Robust Learning of Nonlinear Dynamical Systems with Safety and Stability Properties

TL;DR

This paper introduces a robust learning approach for nonlinear dynamical systems that ensures safety and stability constraints are met, using Extreme Learning Machines and quadratic programming, validated through simulations and robot experiments.

Contribution

It develops a novel constrained learning method that guarantees safety and stability in nonlinear system identification under uncertainties.

Findings

The method achieves accurate trajectory reconstruction compared to state-of-the-art.

It guarantees safety and stability despite disturbances.

Successful implementation on a Baxter robot for pick-and-place tasks.

Abstract

The paper presents a robust parameter learning methodology for identification of nonlinear dynamical system from data while satisfying safety and stability constraints in the context of learning from demonstration (LfD) methods. Extreme Learning Machines (ELM) is used to approximate the system model, whose parameters are learned subject to the safety and stability constraints obtained using zeroing barrier and Lyapunov-based stability analysis in the presence of model uncertainties and external disturbances. A constrained Quadratic Program (QP) is developed, which accounts for the ELM function reconstruction error, to estimate the ELM parameters. Furthermore, a robustness lemma is presented, which proves that the learned system model guarantees safety and stability in the presence of disturbances. The method is tested in simulations. Trajectory reconstruction accuracy of the method is compared against state-of-the-art LfD methods using swept error area (SEA) metric. Robustness of the learned model is tested by conducting Monte Carlo tests. The proposed method is implemented on a Baxter robot for a pick-and-place task where the robot is constrained to an ellipsoidal safety region.