Provably Robust Learning-Based Approach for High-Accuracy Tracking Control of Lagrangian Systems

Abstract

Lagrangian systems represent a wide range of robotic systems, including manipulators, wheeled and legged robots, and quadrotors. Inverse dynamics control and feedforward linearization techniques are typically used to convert the complex nonlinear dynamics of Lagrangian systems to a set of decoupled double integrators, and then a standard, outer-loop controller can be used to calculate the commanded acceleration for the linearized system. However, these methods typically depend on having a very accurate system model, which is often not available in practice. While this challenge has been addressed in the literature using different learning approaches, most of these approaches do not provide safety guarantees in terms of stability of the learning-based control system. In this paper, we provide a novel, learning-based control approach based on Gaussian processes (GPs) that ensures both stability of the closed-loop system and high-accuracy tracking. We use GPs to approximate the error between the commanded acceleration and the actual acceleration of the system, and then use the predicted mean and variance of the GP to calculate an upper bound on the uncertainty of the linearized model. This uncertainty bound is then used in a robust, outer-loop controller to ensure stability of the overall system. Moreover, we show that the tracking error converges to a ball with a radius that can be made arbitrarily small. Furthermore, we verify the effectiveness of our approach via simulations on a 2 degree-offreedom (DOF) planar manipulator and experimentally on a 6 DOF industrial manipulator.

Towards Efficient Learning-Based Model Predictive Control via Feedback Linearization and Gaussian Process Regression

“…GPR provides a variance estimate, which can be used for uncertainty evaluation [2], [8], [10]. In [2], GPR is used with feedback linearization to augment a linear quadratic regulator.…”

Gaussian Processes Model-Based Control of Underactuated Balance Robots

“…The work in [26] proposes a GP-based inverse dynamics control law and the feedback gain is adapted to the variance of the predictive distribution, that is, using low gains if the learned model is precise and otherwise high gains. The work in [20], [26], [27] give theoretically guaranteed stability or safety regions of GPs-based inverse dynamics control. Besides GPs, polynomial kernal functions are also used to predict the inverse dynamics of robotic systems (e.g., [28]).…”

Parameterizing robust manipulator controllers under approximate inverse dynamics: A double‐Youla approach

“…The conservatism is determined by the accuracy of the model bounds and nominal outer-loop compensator gains. Helwa et al 58 consequently propose a learning-based adjustment of the uncertainty bounds in the Lyapunov-based robust design. Nonetheless, the robustification term is a switching signal of potentially high frequency, and the overall design is tailored towards tracking control; one could then also work with a robust-adaptive scheme.…”