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

Core Concepts
Developing a robust rollover prevention method using control barrier functions and differentiators for mobile robots.
This paper focuses on developing a rollover prevention method for mobile robots using control barrier functions (CBF) theory. It addresses the importance of safety in diverse environments where mobile robots operate, emphasizing the prevention of rollovers as a critical aspect. The study introduces safety measures based on the zero moment point to provide conditions on control inputs through CBFs. By incorporating differentiator-based safety-critical controllers, the paper aims to estimate time-varying and noisy parameters to achieve rigorous safety guarantees. Additionally, it explores the use of Projection-to-State Safety (PSSf) to ensure safety in the presence of disturbances. The effectiveness of the proposed method is demonstrated through experiments on a tracked robot facing rollover potential on steep slopes. Several methods have been developed to measure the risk of rollover in mobile robots, including stability measures like force-angle stability, moment-height stability, and zero moment point (ZMP). Leveraging these characterizations, various control techniques have been devised to prevent rollovers such as nonlinear programming, chance-constrained optimal control, and invariance control. However, these methods often rely on high-fidelity models or require numerous sensors, limiting their practical applicability in real-world scenarios. The paper introduces a theoretic framework for synthesizing safety filters that are robust to time-varying parameters and applies this experimentally to achieve rollover prevention on a mobile robot. By integrating ISS differentiator dynamics with CBFs, the study aims to provide robust safety guarantees against disturbances while preventing rollovers effectively.
DARPA supported under LINC program. Tracked robot used for experiments. Inclined surface at approximately 27 degrees tested for tipover. Controller gains Kv and Kω utilized in experimental validation.
"The proposed DA-CBF-QP-based safety filter maintains safety." "Control barrier functions have emerged as a tool for synthesizing controllers guaranteeing forward invariant safe sets." "Time-varying Projection-to-State Safety considers model uncertainty in time-varying CBFs."

Deeper Inquiries

How can differentiator-based adaptive CBFs be applied to other robotic systems beyond mobile robots

Differentiator-based adaptive Control Barrier Functions (CBFs) can be applied to various robotic systems beyond mobile robots by incorporating them into the control design of different types of robots. For instance, in industrial robotic arms, differentiators can be used to estimate parameters like joint velocities or external forces acting on the end-effector. By integrating these estimations with CBFs, safety-critical controllers can be developed to prevent collisions or ensure safe operation in dynamic environments. Additionally, in aerial drones, differentiators can help estimate wind disturbances or variations in altitude, allowing for the synthesis of robust controllers using CBFs to maintain stability and avoid crashes.

What are potential limitations or drawbacks of relying heavily on control barrier functions for ensuring safety

While Control Barrier Functions (CBFs) are powerful tools for synthesizing safety-critical controllers and ensuring forward invariance of predefined safe sets, there are potential limitations and drawbacks associated with relying heavily on them for safety assurance: Model Uncertainty: CBFs rely on accurate system models to define safe sets and constraints. In real-world applications where models may not capture all dynamics accurately, uncertainties could lead to conservative control actions. Complexity: Designing CBF-based controllers often requires a deep understanding of system dynamics and complex mathematical formulations. Implementing these controllers on hardware platforms might introduce challenges related to computational resources and real-time performance. Sensor Requirements: Effective implementation of CBFs may necessitate precise sensor measurements for state estimation and disturbance detection. This reliance on sensors introduces vulnerabilities related to sensor noise or failures that could impact controller performance.

How can the concept of Projection-to-State Safety be extended to address uncertainties beyond disturbances in dynamic environments

The concept of Projection-to-State Safety (PSSf) can be extended beyond addressing uncertainties due to disturbances in dynamic environments by considering additional sources of uncertainty such as modeling errors or sensor inaccuracies: Model Uncertainty Extension: Instead of focusing solely on disturbances affecting system dynamics, an extension of PSSf could incorporate methods for quantifying model uncertainty directly into the safety guarantees provided by the controller. Sensor Noise Mitigation: Addressing uncertainties arising from noisy sensor measurements is crucial for robust control design. Extending PSSf frameworks to include mechanisms that account for sensor noise effects would enhance the overall reliability of safety-critical systems operating under uncertain conditions. Adaptive Safety Strategies: Introducing adaptive elements into PSSf approaches could enable systems to dynamically adjust their safety margins based on varying levels of uncertainty encountered during operation. By broadening the scope of Projection-to-State Safety beyond disturbances alone, it becomes a more comprehensive framework capable of handling a wider range of uncertainties inherent in practical robotic applications while maintaining rigorous safety guarantees throughout operation.