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Real-time MPC with Control Barrier Functions for Autonomous Driving using Safety Enhanced Collocation

Jean Pierre Allamaa, Panagiotis Patrinos, Toshiyuki Ohtsuka, Tong Duy Son

TL;DR

This work tackles safety-critical autonomous driving by integrating Control Barrier Functions (CBFs) into a real-time nonlinear model predictive control (NMPC) framework. It introduces RESAFE/COL, a collocation-based transcription that uses regional convex hull approximations to enforce nonlinear constraints over the full horizon more efficiently than traditional multiple shooting. The approach improves crash avoidance and computational tractability, achieving up to 5× speedups over direct methods and enabling real-time operation at 50 ms sampling; with CBFs, it enables smoother, forward-looking avoidance maneuvers and robust performance in safety-critical scenarios, validated on digital twins of vehicle and urban environments. The results demonstrate substantial safety gains (e.g., 91% improvement in crash avoidance versus baselines) and practical viability for urban autonomous driving, offering a scalable path toward real-time NMPC deployment in industry.

Abstract

The autonomous driving industry is continuously dealing with safety-critical scenarios, and nonlinear model predictive control (NMPC) is a powerful control strategy for handling such situations. However, standard safety constraints are not scalable and require a long NMPC horizon. Moreover, the adoption of NMPC in the automotive industry is limited by the heavy computation of numerical optimization routines. To address those issues, this paper presents a real-time capable NMPC for automated driving in urban environments, using control barrier functions (CBFs). Furthermore, the designed NMPC is based on a novel collocation transcription approach, named RESAFE/COL, that allows to reduce the number of optimization variables while still guaranteeing the continuous time (nonlinear) inequality constraints satisfaction, through regional convex hull approximation. RESAFE/COL is proven to be 5 times faster than multiple shooting and more tractable for embedded hardware without a decrease in the performance, nor accuracy and safety of the numerical solution. We validate our NMPC-CBF with RESAFE/COL on digital twins of the vehicle and the urban environment and show the safe controller's ability to improve crash avoidance by 91\%. Supplementary visual material can be found at https://youtu.be/_EnbfYwljp4.

Real-time MPC with Control Barrier Functions for Autonomous Driving using Safety Enhanced Collocation

TL;DR

This work tackles safety-critical autonomous driving by integrating Control Barrier Functions (CBFs) into a real-time nonlinear model predictive control (NMPC) framework. It introduces RESAFE/COL, a collocation-based transcription that uses regional convex hull approximations to enforce nonlinear constraints over the full horizon more efficiently than traditional multiple shooting. The approach improves crash avoidance and computational tractability, achieving up to 5× speedups over direct methods and enabling real-time operation at 50 ms sampling; with CBFs, it enables smoother, forward-looking avoidance maneuvers and robust performance in safety-critical scenarios, validated on digital twins of vehicle and urban environments. The results demonstrate substantial safety gains (e.g., 91% improvement in crash avoidance versus baselines) and practical viability for urban autonomous driving, offering a scalable path toward real-time NMPC deployment in industry.

Abstract

The autonomous driving industry is continuously dealing with safety-critical scenarios, and nonlinear model predictive control (NMPC) is a powerful control strategy for handling such situations. However, standard safety constraints are not scalable and require a long NMPC horizon. Moreover, the adoption of NMPC in the automotive industry is limited by the heavy computation of numerical optimization routines. To address those issues, this paper presents a real-time capable NMPC for automated driving in urban environments, using control barrier functions (CBFs). Furthermore, the designed NMPC is based on a novel collocation transcription approach, named RESAFE/COL, that allows to reduce the number of optimization variables while still guaranteeing the continuous time (nonlinear) inequality constraints satisfaction, through regional convex hull approximation. RESAFE/COL is proven to be 5 times faster than multiple shooting and more tractable for embedded hardware without a decrease in the performance, nor accuracy and safety of the numerical solution. We validate our NMPC-CBF with RESAFE/COL on digital twins of the vehicle and the urban environment and show the safe controller's ability to improve crash avoidance by 91\%. Supplementary visual material can be found at https://youtu.be/_EnbfYwljp4.
Paper Structure (2 sections, 4 figures, 1 table)

This paper contains 2 sections, 4 figures, 1 table.

Table of Contents

  1. Comparison between position and CBF constraints
  2. Conclusion

Figures (4)

  • Figure 4: Comparison of the different numerical methods and collision avoidance approaches with a long horizon length, over all instances of the closed-loop scenarios
  • Figure 5: Sensitivity of computation time and closed-loop performance in terms of collision avoidance to the number of regions in RESAFE/COL, with a large horizon length: RESAFE/COL with CBF (black); RESAFE/COL with position constraint only (red), PSC order 5 (blue) and DMS with 60 nodes (green)
  • Figure 6: Open-loop trajectory during collision avoidance using forward invariant CBF with RESAFE/COL (black) in comparison with position constraint with RESAE/COL (red), PSC(blue) and DMS (green)
  • Figure 7: Collision avoidance at an intersection with and without CBF. The CBF formulation embeds both motion planning and control as it performs a stop-and-go