DISCO: Double Likelihood-free Inference Stochastic Control

Accurate simulation of complex physical systems enables the development, testing, and certification of control strategies before they are deployed into the real systems. As simulators become more advanced, the analytical tractability of the differential equations and associated numerical solvers incorporated in the simulations diminishes, making them difficult to analyse. A potential solution is the use of probabilistic inference to assess the uncertainty of the simulation parameters given real observations of the system. Unfortunately the likelihood function required for inference is generally expensive to compute or totally intractable. In this paper we propose to leverage the power of modern simulators and recent techniques in Bayesian statistics for likelihood-free inference to design a control framework that is efficient and robust with respect to the uncertainty over simulation parameters. The posterior distribution over simulation parameters is propagated through a potentially non-analytical model of the system with the unscented transform, and a variant of the information theoretical model predictive control. This approach provides a more efficient way to evaluate trajectory roll outs than Monte Carlo sampling, reducing the online computation burden. Experiments show that the controller proposed attained superior performance and robustness on classical control and robotics tasks when compared to models not accounting for the uncertainty over model parameters.

[1]  Wojciech Zaremba,et al.  OpenAI Gym , 2016, ArXiv.

[2]  A. Mesbah,et al.  Stochastic Model Predictive Control: An Overview and Perspectives for Future Research , 2016, IEEE Control Systems.

[3]  Moritz Diehl,et al.  ACADO toolkit—An open‐source framework for automatic control and dynamic optimization , 2011 .

[4]  Lucas Barcelos de Oliveira,et al.  Multi-agent Model Predictive Control of Signaling Split in Urban Traffic Networks ∗ , 2010 .

[5]  David Q. Mayne,et al.  Model predictive control: Recent developments and future promise , 2014, Autom..

[6]  Rolf Findeisen,et al.  Parameterized Tube Model Predictive Control , 2012, IEEE Transactions on Automatic Control.

[7]  Sebastian Engell,et al.  Robust nonlinear model predictive control with reduction of uncertainty via dual control , 2017, 2017 21st International Conference on Process Control (PC).

[8]  Yuval Tassa,et al.  An integrated system for real-time model predictive control of humanoid robots , 2013, 2013 13th IEEE-RAS International Conference on Humanoid Robots (Humanoids).

[9]  Yevgen Chebotar,et al.  Closing the Sim-to-Real Loop: Adapting Simulation Randomization with Real World Experience , 2018, 2019 International Conference on Robotics and Automation (ICRA).

[10]  Nando de Freitas,et al.  An Introduction to MCMC for Machine Learning , 2004, Machine Learning.

[11]  Fabio Tozeto Ramos,et al.  Online Adaptation of Deep Architectures with Reinforcement Learning , 2016, ECAI.

[12]  Pieter Abbeel,et al.  Autonomous Helicopter Aerobatics through Apprenticeship Learning , 2010, Int. J. Robotics Res..

[13]  Lars Imsland,et al.  Stochastic Nonlinear Model Predictive Control with State Estimation by Incorporation of the Unscented Kalman Filter , 2017 .

[14]  Benjamin Recht,et al.  A Tour of Reinforcement Learning: The View from Continuous Control , 2018, Annu. Rev. Control. Robotics Auton. Syst..

[15]  Michael I. Jordan,et al.  Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification , 2018, COLT.

[16]  Simon J. Julier,et al.  The scaled unscented transformation , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[17]  Dariusz Pazderski,et al.  Modeling and control of a 4-wheel skid-steering mobile robot , 2004 .

[18]  Dieter Fox,et al.  BayesSim: adaptive domain randomization via probabilistic inference for robotics simulators , 2019, Robotics: Science and Systems.

[19]  Jeffrey K. Uhlmann,et al.  Unscented filtering and nonlinear estimation , 2004, Proceedings of the IEEE.

[20]  James M. Rehg,et al.  Information-Theoretic Model Predictive Control: Theory and Applications to Autonomous Driving , 2017, IEEE Transactions on Robotics.

[21]  Nolan Wagener,et al.  Information theoretic MPC for model-based reinforcement learning , 2017, 2017 IEEE International Conference on Robotics and Automation (ICRA).

[22]  Rudolph van der Merwe,et al.  Sigma-point kalman filters for probabilistic inference in dynamic state-space models , 2004 .

[23]  Dezhen Song,et al.  Kinematic Modeling and Analysis of Skid-Steered Mobile Robots With Applications to Low-Cost Inertial-Measurement-Unit-Based Motion Estimation , 2009, IEEE Transactions on Robotics.

[24]  Michael Mistry,et al.  Uncertainty averse pushing with model predictive path integral control , 2017, 2017 IEEE-RAS 17th International Conference on Humanoid Robotics (Humanoids).

[25]  Stefan Schaal,et al.  Learning from Demonstration , 1996, NIPS.