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Fault Tolerant Neural Control Barrier Functions for Robotic Systems under Sensor Faults and Attacks

Hongchao Zhang, Luyao Niu, Andrew Clark, Radha Poovendran

TL;DR

Fault-tolerant neural control barrier functions (FT-NCBFs) address safety guarantees for stochastic robotic systems under sensor faults and attacks by learning a neural barrier function that enforces a safe invariant set. The method derives necessary and sufficient conditions for FT-NCBFs, trains a neural representation via a loss that encodes feasibility and correctness, and uses a bank of extended Kalman filters to handle unknown attack patterns and resolve conflicting estimates. Safety guarantees are established: if training losses converge to zero and the derived conditions hold, a control input exists to keep the system in the safe set with probability at least $1-\epsilon$ for all attack patterns. The approach is demonstrated on obstacle avoidance and spacecraft rendezvous, showing safe performance where baseline NCBFs fail, with code publicly available.

Abstract

Safety is a fundamental requirement of many robotic systems. Control barrier function (CBF)-based approaches have been proposed to guarantee the safety of robotic systems. However, the effectiveness of these approaches highly relies on the choice of CBFs. Inspired by the universal approximation power of neural networks, there is a growing trend toward representing CBFs using neural networks, leading to the notion of neural CBFs (NCBFs). Current NCBFs, however, are trained and deployed in benign environments, making them ineffective for scenarios where robotic systems experience sensor faults and attacks. In this paper, we study safety-critical control synthesis for robotic systems under sensor faults and attacks. Our main contribution is the development and synthesis of a new class of CBFs that we term fault tolerant neural control barrier function (FT-NCBF). We derive the necessary and sufficient conditions for FT-NCBFs to guarantee safety, and develop a data-driven method to learn FT-NCBFs by minimizing a loss function constructed using the derived conditions. Using the learned FT-NCBF, we synthesize a control input and formally prove the safety guarantee provided by our approach. We demonstrate our proposed approach using two case studies: obstacle avoidance problem for an autonomous mobile robot and spacecraft rendezvous problem, with code available via https://github.com/HongchaoZhang-HZ/FTNCBF.

Fault Tolerant Neural Control Barrier Functions for Robotic Systems under Sensor Faults and Attacks

TL;DR

Fault-tolerant neural control barrier functions (FT-NCBFs) address safety guarantees for stochastic robotic systems under sensor faults and attacks by learning a neural barrier function that enforces a safe invariant set. The method derives necessary and sufficient conditions for FT-NCBFs, trains a neural representation via a loss that encodes feasibility and correctness, and uses a bank of extended Kalman filters to handle unknown attack patterns and resolve conflicting estimates. Safety guarantees are established: if training losses converge to zero and the derived conditions hold, a control input exists to keep the system in the safe set with probability at least for all attack patterns. The approach is demonstrated on obstacle avoidance and spacecraft rendezvous, showing safe performance where baseline NCBFs fail, with code publicly available.

Abstract

Safety is a fundamental requirement of many robotic systems. Control barrier function (CBF)-based approaches have been proposed to guarantee the safety of robotic systems. However, the effectiveness of these approaches highly relies on the choice of CBFs. Inspired by the universal approximation power of neural networks, there is a growing trend toward representing CBFs using neural networks, leading to the notion of neural CBFs (NCBFs). Current NCBFs, however, are trained and deployed in benign environments, making them ineffective for scenarios where robotic systems experience sensor faults and attacks. In this paper, we study safety-critical control synthesis for robotic systems under sensor faults and attacks. Our main contribution is the development and synthesis of a new class of CBFs that we term fault tolerant neural control barrier function (FT-NCBF). We derive the necessary and sufficient conditions for FT-NCBFs to guarantee safety, and develop a data-driven method to learn FT-NCBFs by minimizing a loss function constructed using the derived conditions. Using the learned FT-NCBF, we synthesize a control input and formally prove the safety guarantee provided by our approach. We demonstrate our proposed approach using two case studies: obstacle avoidance problem for an autonomous mobile robot and spacecraft rendezvous problem, with code available via https://github.com/HongchaoZhang-HZ/FTNCBF.
Paper Structure (12 sections, 7 theorems, 25 equations, 2 figures)

This paper contains 12 sections, 7 theorems, 25 equations, 2 figures.

Table of Contents

  1. Preliminaries and Problem Formulation
  2. System and Adversary Model
  3. Preliminaries
  4. Solution Approach to Safety-Critical Control and Synthesis of Fault Tolerant NCBF
  5. Overview of Proposed Solution
  6. Synthesis of NCBF
  7. Synthesis of FT-NCBF
  8. Safety Guarantee of Proposed Approach
  9. Experiments
  10. Obstacle Avoidance Problem of Mobile Robot
  11. Spacecraft Rendezvous Problem
  12. Conclusion

Key Result

Theorem 1

Suppose that Assumption assumption:ekf holds. Then there exists $\delta > 0$ such that $\sigma_{t}\sigma_{t}^{T} \leq \delta I$ and $\nu_{t}\nu_{t}^{T} \leq \delta I$. For any $0<\epsilon <1$, there exists $\gamma > 0$ such that

Figures (2)

  • Figure 1: This figure presents the experimental results on obstacle avoidance of an autonomous mobile robot. Fig. \ref{['fig:training_curve']} presents the values of loss function, $\mathcal{L}_f(\mathcal{T})$, and $\mathcal{L}_c(\mathcal{T})$. The loss function decreases towards zero during the training process. Fig. \ref{['fig:obs0level']} shows the zero-level set of $\mathcal{D}_\theta$ corresponding to the FT-NCBF $b_\theta$. The set $\mathcal{D}_\theta$ does not overlap with the unsafe region in red color. Fig. \ref{['fig:carla_traj']} presents the trajectory of the mobile robot when using control policies obtained by our approach and the baseline approach. We observe that our approach guarantees safety whereas the baseline crashes with the pedestrian.
  • Figure 2: This figure presents the experimental results on spacecraft rendezvous problem. In Fig. \ref{['fig:lstraining_curve']}, we demonstrate that the value of loss function in Eq. \ref{['eq:uncons_opt']} quickly converges to zero during training. Fig. \ref{['fig:ls0level']} presents the zero-level set of $\mathcal{D}_\theta$, which never overlaps with the unsafe region in red color. Fig. \ref{['fig:dis_traj']} simulates the trajectories of the chaser satellite using our approach and the baseline. We observe that our approach allows the chaser satellite to maintain a proper distance to the target satellite (green curve), whereas the baseline fails (red curve).

Theorems & Definitions (13)

  • Definition 1: Safety
  • Theorem 1: reif2000stochastic
  • Theorem 2: clark2020control
  • Theorem 3: clark2020control
  • Definition 2
  • Proposition 1
  • Definition 3: Correct NCBFs
  • Definition 4: Feasible NCBF
  • Proposition 2
  • Proposition 3
  • ...and 3 more