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CBF-Based Motion Planning for Socially Responsible Robot Navigation Guaranteeing STL Specification

Andrea Ruo, Lorenzo Sabattini, Valeria Villani

TL;DR

This paper addresses the safety-critical navigation problem, in Socially Responsible Navigation (SRN) context, presenting a CBF -based STL motion planning methodology that enables task completion at any time within a specified time interval considering a dynamic system subject to velocity constraints.

Abstract

In the field of control engineering, the connection between Signal Temporal Logic (STL) and time-varying Control Barrier Functions (CBF) has attracted considerable attention. CBFs have demonstrated notable success in ensuring the safety of critical applications by imposing constraints on system states, while STL allows for precisely specifying spatio-temporal constraints on the behavior of robotic systems. Leveraging these methodologies, this paper addresses the safety-critical navigation problem, in Socially Responsible Navigation (SRN) context, presenting a CBF-based STL motion planning methodology. This methodology enables task completion at any time within a specified time interval considering a dynamic system subject to velocity constraints. The proposed approach involves real-time computation of a smooth CBF, with the computation of a dynamically adjusted parameter based on the available path space and the maximum allowable velocity. A simulation study is conducted to validate the methodology, ensuring safety in the presence of static and dynamic obstacles and demonstrating its compliance with spatio-temporal constraints under non-linear velocity constraints.

CBF-Based Motion Planning for Socially Responsible Robot Navigation Guaranteeing STL Specification

TL;DR

This paper addresses the safety-critical navigation problem, in Socially Responsible Navigation (SRN) context, presenting a CBF -based STL motion planning methodology that enables task completion at any time within a specified time interval considering a dynamic system subject to velocity constraints.

Abstract

In the field of control engineering, the connection between Signal Temporal Logic (STL) and time-varying Control Barrier Functions (CBF) has attracted considerable attention. CBFs have demonstrated notable success in ensuring the safety of critical applications by imposing constraints on system states, while STL allows for precisely specifying spatio-temporal constraints on the behavior of robotic systems. Leveraging these methodologies, this paper addresses the safety-critical navigation problem, in Socially Responsible Navigation (SRN) context, presenting a CBF-based STL motion planning methodology. This methodology enables task completion at any time within a specified time interval considering a dynamic system subject to velocity constraints. The proposed approach involves real-time computation of a smooth CBF, with the computation of a dynamically adjusted parameter based on the available path space and the maximum allowable velocity. A simulation study is conducted to validate the methodology, ensuring safety in the presence of static and dynamic obstacles and demonstrating its compliance with spatio-temporal constraints under non-linear velocity constraints.
Paper Structure (12 sections, 14 equations, 5 figures, 1 table)

This paper contains 12 sections, 14 equations, 5 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. PRELIMINARIES
  3. Signal Temporal Logic
  4. Control Barrier Functions encoding STL formulation
  5. PROBLEM STATEMENT
  6. PROPOSED APPROACH
  7. Online computation of smooth CBF-STL motion planning
  8. CBF-based STL motion planning methodology
  9. STEP 1
  10. STEP 2
  11. SIMULATION RESULTS
  12. CONCLUSION

Figures (5)

  • Figure 1: Example 1: The robot must reach the final state $\boldsymbol{x}_G$ within 10 seconds while being subject to two maximum velocity constraints defined by different colored areas along its path.
  • Figure 2: Example 2: The robot must reach the final state $\boldsymbol{x}_G$ within 10 seconds while being subject to two maximum velocity constraints defined by different colored areas along its path in the case of obstacle avoidance.
  • Figure 3: Robot trajectory in simulated environment.
  • Figure 4: Time evolution of real speed in reference to maximum speed.
  • Figure 5: The behavior of the control barrier function $\mathfrak{b}({\boldsymbol{x}},t)$ has a value always greater than zero, indicating the satisfaction of the STL formula $\phi$.