Non-Smooth Control Barrier Navigation Functions for STL Motion Planning

Area of Science:

• Robotics and Control Systems
• Formal Methods in AI
• Artificial Intelligence

Background:

• Existing Signal Temporal Logic (STL) control synthesis methods face limitations in the fragment of STL they can cover and computational efficiency.
• Control Barrier Functions (CBFs) are widely used for safety-critical control, but their composition for complex specifications can be conservative and computationally intensive.

Purpose of the Study:

• To develop a new approach for STL control synthesis that overcomes limitations of existing methods.
• To enable the synthesis of controllers for a larger fragment of STL specifications.
• To reduce the computational cost and conservativeness associated with STL control synthesis.

Main Methods:

• Utilizes a navigation function to construct a Control Barrier Function (CBF).
• Composes navigation function-based barrier functions using nonsmooth mappings to encode Boolean operations.
• Applies the developed methodology to three simulation case studies, including complex motion planning and human-robot interaction.

Main Results:

• The proposed approach covers a larger fragment of STL compared to existing methods.
• It alleviates the computational cost of evaluating the control law.
• It relaxes the conservativeness often associated with smooth combinations of barrier functions for Boolean operations.

Conclusions:

• The novel approach offers a more effective and efficient method for STL control synthesis.
• Demonstrated efficacy in complex scenarios, including advanced motion planning and human-robot social interaction.
• Provides a less conservative alternative to existing barrier function composition techniques.