RPCBF: Constructing Safety Filters Robust to Model Error and Disturbances via Policy Control Barrier Functions (2410.11157v2)

Abstract: Control Barrier Functions (CBFs) have proven to be an effective tool for performing safe control synthesis for nonlinear systems. However, guaranteeing safety in the presence of disturbances and input constraints for high relative degree systems is a difficult problem. In this work, we propose the Robust Policy CBF (RPCBF), a practical method of constructing CBF approximations that is easy to implement and robust to disturbances via the estimation of a value function. We demonstrate the effectiveness of our method in simulation on a variety of high relative degree input-constrained systems. Finally, we demonstrate the benefits of RPCBF in compensating for model errors on a hardware quadcopter platform by treating the model errors as disturbances. The project page can be found at https://oswinso.xyz/rpcbf.

• The paper introduces a Robust Policy Control Barrier Functions framework to construct safety filters that operate efficiently despite model errors and disturbances.
• It employs a finite horizon approximation method to enable real-time implementation in high relative degree systems under input constraints.
• Simulations and hardware experiments validate the approach by demonstrating reduced collision rates and enhanced safety in autonomous platforms.

An Analysis of RPCBF: Constructing Safety Filters Robust to Model Error and Disturbances

The paper "RPCBF: Constructing Safety Filters Robust to Model Error and Disturbances via Policy Control Barrier Functions" introduces a methodology to address safety in control systems where model inaccuracies and disturbances are prevalent. This paper leverages Control Barrier Functions (CBFs) and extends them through Robust Policy Control Barrier Functions (RPCBF) to manage high relative degree systems under input constraints effectively.

Overview and Problem Formulation

The fundamental challenge addressed in the paper is the construction of safety filters that ensure the system's state remains outside an unsafe set, especially when system models are imperfect. The authors propose the Robust Policy CBF (RPCBF) approach to approximate CBFs using a robust policy value function, enabling real-time application. The method is designed to provide a more reliable safety guarantee by considering worst-case disturbances within a finite time horizon, a significant advancement over conventional CBFs that assume more accurate model fidelity.

Methodological Contributions

1. Robust Policy CBF (RPCBF) Development: The paper introduces an RPCBF framework, designed to accommodate disturbances and input constraints by using finite horizon policy rollouts. This is a key development, as it doesn't rely on extensive domain-specific knowledge but rather extrapolates robustness from policy value evaluations.
2. Finite Horizon Approximation: The authors present a novel approximation strategy where the infinite-horizon policy value function is reduced to a finite one, allowing for practical real-time safety filter implementations.
3. Applications and Simulations: The methodology is validated through simulations on systems with high relative degrees and is further demonstrated on a hardware quadcopter platform, treating model errors as disturbances.

Numerical Results and Implications

The paper reports on simulation outcomes where RPCBF-based safety filters show superior performance in maintaining safety compared to traditional methods like HOCBF and MPC-based filters. Notable results include a marked reduction in collision rates in autonomous vehicle simulations and successful avoidance of unsafe regions in dynamic systems like quadcopters. These results underline the practical applicability of RPCBF in systems where model inaccuracies are non-negligible.

Theoretical and Practical Implications

Theoretically, this work advances the understanding of control barrier functions by integrating robustness to disturbances, thus broadening the scope of systems to which these techniques can be applied. Practically, the proposed framework opens new paths for autonomous systems in unpredictable environments, offering a safety layer that inherently accounts for uncertainties within model dynamics.

Future Directions

The paper points to several avenues for future exploration. These include refining safety guarantees under discretization in time and expanding the method's applicability to a wider range of dynamical systems. Additionally, enhancing disturbance sampling strategies could further improve robustness to unforeseen external factors.

Conclusion

This paper presents significant methodological advancements in utilizing Control Barrier Functions through RPCBFs for robust safety filter construction. Through a thorough integration of disturbances and input constraints into the CBF framework, this research provides a comprehensive approach to enhancing safety in autonomous systems with imperfect models. The work sets a strong foundation for further research in robust control methodologies applicable in real-world scenarios involving uncertain, dynamic environments.