Learning Adaptive Control for SE(3) Hamiltonian Dynamics

Fast adaptive control is a critical component for reliable robot autonomy in rapidly changing operational conditions. While a robot dynamics model may be obtained from first principles or learned from data, updating its parameters is often too slow for online adaptation to environment changes. This motivates the use of machine learning techniques to learn disturbance descriptors from trajectory data offline as well as the design of adaptive control to estimate and compensate the disturbances online. This paper develops adaptive geometric control for rigid-body systems, such as ground, aerial, and underwater vehicles, that satisfy Hamilton’s equations of motion over the SE(3) manifold. Our design consists of an offline system identification stage, followed by an online adaptive control stage. In the first stage, we learn a Hamiltonian model of the system dynamics using a neural ordinary differential equation (ODE) network trained from state-control trajectory data with different disturbance realizations. The disturbances are modeled as a linear combination of nonlinear descriptors. In the second stage, we design a trajectory tracking controller with disturbance compensation from an energy-based perspective. An adaptive control law is employed to adjust the disturbance model online proportional to the geometric tracking errors on the SE(3) manifold. We verify our adaptive geometric controller for trajectory tracking on a fully-actuated pendulum and an under-actuated quadrotor.

[1]  D. A. Dirksz,et al.  Adaptive control of port-Hamiltonian systems , 2010 .

[2]  R. Calandra,et al.  Control Adaptation via Meta-Learning Dynamics , 2018 .

[3]  Juraj Kabzan,et al.  Cautious Model Predictive Control Using Gaussian Process Regression , 2017, IEEE Transactions on Control Systems Technology.

[4]  Taeyoung Lee,et al.  Robust adaptive geometric tracking controls on SO(3) with an application to the attitude dynamics of a quadrotor UAV , 2011, IEEE Conference on Decision and Control and European Control Conference.

[5]  Davide Scaramuzza,et al.  Performance, Precision, and Payloads: Adaptive Nonlinear MPC for Quadrotors , 2021, IEEE Robotics and Automation Letters.

[6]  Lakmal Seneviratne,et al.  Adaptive Control Of Robot Manipulators , 1992, Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems.

[7]  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).

[8]  Jacquelien M. A. Scherpen,et al.  Structure Preserving Adaptive Control of Port-Hamiltonian Systems , 2012, IEEE Transactions on Automatic Control.

[9]  Girish Chowdhary,et al.  Deep Model Reference Adaptive Control , 2019, 2019 IEEE 58th Conference on Decision and Control (CDC).

[10]  Taeyoung Lee,et al.  Geometric tracking control of a quadrotor UAV on SE(3) , 2010, 49th IEEE Conference on Decision and Control (CDC).

[11]  Aaron D. Ames,et al.  Learning to jump in granular media: Unifying optimal control synthesis with Gaussian process-based regression , 2017, 2017 IEEE International Conference on Robotics and Automation (ICRA).

[12]  David Duvenaud,et al.  Neural Ordinary Differential Equations , 2018, NeurIPS.

[13]  Amit Chakraborty,et al.  Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control , 2020, ICLR.

[14]  Biao Huang,et al.  System Identification , 2000, Control Theory for Physicists.

[15]  Taeyoung Lee,et al.  Geometric Adaptive Control for a Quadrotor UAV with Wind Disturbance Rejection , 2018, 2018 IEEE Conference on Decision and Control (CDC).

[16]  Daewon Lee,et al.  Geometric Adaptive Tracking Control of a Quadrotor Unmanned Aerial Vehicle on SE(3) for Agile Maneuvers , 2015 .

[17]  Robert M. Sanner,et al.  Gaussian Networks for Direct Adaptive Control , 1991, 1991 American Control Conference.

[18]  Naira Hovakimyan,et al.  L1 Adaptive Control Theory - Guaranteed Robustness with Fast Adaptation , 2010, Advances in design and control.

[19]  Weiping Li,et al.  Composite adaptive control of robot manipulators , 1989, Autom..

[20]  Girish Chowdhary,et al.  Asynchronous Deep Model Reference Adaptive Control , 2020, CoRL.

[21]  R. Babuška,et al.  Port-Hamiltonian Systems in Adaptive and Learning Control: A Survey , 2016, IEEE Transactions on Automatic Control.

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

[23]  Marco Pavone,et al.  Adaptive-Control-Oriented Meta-Learning for Nonlinear Systems , 2021, Robotics: Science and Systems.

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

[25]  G. Karniadakis,et al.  Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems , 2018, 1801.01236.

[26]  R. Sanner,et al.  Gaussian Networks for Direct Adaptive Control , 1991 .

[27]  Martin Guay,et al.  Adaptive Model Predictive Control for Constrained Nonlinear Systems , 2008 .

[28]  Bjarne A. Foss,et al.  Dual adaptive model predictive control , 2017, Autom..

[29]  Davide Scaramuzza,et al.  Data-Driven MPC for Quadrotors , 2021, IEEE Robotics and Automation Letters.

[30]  Andreas Krause,et al.  Safe controller optimization for quadrotors with Gaussian processes , 2015, 2016 IEEE International Conference on Robotics and Automation (ICRA).

[31]  Jean-Jacques E. Slotine,et al.  Hamiltonian adaptive control of spacecraft , 1990 .

[32]  Frank Allgöwer,et al.  Adaptive Model Predictive Control with Robust Constraint Satisfaction , 2017 .

[33]  Peter Kuster,et al.  Nonlinear And Adaptive Control Design , 2016 .

[34]  Carl E. Rasmussen,et al.  Gaussian Processes for Data-Efficient Learning in Robotics and Control , 2015, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[35]  A. Isidori,et al.  Adaptive control of linearizable systems , 1989 .

[36]  Taeyoung,et al.  Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds , 2017 .

[37]  Soon-Jo Chung,et al.  Meta-Learning-Based Robust Adaptive Flight Control Under Uncertain Wind Conditions , 2019, ArXiv.

[38]  Mahdis Bisheban,et al.  Geometric Adaptive Control With Neural Networks for a Quadrotor in Wind Fields , 2019, IEEE Transactions on Control Systems Technology.

[39]  Taeyoung Lee,et al.  Robust Adaptive Attitude Tracking on ${\rm SO}(3)$ With an Application to a Quadrotor UAV , 2013, IEEE Transactions on Control Systems Technology.

[40]  Hannu Tenhunen,et al.  A Survey on Odometry for Autonomous Navigation Systems , 2019, IEEE Access.

[41]  Arjan van der Schaft,et al.  Port-Hamiltonian Systems Theory: An Introductory Overview , 2014, Found. Trends Syst. Control..

[42]  Marco Pavone,et al.  Meta-Learning Priors for Efficient Online Bayesian Regression , 2018, WAFR.

[43]  Raia Hadsell,et al.  Graph networks as learnable physics engines for inference and control , 2018, ICML.

[44]  Maria Adler,et al.  Stable Adaptive Systems , 2016 .

[45]  Nikolay Atanasov,et al.  Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Control , 2021, Robotics: Science and Systems.

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

[47]  Alexander Liniger,et al.  Learning-Based Model Predictive Control for Autonomous Racing , 2019, IEEE Robotics and Automation Letters.

[48]  J. Webster,et al.  Wiley Encyclopedia of Electrical and Electronics Engineering , 2010 .

[49]  Jonathan P. How,et al.  Nonparametric adaptive control using Gaussian Processes with online hyperparameter estimation , 2013, 52nd IEEE Conference on Decision and Control.

[50]  Anuradha M. Annaswamy,et al.  Robust Adaptive Control , 1984, 1984 American Control Conference.

[51]  Angela P. Schoellig,et al.  Adaptive Model Predictive Control for High-Accuracy Trajectory Tracking in Changing Conditions , 2018, 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[52]  Gang Tao,et al.  Multivariable adaptive control: A survey , 2014, Autom..

[53]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[54]  Davide Scaramuzza,et al.  A Benchmark Comparison of Monocular Visual-Inertial Odometry Algorithms for Flying Robots , 2018, 2018 IEEE International Conference on Robotics and Automation (ICRA).