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Rollover Prevention for Mobile Robots with Control Barrier Functions: Differentiator-Based Adaptation and Projection-to-State Safety

Ersin Das, Aaron D. Ames, Joel W. Burdick

TL;DR

This work tackles rollover prevention in mobile robots under time-varying and noisy conditions by casting rollover safety as a control barrier function (CBF) problem based on a zero moment point (ZMP) constraint. It introduces a time-varying projection-to-state safety ($tPSSf$) framework to account for disturbances in CBF derivatives and couples it with differentiator-adaptive CBFs (DA-CBFs) that embed an ISS differentiator for time-varying parameters into the safety constraint, yielding a robust CBF-QP safety filter. The key contributions are the formal development of $tPSSf$, the DA-CBF construction that tolerates differentiation errors, and the experimental validation on a tracked robot showing safer rollover performance with reduced conservatism compared to time-invariant bounds. The approach enables reliable rollover prevention in real-world terrains with disturbances and noisy measurements, providing a practical safety mechanism for autonomous mobile robots.

Abstract

This paper develops rollover prevention guarantees for mobile robots using control barrier function (CBF) theory, and demonstrates the method experimentally. We consider a safety measure based on a zero moment point condition through the lens of CBFs. However, these conditions depend on time-varying and noisy parameters. To address this issue, we present a differentiator-based safety-critical controller that estimates these parameters and pairs Input-to-State Stable (ISS) differentiator dynamics with CBFs to achieve rigorous safety guarantees. Additionally, to ensure safety in the presence of disturbances, we utilize a time-varying extension of Projection-to-State Safety (PSSf). The effectiveness of the proposed method is demonstrated via experiments on a tracked robot with a rollover potential on steep slopes.

Rollover Prevention for Mobile Robots with Control Barrier Functions: Differentiator-Based Adaptation and Projection-to-State Safety

TL;DR

This work tackles rollover prevention in mobile robots under time-varying and noisy conditions by casting rollover safety as a control barrier function (CBF) problem based on a zero moment point (ZMP) constraint. It introduces a time-varying projection-to-state safety () framework to account for disturbances in CBF derivatives and couples it with differentiator-adaptive CBFs (DA-CBFs) that embed an ISS differentiator for time-varying parameters into the safety constraint, yielding a robust CBF-QP safety filter. The key contributions are the formal development of , the DA-CBF construction that tolerates differentiation errors, and the experimental validation on a tracked robot showing safer rollover performance with reduced conservatism compared to time-invariant bounds. The approach enables reliable rollover prevention in real-world terrains with disturbances and noisy measurements, providing a practical safety mechanism for autonomous mobile robots.

Abstract

This paper develops rollover prevention guarantees for mobile robots using control barrier function (CBF) theory, and demonstrates the method experimentally. We consider a safety measure based on a zero moment point condition through the lens of CBFs. However, these conditions depend on time-varying and noisy parameters. To address this issue, we present a differentiator-based safety-critical controller that estimates these parameters and pairs Input-to-State Stable (ISS) differentiator dynamics with CBFs to achieve rigorous safety guarantees. Additionally, to ensure safety in the presence of disturbances, we utilize a time-varying extension of Projection-to-State Safety (PSSf). The effectiveness of the proposed method is demonstrated via experiments on a tracked robot with a rollover potential on steep slopes.
Paper Structure (9 sections, 4 theorems, 45 equations, 2 figures)

This paper contains 9 sections, 4 theorems, 45 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Main Result
  4. Time-Varying Projection-to-State Safety
  5. Safety with Differentiator-based CBFs
  6. Rollover Prevention: Theory and Application
  7. Rollover CBF Synthesis
  8. Experimental Validation
  9. Conclusion

Key Result

Theorem 1

If $h$ is a CBF for system on $\mathcal{C}$ with an ${\alpha \!\in\! \mathcal{K}_{\infty, e}}$, then any Lipschitz continuous controller ${\mathbf{k}\!:\! X \!\to\! U}$ satisfying renders eq:clsystem1 safe with respect to $\mathcal{C}$.

Figures (2)

  • Figure 1: Experimental results for robot rollover prevention. The proposed DA-CBF-QP safety filter maintains safety (Left, video montage of robot motion). However, under the nominal controller, the robot leaves the safe set (Right). The value of CBF $h$ vs. time (Bottom).
  • Figure 2: Zero moment point illustration for a mobile robot (Left). The simple backward differentiator (BD) results in noisy values that cause safety violations. The system leaves the safe set for a small and time-invariant projected disturbance bound, ${\Bar{\delta} \!=\! \Bar{\delta}_1}$. Choosing ${\Bar{\delta} \!=\! \Bar{\delta}_2 }$ or ${\Bar{\delta} \!=\! \Bar{\delta}_3 }$, where ${\Bar{\delta}_1 \!<\! \Bar{\delta}_2 \!<\! \Bar{\delta}_3 }$, ensures that ${h_2(t) \geq 0}$, but at the cost of decreased performance due to added conservatives (Right).

Theorems & Definitions (14)

  • Definition 1: Control Barrier Function, ames2017control
  • Theorem 1
  • Definition 2: Time-Varying Projection-to-State Safety
  • Remark 1
  • Theorem 2
  • proof
  • Definition 3: Input-to-state Stable Differentiator
  • Remark 2
  • Definition 4: Differentiator-Adaptive CBFs
  • Theorem 3
  • ...and 4 more