A Differentiable Newton Euler Algorithm for Multi-body Model Learning

In this work, we examine a spectrum of hybrid model for the domain of multi-body robot dynamics. We motivate a computation graph architecture that embodies the Newton Euler equations, emphasizing the utility of the Lie Algebra form in translating the dynamical geometry into an efficient computational structure for learning. We describe the used virtual parameters that enable unconstrained physical plausible dynamics and the used actuator models. In the experiments, we define a family of 26 grey-box models and evaluate them for system identification of the simulated and physical Furuta Pendulum and Cartpole. The comparison shows that the kinematic parameters, required by previous white-box system identification methods, can be accurately inferred from data. Furthermore, we highlight that models with guaranteed bounded energy of the uncontrolled system generate non-divergent trajectories, while more general models have no such guarantee, so their performance strongly depends on the data distribution. Therefore, the main contributions of this work is the introduction of a white-box model that jointly learns dynamic and kinematics parameters and can be combined with black-box components. We then provide extensive empirical evaluation on challenging systems and different datasets that elucidates the comparative performance of our grey-box architecture with comparable white- and black-box models.

[1]  Christopher G. Atkeson,et al.  Estimation of Inertial Parameters of Manipulator Loads and Links , 1986 .

[2]  M. Spong,et al.  Robot Modeling and Control , 2005 .

[3]  Adrien Escande,et al.  Identification of fully physical consistent inertial parameters using optimization on manifolds , 2016, 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[4]  Mykel J. Kochenderfer,et al.  A General Framework for Structured Learning of Mechanical Systems , 2019, ArXiv.

[5]  Junggon Kim Lie Group Formulation of Articulated Rigid Body Dynamics , 2012 .

[6]  Sami Haddadin,et al.  First-order-principles-based constructive network topologies: An application to robot inverse dynamics , 2017, 2017 IEEE-RAS 17th International Conference on Humanoid Robotics (Humanoids).

[7]  Sergey Levine,et al.  Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models , 2018, NeurIPS.

[8]  G. Palli Intelligent Robots And Systems , 1993, Proceedings of 1993 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS '93).

[9]  Jan Peters,et al.  Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning , 2019, ICLR.

[10]  Kim D. Listmann,et al.  Deep Lagrangian Networks for end-to-end learning of energy-based control for under-actuated systems , 2019, 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[11]  Jan Peters,et al.  Model learning for robot control: a survey , 2011, Cognitive Processing.

[12]  Carl E. Rasmussen,et al.  PILCO: A Model-Based and Data-Efficient Approach to Policy Search , 2011, ICML.

[13]  Viorica Patraucean,et al.  gvnn: Neural Network Library for Geometric Computer Vision , 2016, ECCV Workshops.

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

[15]  Jean-Jacques E. Slotine,et al.  Linear Matrix Inequalities for Physically Consistent Inertial Parameter Identification: A Statistical Perspective on the Mass Distribution , 2017, IEEE Robotics and Automation Letters.

[16]  Austin Wang,et al.  Encoding Physical Constraints in Differentiable Newton-Euler Algorithm , 2020, L4DC.

[17]  Roy Featherstone,et al.  Rigid Body Dynamics Algorithms , 2007 .

[18]  Jun Nakanishi,et al.  A Bayesian Approach to Nonlinear Parameter Identification for Rigid Body Dynamics , 2006, Robotics: Science and Systems.

[19]  Karl Johan Åström,et al.  BOOK REVIEW SYSTEM IDENTIFICATION , 1994, Econometric Theory.