Talk@Princeton - Ensuring Robot Safety Through Safety Index Synthesis

Changliu gave a talk at Princeton Robotics Seminar, titled Ensuring Robot Safety Through Safety Index Synthesis.

Safety Index is a special class of high order control barrier functions. Its purpose is to ensure forward invariance within a user-specified safe set and achieve finite time convergence to that set. Synthesizing a valid safety index poses significant challenges, particularly when dealing with control limits, uncertainties, and time-varying dynamics. In this talk, I will introduce a variety of approaches that can be used for safety index synthesis, including a rule-based method, an evolutionary optimization-based approach, a constrained reinforcement learning-based approach, an adversarial optimization-based approach, as well as sum of square programming. The parameterization of the safety index can either take an analytical form or be a neural network. I will conclude the talk by highlighting the limitations of existing work and discuss potential future directions, including integrating formal verification into neural safety index synthesis.

This talk highlights the following work from ICL:

[C38] Model-free Safe Control for Zero-Violation Reinforcement Learning
Weiye Zhao, Tairan He and Changliu Liu
Conference on Robot Learning, 2021
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Abstract:

Maintaining safety under adaptation has long been considered to be an important capability for autonomous systems. As these systems estimate and change the ego-model of the system dynamics, questions regarding how to develop safety guarantees for such systems continue to be of interest. We propose a novel robust safe control methodology that uses set-based safety constraints to make a robotic system with dynamical uncertainties safely adapt and operate in its environment. The method consists of designing a scalar energy function (safety index) for an adaptive system with parametric uncertainty and an optimization-based approach for control synthesis. Simulation studies on a two-link manipulator are conducted and the results demonstrate the effectiveness of our proposed method in terms of generating provably safe control for adaptive systems with parametric uncertainty.

[C40] Safe Control with Neural Network Dynamic Models
Tianhao Wei and Changliu Liu
Learning for Dynamics and Control Conference, 2022
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Safety is critical in autonomous robotic systems. A safe control law should ensure forward invariance of a safe set (a subset in the state space). It has been extensively studied regarding how to derive a safe control law with a control-affine analytical dynamic model. However, how to formally derive a safe control law with Neural Network Dynamic Models (NNDM) remains unclear due to the lack of computationally tractable methods to deal with these black-box functions. In fact, even finding the control that minimizes an objective for NNDM without any safety constraint is still challenging. In this work, we propose MIND-SIS (Mixed Integer for Neural network Dynamic model with Safety Index Synthesis), the first method to synthesize safe control for NNDM. The method includes two parts: 1) SIS: an algorithm for the offline synthesis of the safety index (also called as a barrier function), which uses evolutionary methods and 2) MIND: an algorithm for online computation of the optimal and safe control signal, which solves a constrained optimization using a computationally efficient encoding of neural networks. It has been theoretically proved that MIND-SIS guarantees forward invariance and finite convergence to a subset of the user-defined safe set. And it has been numerically validated that MIND-SIS achieves safe and optimal control of NNDM. The optimality gap is less than 10−8, and the safety constraint violation is 0.

[C41] Joint Synthesis of Safety Certificate and Safe Control Policy Using Constrained Reinforcement Learning
Haitong Ma, Changliu Liu, Shengbo Eben Li, Sifa Zheng and Jianyu Chen
Learning for Dynamics and Control Conference, 2022
Best Paper Finalist
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Abstract:

Safety is the major consideration in controlling complex dynamical systems using reinforcement learning (RL), where the safety certificates can provide provable safety guarantees. A valid safety certificate is an energy function indicating that safe states are with low energy, and there exists a corresponding safe control policy that allows the energy function to always dissipate. The safety certificates and the safe control policies are closely related to each other and both challenging to synthesize. Therefore, existing learning-based studies treat either of them as prior knowledge to learn the other, limiting their applicability to general systems with unknown dynamics. This paper proposes a novel approach that simultaneously synthesizes the energy-function-based safety certificates and learns the safe control policies with constrained reinforcement learning (CRL). We do not rely on prior knowledge about either a prior control law or a perfect safety certificate. In particular, we formulate a loss function to optimize the safety certificate parameters by minimizing the occurrence of energy increases. By adding this optimization procedure as an outer loop to the Lagrangian-based CRL, we jointly update the policy and safety certificate parameters, and prove that they will converge to their respective local optima, the optimal safe policies and valid safety certificates. Finally, we evaluate our algorithms on multiple safety-critical benchmark environments. The results show that the proposed algorithm learns solidly safe policies with no constraint violation. The validity, or feasibility of synthesized safety certificates is also verified numerically.

Video:

[C53] Safe Control Under Input Limits with Neural Control Barrier Functions
Simin Liu, Changliu Liu and John Dolan
Conference on Robot Learning, 2022
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[C56] Safety index synthesis via sum-of-squares programming
Weiye Zhao, Tairan He, Tianhao Wei, Simin Liu and Changliu Liu
American Control Conference, 2023
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The work is supported by National Science Foundation. Read more about the work at this research page.