Provably Robust Learning-Based Approach for High-Accuracy Tracking Control of Lagrangian Systems (1804.01031v2)

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-of-freedom (DOF) planar manipulator and experimentally on a 6 DOF industrial manipulator.

• The paper proposes an innovative control framework that blends inverse dynamics with GP-based learning to mitigate model uncertainties.
• It leverages a robust outer-loop controller to ensure system stability by achieving uniformly bounded tracking errors through adjustable design parameters.
• Experimental validations on planar and industrial manipulators demonstrate substantial tracking error reductions compared to conventional control methods.

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

This paper introduces a novel learning-based control strategy to address the inherent challenges in high-accuracy tracking control of Lagrangian systems, particularly in robotic applications such as manipulators, legged robots, and quadrotors. Conventional approaches like inverse dynamics control are contingent upon highly accurate system models to decouple complex nonlinear dynamics into linear responses. However, system inaccuracies often lead to inadequate control performance and stability issues. The proposed methodology leverages Gaussian processes (GPs) for approximating model uncertainties and incorporates them into a robust control framework to ensure both stability and precise trajectory tracking.

Main Contributions

The authors propose a three-part strategy combining inverse dynamics control with learning and robust control techniques:

• Inverse Dynamics Control: This serves as the inner-loop mechanism to convert the nonlinear dynamics into linearizable forms using estimated system parameters.
• Gaussian Process-Based Learning: A set of GPs is employed to learn the discrepancy between commanded and actual accelerations, thereby estimating the uncertainty bounds of the model. These GPs provide not only mean estimates but also predictive variance, used in calculating confidence intervals that are crucial for ensuring robust control design.
• Robust Outer-Loop Controller: The calculated uncertainty bounds guide the design of an outer-loop controller, ensuring the stability of the closed-loop system while minimizing tracking errors.

Theoretical Results

The paper provides rigorous theoretical guarantees underpinning the proposed method. Under the assumption of bounded regression errors and sufficiently fast sampling rates, the method achieves uniform ultimate boundedness of the tracking error. Critically, the radius of the convergence ball for the tracking error can be adjusted via design parameters, allowing for high-accuracy tracking that can be tailored to system capabilities.

Empirical Validation

The effectiveness of the proposed method is verified through simulation on a 2 DOF planar manipulator and experiments on a UR10 6 DOF industrial manipulator. Results indicate substantial improvements in tracking error reduction—on average, a 95.8% reduction compared to the nominal controller in simulation settings, and a 41.5% improvement for various uncertainty scenarios in experimental settings. The robust learning controller consistently outperformed fixed robust controllers and non-robust learning alternatives by effectively adapting to parameter variations and achieving less conservative control strategies.

Implications and Future Work

The integration of GPs into control systems as proposed establishes a significant advancement in accommodating system model inaccuracies while ensuring stability. Practically, this makes the approach suitable for systems lacking direct torque control interfaces, such as certain industrial robots that necessitate velocity-controlled implementations. Theoretically, the method facilitates a balance between learning exploration and safety assurances, a crucial aspect for real-world deployments, especially in safety-critical applications like medical robotics.

Looking forward, extensions of this work could encompass incorporating actuator limits in the stability analysis and generalizing the framework to other classes of nonlinear systems beyond those addressed here. Furthermore, the scalability of the approach to complex, high-dimensional systems remains an inviting avenue for exploration. By continuing to bridge machine learning with control theory in this manner, further prospects in autonomous precision and adaptability for dynamic systems are anticipated.