Fast, Generic, and Reliable Control and Simulation of Soft Robots Using Model Order Reduction

Obtaining an accurate mechanical model of a soft deformable robot compatible with the computation time imposed by robotic applications is often considered an unattainable goal. This paper should invert this idea. The proposed methodology offers the possibility to dramatically reduce the size and the online computation time of a finite element model (FEM) of a soft robot. After a set of expensive offline simulations based on the whole model, we apply snapshot-proper orthogonal decomposition to sharply reduce the number of state variables of the soft-robot model. To keep the computational efficiency, hyperreduction is used to perform the integration on a reduced domain. The method allows to tune the error during the two main steps of complexity reduction. The method handles external loads (contact, friction, gravity, etc.) with precision as long as they are tested during the offline simulations. The method is validated on two very different examples of FEMs of soft robots and on one real soft robot. It enables acceleration factors of more than 100, while saving accuracy, in particular compared to coarsely meshed FEMs and provides a generic way to control soft robots.

[1]  Francisco Chinesta,et al.  Reduced-order modeling of soft robots , 2018, PloS one.

[2]  Paolo Dario,et al.  Soft Robot Arm Inspired by the Octopus , 2012, Adv. Robotics.

[3]  Shuuji Kajita,et al.  OpenHRP: Open Architecture Humanoid Robotics Platform , 2004, Int. J. Robotics Res..

[4]  Cecilia Laschi,et al.  Soft robotics: a bioinspired evolution in robotics. , 2013, Trends in biotechnology.

[5]  Danny C. Sorensen,et al.  Discrete Empirical Interpolation for nonlinear model reduction , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[6]  Jérémie Dequidt,et al.  Framework for online simulation of soft robots with optimization-based inverse model , 2016, 2016 IEEE International Conference on Simulation, Modeling, and Programming for Autonomous Robots (SIMPAR).

[7]  Gianluigi Rozza,et al.  Certified reduced basis approximation for parametrized partial differential equations and applications , 2011 .

[8]  Jernej Barbic,et al.  Vega: Non‐Linear FEM Deformable Object Simulator , 2013, Comput. Graph. Forum.

[9]  M. Mooney.  A Theory of Large Elastic Deformation , 1940 .

[10]  Olivier Goury,et al.  Computational time savings in multiscale fracturemechanics using model order reduction , 2015 .

[11]  Yuval Tassa,et al.  Simulation tools for model-based robotics: Comparison of Bullet, Havok, MuJoCo, ODE and PhysX , 2015, 2015 IEEE International Conference on Robotics and Automation (ICRA).

[12]  C. Farhat,et al.  Dimensional reduction of nonlinear finite element dynamic models with finite rotations and energy‐based mesh sampling and weighting for computational efficiency , 2014 .

[13]  Franz Pernkopf,et al.  Sparse nonnegative matrix factorization with ℓ0-constraints , 2012, Neurocomputing.

[14]  LipsonHod,et al.  Dynamic Simulation of Soft Multimaterial 3D-Printed Objects , 2014 .

[15]  L. Sirovich.  TURBULENCE AND THE DYNAMICS OF COHERENT STRUCTURES PART I : COHERENT STRUCTURES , 2016 .

[16]  M. Caicedo,et al.  Dimensional hyper-reduction of nonlinear finite element models via empirical cubature , 2017 .

[17]  Christian Duriez,et al.  Control of elastic soft robots based on real-time finite element method , 2013, 2013 IEEE International Conference on Robotics and Automation.

[18]  Matteo Bianchi,et al.  Controlling Soft Robots: Balancing Feedback and Feedforward Elements , 2017, IEEE Robotics & Automation Magazine.

[19]  Ian D. Walker,et al.  Soft robotics: Biological inspiration, state of the art, and future research , 2008 .

[20]  D. Ryckelynck,et al.  A priori hyperreduction method: an adaptive approach , 2005 .

[21]  J. Spillmann,et al.  CoRdE: Cosserat rod elements for the dynamic simulation of one-dimensional elastic objects , 2007, SCA '07.

[22]  Michael Yu Wang,et al.  Design and Analysis of Soft Grippers for Hand Rehabilitation , 2017 .

[23]  Charles L. Lawson,et al.  Solving least squares problems , 1976, Classics in applied mathematics.

[24]  Andrew Howard,et al.  Design and use paradigms for Gazebo, an open-source multi-robot simulator , 2004, 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE Cat. No.04CH37566).

[25]  Jernej Barbic,et al.  FEM simulation of 3D deformable solids: a practitioner's guide to theory, discretization and model reduction , 2012, SIGGRAPH '12.

[26]  Karen Willcox,et al.  Model Reduction for Large-Scale Systems with High-Dimensional Parametric Input Space , 2008, SIAM J. Sci. Comput..

[27]  David Amsallem,et al.  Automatised selection of load paths to construct reduced-order models in computational damage micromechanics: from dissipation-driven random selection to Bayesian optimization , 2016, Computational Mechanics.

[28]  Yong Chen,et al.  Interactive Material Design Using Model Reduction , 2015, TOGS.

[29]  Filip Ilievski,et al.  Multigait soft robot , 2011, Proceedings of the National Academy of Sciences.

[30]  Nobuto Matsuhira,et al.  Virtual Robot Experimentation Platform V-REP: A Versatile 3D Robot Simulator , 2010, SIMPAR.

[31]  Jérémie Dequidt,et al.  Kinematic modeling and observer based control of soft robot using real-time Finite Element Method , 2016, 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[32]  L. Sirovich.  Turbulence and the dynamics of coherent structures. I. Coherent structures , 1987 .

[33]  Christopher D. Rahn,et al.  Geometrically Exact Models for Soft Robotic Manipulators , 2008, IEEE Transactions on Robotics.

[34]  Ian D. Walker,et al.  Kinematics and the Implementation of an Elephant's Trunk Manipulator and Other Continuum Style Robots , 2003, J. Field Robotics.

[35]  C. Farhat,et al.  Efficient non‐linear model reduction via a least‐squares Petrov–Galerkin projection and compressive tensor approximations , 2011 .

[36]  山田 祐,et al.  Open Dynamics Engine を用いたスノーボードロボットシミュレータの開発 , 2007 .

[37]  Soha Hassoun,et al.  Evolving soft robotic locomotion in PhysX , 2009, GECCO '09.

[38]  D. Caleb Rucker,et al.  A Geometrically Exact Model for Externally Loaded Concentric-Tube Continuum Robots , 2010, IEEE Transactions on Robotics.

[39]  Christian Duriez,et al.  Optimization-Based Inverse Model of Soft Robots With Contact Handling , 2017, IEEE Robotics and Automation Letters.

[40]  Jernej Barbic,et al.  Real-Time subspace integration for St. Venant-Kirchhoff deformable models , 2005, ACM Trans. Graph..

[41]  David Amsallem,et al.  An adaptive and efficient greedy procedure for the optimal training of parametric reduced‐order models , 2015 .