An End-to-End Differentiable but Explainable Physics Engine for Tensegrity Robots: Modeling and Control

This work proposes an end-to-end differentiable physics engine for tensegrity robots, which introduces a data-efficient linear contact model for accurately predicting collision responses that arise due to contacting surfaces, and a linear actuator model that can drive these robots by expanding and contracting their flexible cables. To the best of the authors' knowledge, this is the \emph{first} differentiable physics engine for tensegrity robots that supports cable modeling, contact, and actuation. This engine can be used inside an off-the-shelf, RL-based locomotion controller in order to provide training examples. This paper proposes a progressive training pipeline for the differentiable physics engine that helps avoid local optima during the training phase and reduces data requirements. It demonstrates the data-efficiency benefits of using the differentiable engine for learning locomotion policies for NASA's icosahedron SUPERballBot. In particular, after the engine has been trained with few trajectories to match a ground truth simulated model, then a policy learned on the differentiable engine is shown to be transferable back to the ground-truth model. Training the controller requires orders of magnitude more data than training the differential engine.

[1]  Kostas E. Bekris,et al.  A First Principles Approach for Data-Efficient System Identification of Spring-Rod Systems via Differentiable Physics Engines , 2020, L4DC.

[2]  Jason Yosinski,et al.  Hamiltonian Neural Networks , 2019, NeurIPS.

[3]  Marco Pavone,et al.  A Differentiable Augmented Lagrangian Method for Bilevel Nonlinear Optimization , 2019, Robotics: Science and Systems.

[4]  J. W. Humberston Classical mechanics , 1980, Nature.

[5]  Kartic Subr,et al.  Vid2Param: Modeling of Dynamics Parameters From Video , 2020, IEEE Robotics and Automation Letters.

[6]  Roger D. Quinn,et al.  Towards bridging the reality gap between tensegrity simulation and robotic hardware , 2015, 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[7]  K. H. Hunt,et al.  Coefficient of Restitution Interpreted as Damping in Vibroimpact , 1975 .

[8]  Connor Schenck,et al.  SPNets: Differentiable Fluid Dynamics for Deep Neural Networks , 2018, CoRL.

[9]  Jiajun Wu,et al.  Propagation Networks for Model-Based Control Under Partial Observation , 2018, 2019 International Conference on Robotics and Automation (ICRA).

[10]  Kostas E. Bekris,et al.  Kinodynamic planning for spherical tensegrity locomotion with effective gait primitives , 2019, Int. J. Robotics Res..

[11]  Alice M. Agogino,et al.  SUPERball : Exploring Tensegrities for Planetary Probes , 2014 .

[12]  F ROSENBLATT,et al.  The perceptron: a probabilistic model for information storage and organization in the brain. , 1958, Psychological review.

[13]  Joshua B. Tenenbaum,et al.  End-to-End Differentiable Physics for Learning and Control , 2018, NeurIPS.

[14]  Gaurav S. Sukhatme,et al.  Augmenting Differentiable Simulators with Neural Networks to Close the Sim2Real Gap , 2020, ArXiv.

[15]  W. Goldsmith,et al.  Impact: the theory and physical behaviour of colliding solids. , 1960 .

[16]  Andreas A. Polycarpou,et al.  Two-Dimensional Models of Boundary and Mixed Friction at a Line Contact , 1995 .

[17]  Robert E. Skelton,et al.  Design and control of tensegrity morphing airfoils , 2020 .

[18]  Jeffrey C. Trinkle,et al.  An implicit time-stepping scheme for rigid body dynamics with Coulomb friction , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[19]  Adrian K. Agogino,et al.  A bio-inspired tensegrity manipulator with multi-DOF, structurally compliant joints , 2016, 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[20]  Jan Swevers,et al.  Optimal robot excitation and identification , 1997, IEEE Trans. Robotics Autom..

[21]  Daniel L. K. Yamins,et al.  Flexible Neural Representation for Physics Prediction , 2018, NeurIPS.

[22]  Peter Brown,et al.  Contact Modelling for Forward Dynamics of Human Motion , 2017 .

[23]  Razvan Pascanu,et al.  Interaction Networks for Learning about Objects, Relations and Physics , 2016, NIPS.

[24]  David E. Orin,et al.  A compliant contact model with nonlinear damping for simulation of robotic systems , 1999, IEEE Trans. Syst. Man Cybern. Part A.

[25]  Frédo Durand,et al.  DiffTaichi: Differentiable Programming for Physical Simulation , 2020, ICLR.

[26]  Geoffrey E. Hinton,et al.  Learning representations by back-propagating errors , 1986, Nature.

[27]  Ming C. Lin,et al.  Differentiable Cloth Simulation for Inverse Problems , 2019, NeurIPS.

[28]  Yuval Tassa,et al.  MuJoCo: A physics engine for model-based control , 2012, 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[29]  Alice M. Agogino,et al.  Design, Simulation, and Testing of a Flexible Actuated Spine for Quadruped Robots , 2018, 1804.06527.

[30]  Richard W. Cottle,et al.  Linear Complementarity Problem , 2009, Encyclopedia of Optimization.

[31]  Kostas E. Bekris,et al.  Adaptive tensegrity locomotion: Controlling a compliant icosahedron with symmetry-reduced reinforcement learning , 2019, Int. J. Robotics Res..

[32]  Jiancheng Liu,et al.  ChainQueen: A Real-Time Differentiable Physical Simulator for Soft Robotics , 2018, 2019 International Conference on Robotics and Automation (ICRA).

[33]  Richard W. Cottle,et al.  Linear Complementarity Problem. , 1992 .

[34]  E. D. Cubuk,et al.  JAX, M.D.: End-to-End Differentiable, Hardware Accelerated, Molecular Dynamics in Pure Python , 2019, 1912.04232.

[35]  Kartic Subr,et al.  Vid2Param: Online system identification from video for robotics applications , 2019, ArXiv.

[36]  Jiajun Wu,et al.  Combining Physical Simulators and Object-Based Networks for Control , 2019, 2019 International Conference on Robotics and Automation (ICRA).

[37]  E. Todorov,et al.  A generalized iterative LQG method for locally-optimal feedback control of constrained nonlinear stochastic systems , 2005, Proceedings of the 2005, American Control Conference, 2005..

[38]  Benjamin Schrauwen,et al.  Design and control of compliant tensegrity robots through simulation and hardware validation , 2014, Journal of The Royal Society Interface.

[39]  Jeffrey M. Friesen,et al.  Design of SUPERball v2, a Compliant Tensegrity Robot for Absorbing Large Impacts , 2018, 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[40]  Gaurav S. Sukhatme,et al.  Interactive Differentiable Simulation , 2019, ArXiv.

[41]  Roy Featherstone,et al.  Robot Dynamics Algorithms , 1987 .