based control (model predictive control, optimal feedback control, ) Need : Fast and accurate simulator 2
4 Introduction Robots model complexity (#dof, soft actuation, ) Model-based control (model predictive control, optimal feedback control, ) Need : Fast and accurate simulator Speed-accuracy tradeoff ODE should not be used for quantitative engineering. (ODE Manual) Simbody slower than real-time for CoMan 2
5 Introduction Robots model complexity (#dof, soft actuation, ) Model-based control (model predictive control, optimal feedback control, ) Need : Fast and accurate simulator Speed-accuracy tradeoff ODE should not be used for quantitative engineering. (ODE Manual) Simbody slower than real-time for CoMan Solution : Robotran symbolic simulator 2
6 Outline Robotran Principles Generation of symbolic routines for dynamics Robotics Simulator Available features for robot simulation Robotran-Yarp interface Running a Yarp module with Robotran 3
7 Outline Robotran Principles Generation of symbolic routines for dynamics Robotics Simulator Available features for robot simulation Robotran-Yarp interface Running a Yarp module with Robotran 4
8 Symbolic software to model and analyze Multibody Systems Developed since 1990 at Université catholique de Louvain (UCL) Used in a wide range of applications : 5
9 Symbolic software to model and analyze Multibody Systems Developed since 1990 at Université catholique de Louvain (UCL) Used in a wide range of applications : Redundant actuators 5
10 Symbolic software to model and analyze Multibody Systems Developed since 1990 at Université catholique de Louvain (UCL) Used in a wide range of applications : Redundant actuators Biomechanics 5
11 Symbolic software to model and analyze Multibody Systems Developed since 1990 at Université catholique de Louvain (UCL) Used in a wide range of applications : Redundant actuators Biomechanics Piano action 5
12 Symbolic software to model and analyze Multibody Systems Developed since 1990 at Université catholique de Louvain (UCL) Used in a wide range of applications : Redundant actuators Biomechanics Piano action Road vehicles 5
13 Symbolic software to model and analyze Multibody Systems Developed since 1990 at Université catholique de Louvain (UCL) Used in a wide range of applications : Redundant actuators Biomechanics Piano action Road vehicles Railway dynamics 5
14 Symbolic software to model and analyze Multibody Systems Developed since 1990 at Université catholique de Louvain (UCL) Used in a wide range of applications : Redundant actuators Biomechanics Piano action Road vehicles Railway dynamics Robotics 5
15 Robotran formalism Abstraction 15
16 Robotran formalism Abstraction 16
17 Robotran formalism Abstraction Leaf body body 8 joint 1 7 Base body 0 External force 17
18 Robotran formalism Abstraction Leaf body loop body 8 joint 1 7 Base body 0 External force 18
19 Robotran formalism Abstraction Leaf body loop body 8 joint 1 7 Base body 0 External force Equations Newton: Each body must satisfy : Euler: 19
20 Robotran formalism Body (Rigid) Joint 10 parameters : mass (1), center of mass (3), inertia matrix (6) Relative coordinates 6 basic joints (1dof) Any joints Revolute X,Y,Z Cardan (2 dof) Planar (3 dof) Prismatic X,Y,Z combination Ball joint (3 dof) Telescopic (2 dof) 20
21 Symbolic generation ways to generate multibody equations: 8
22 Symbolic generation ways to generate multibody equations: 1) Manually Generating by hand the equations of motion (E.O.M) specific to the model. + : simplification of math - : small system only 8
23 Symbolic generation ways to generate multibody equations: 1) Manually Generating by hand the equations of motion (E.O.M) specific to the model. + : simplification of math - : small system only 2) Numerically Solving the E.O.M with generic code. If (next_joint == revolute) then F = matrix_mult(a,b) ++ : handle very large system - : code not optimized for the system - : rebuilt model at each time step 8
24 Symbolic generation ways to generate multibody equations: 1) Manually Generating by hand the equations of motion (E.O.M) specific to the model. + : simplification of math - : small system only 2) Numerically Solving the E.O.M with generic code. If (next_joint == revolute) then F = matrix_mult(a,b) ++ : handle very large system - : code not optimized for the system - : rebuilt model at each time step 3) Symbolically Automatic generation of E.O.M by a software specific to the model + : simplification of math + : handle large systems - : fixed topology 8
25 Symbolic generation Robotran : a symbolic generator 9
26 Symbolic generation Robotran : a symbolic generator 9
27 Symbolic generation Robotran : a symbolic generator Robot description 9
28 Symbolic generation Robotran : a symbolic generator Formalism Recursive Newton-Euler scheme Virtual principles Order N formulation Robot description 9
29 Symbolic generation Robotran : a symbolic generator Formalism Recursive Newton-Euler scheme Virtual principles Order N formulation Robot description Symbolic routines (C,Matlab, Python) Direct Dynamics Inverse Dynamics certified up to 300 dof. 9
30 Symbolic generation Symbolic routine : example 10
31 Symbolic generation Symbolic routine : example Trigo of joint angles 10
32 Symbolic generation Symbolic routine : example Trigo of joint angles Joint location 10
33 Symbolic generation Symbolic routine : example Trigo of joint angles Joint location Body mass 10
34 Symbolic generation Symbolic routine : example Trigo of joint angles Joint location Body mass Mass matrix 10
35 Symbolic generation Symbolic routine : example Trigo of joint angles Joint location Body mass Mass matrix M ( q) q C( q, q ) Q q 10
36 Symbolic generation Symbolic simplifications : [1] Rosenthal, D.E. and Sherman, M.A., High performance multibody simulations via symbolic equation manipulation and Kane s method, The Journal of the Astronautical Sciences, Vol. 34, No. 3, July-September
37 Symbolic generation Symbolic simplifications : Arithmetic a + b + c - b 0*a [1] Rosenthal, D.E. and Sherman, M.A., High performance multibody simulations via symbolic equation manipulation and Kane s method, The Journal of the Astronautical Sciences, Vol. 34, No. 3, July-September
38 Symbolic generation Symbolic simplifications : Arithmetic a + b + c - b 0*a a + 0 e.g. Gravity = [0,0,-9.81] [1] Rosenthal, D.E. and Sherman, M.A., High performance multibody simulations via symbolic equation manipulation and Kane s method, The Journal of the Astronautical Sciences, Vol. 34, No. 3, July-September
39 Symbolic generation Symbolic simplifications : Arithmetic a + b + c - b 0*a a + 0 e.g. Gravity = [0,0,-9.81] Trigonometric 2 cos ( ) sin 2 2cos( )sin( ) ( ) [1] Rosenthal, D.E. and Sherman, M.A., High performance multibody simulations via symbolic equation manipulation and Kane s method, The Journal of the Astronautical Sciences, Vol. 34, No. 3, July-September
40 Symbolic generation Symbolic simplifications : Arithmetic a + b + c - b 0*a a + 0 e.g. Gravity = [0,0,-9.81] Trigonometric 2 cos ( ) sin 2 2cos( )sin( ) ( ) 1 sin(2 ) [1] Rosenthal, D.E. and Sherman, M.A., High performance multibody simulations via symbolic equation manipulation and Kane s method, The Journal of the Astronautical Sciences, Vol. 34, No. 3, July-September
41 Symbolic generation Symbolic simplifications : Arithmetic a + b + c - b 0*a e.g. Gravity = [0,0,-9.81] Trigonometric 2 cos ( ) sin 2 2cos( )sin( ) ( ) a sin(2 ) Recursive // Data A B C D // Equations A1 = A + B A2 =2 * C B1 = A1+ C B2 = A2 * A2 B3 = C * A2 C1 = A1 + B2 C2 = B + B2 D1 = C2 - C1 D2 = C1 + C2 // Results M = D2 [1] Rosenthal, D.E. and Sherman, M.A., High performance multibody simulations via symbolic equation manipulation and Kane s method, The Journal of the Astronautical Sciences, Vol. 34, No. 3, July-September
42 Symbolic generation Symbolic simplifications : Arithmetic a + b + c - b 0*a e.g. Gravity = [0,0,-9.81] Trigonometric 2 cos ( ) sin 2 2cos( )sin( ) ( ) a sin(2 ) Recursive // Data A B C D // Equations A1 = A + B A2 =2 * C B1 = A1+ C B2 = A2 * A2 B3 = C * A2 C1 = A1 + B2 C2 = B + B2 D1 = C2 - C1 D2 = C1 + C2 // Results M = D2 [1] Rosenthal, D.E. and Sherman, M.A., High performance multibody simulations via symbolic equation manipulation and Kane s method, The Journal of the Astronautical Sciences, Vol. 34, No. 3, July-September
43 Symbolic generation Symbolic simplifications : Arithmetic a + b + c - b 0*a e.g. Gravity = [0,0,-9.81] Trigonometric 2 cos ( ) sin 2 2cos( )sin( ) ( ) a to 90% of the operations are typically removed [1] 1 sin(2 ) Recursive // Data A B C D // Equations A1 = A + B A2 =2 * C B1 = A1+ C B2 = A2 * A2 B3 = C * A2 C1 = A1 + B2 C2 = B + B2 D1 = C2 - C1 D2 = C1 + C2 // Results M = D2 [1] Rosenthal, D.E. and Sherman, M.A., High performance multibody simulations via symbolic equation manipulation and Kane s method, The Journal of the Astronautical Sciences, Vol. 34, No. 3, July-September
44 Symbolic generation Symbolic (Robotran) is much faster than numeric (Simbody) direct dynamics computational time Robotran 3.5 times faster than Simbody CoMan model Note : Both Robotran and Simbody use relative coordinates. Their results were similar (diff = ) 12
45 Robotran in Practice Step 1 : Draw your multibody system robot description file (xml) Step 2 : Generate your multibody equations Symbolic routines (C, Matlab, python) Step 3 : Simulate and analyse your multibody model Results, video 13
46 Robotran in Practice Step 1 : Draw your multibody system using 14
47 Robotran in Practice Step 1 : Draw your multibody system using 15
48 Robotran in Practice Step 2 : Generate your multibody equations using Your model is sent to a sever, which sends back the model symbolic function 16
49 Robotran in Practice Step 3 : Simulate and analyze your multibody model using Cross-language Collection of routines in 3 different environments : Matlab : fast code prototyping + Matlab toolbox Python : like Matlab but free C/C++ : Fast execution + embedded code Available in pure C (Cmake) or with Simulink Cross-platform Open source easy to interface with user code Note : User interact with symbolic routines through user functions (e.g. external forces, joint force, constraints, ). 17
50 Outline Robotran Principles Generation of symbolic routines for dynamics Robotics Simulator Available features for robot simulation Robotran-Yarp interface Running a Yarp module with Robotran 18
51 Models Data from mechanical design Series Elastic Actuators Ground contact model 19
52 Models Data from mechanical design Series Elastic Actuators Ground contact model Walkman CoMan 19
53 Models Data from mechanical design Series Elastic Actuators Ground contact model Walkman CoMan Available Soon icub Armar IV (KIT) 19
54 20 Actuator model Actuation Model Equation L f C dt d M,,, 2 2 L t m m m i K dt d b dt d J 2 2 dt d dt d D K m s m s L ) ( t v K Ri dt di L m w
![Contact handling Mesh to mesh contact library (Simbody) Body position & velocity Contact Force & moment Image adapted from [3] Multibody dynamics model [3] G.](/docs-images/74/70857310/images/55-1.jpg "Hippmann, An algorithm for compliant contact between complexly shaped surfaces in multibody dynamics, Multibody Dyn. Jorge AC Ambrosio Ed IDMECIST Lisbon Port. July, vol.")
55 Contact handling Mesh to mesh contact library (Simbody) Body position & velocity Contact Force & moment Image adapted from [3] Multibody dynamics model [3] G. Hippmann, An algorithm for compliant contact between complexly shaped surfaces in multibody dynamics, Multibody Dyn. Jorge AC Ambrosio Ed IDMECIST Lisbon Port. July, vol. 14,
56 Realtime features 22
57 Outline Robotran Principles Generation of symbolic routines for dynamics Robotics Simulator Available features for robot simulation Robotran-Yarp interface Running a Yarp module with Robotran 23
58 Robotran-Yarp plugin Controller decoupled from the robot. Controllers are robot-platform agnostic. Yarp Module (e.g. controller) Accurate dynamics High level task Run module on simulator : before robot : fast software development + parallel work within robot : internal model (prediction, teleoperation, ) Real test 24
59 Robotran interfaced with Yarp 25
60 Robotran and real CoMan 26
61 Conclusion An new simulator is available for running Yarp modules fast accurate dynamics open source lightweight see also Acknowledgment IIT : Alberto Cardellino, Lorenzo Natale, Nikos Tsagarakis UCL : Nicolas Van der Noot, Aubain Verle, Nicolas Docquier, Paul Fisette, Renaud Ronsse Moscow State Univ : Alexandra Zobova 27
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