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Real-time Mixed-Integer Quadratic Programming for Driving Behavior-Inspired Speed Bump Optimal Trajectory Planning

Van Nam Dinh, Van Vy Phan, Thai Son Dang, Van Du Phan, The Anh Mai, Van Chuong Le, Sy Phuong Ho, Dinh Tu Duong, Hung Cuong Ta

TL;DR

The paper tackles autonomous-vehicle trajectory planning in urban settings by formulating a unified MIQP-MPC framework that explicitly handles speed-bump negotiation. It employs a discrete-time $3^{\text{rd}}$-order linear point-mass model with linearized nonholonomic constraints to maintain real-time tractability, and introduces binary indicators to mimic human driving around speed bumps within the optimization. A detailed MIQP objective combines speed regulation, comfort, and jerk minimization, while constraints enforce bump-specific behaviors and turning decisions, solved efficiently via Gurobi. Experimental results in simulated urban scenarios demonstrate smooth speed and steering profiles, with real-time solution times, underscoring the framework's potential for practical deployment in complex road environments.

Abstract

This paper proposes a novel methodology for trajectory planning in autonomous vehicles (AVs), addressing the complex challenge of negotiating speed bumps within a unified Mixed-Integer Quadratic Programming (MIQP) framework. By leveraging Model Predictive Control (MPC), we develop trajectories that optimize both the traversal of speed bumps and overall passenger comfort. A key contribution of this work is the formulation of speed bump handling constraints that closely emulate human driving behavior, seamlessly integrating these with broader road navigation requirements. Through extensive simulations in varied urban driving environments, we demonstrate the efficacy of our approach, highlighting its ability to ensure smooth speed transitions over speed bumps while maintaining computational efficiency suitable for real-time deployment. The method's capability to handle both static road features and dynamic constraints, alongside expert human driving, represents a significant step forward in trajectory planning for urban

Real-time Mixed-Integer Quadratic Programming for Driving Behavior-Inspired Speed Bump Optimal Trajectory Planning

TL;DR

The paper tackles autonomous-vehicle trajectory planning in urban settings by formulating a unified MIQP-MPC framework that explicitly handles speed-bump negotiation. It employs a discrete-time -order linear point-mass model with linearized nonholonomic constraints to maintain real-time tractability, and introduces binary indicators to mimic human driving around speed bumps within the optimization. A detailed MIQP objective combines speed regulation, comfort, and jerk minimization, while constraints enforce bump-specific behaviors and turning decisions, solved efficiently via Gurobi. Experimental results in simulated urban scenarios demonstrate smooth speed and steering profiles, with real-time solution times, underscoring the framework's potential for practical deployment in complex road environments.

Abstract

This paper proposes a novel methodology for trajectory planning in autonomous vehicles (AVs), addressing the complex challenge of negotiating speed bumps within a unified Mixed-Integer Quadratic Programming (MIQP) framework. By leveraging Model Predictive Control (MPC), we develop trajectories that optimize both the traversal of speed bumps and overall passenger comfort. A key contribution of this work is the formulation of speed bump handling constraints that closely emulate human driving behavior, seamlessly integrating these with broader road navigation requirements. Through extensive simulations in varied urban driving environments, we demonstrate the efficacy of our approach, highlighting its ability to ensure smooth speed transitions over speed bumps while maintaining computational efficiency suitable for real-time deployment. The method's capability to handle both static road features and dynamic constraints, alongside expert human driving, represents a significant step forward in trajectory planning for urban
Paper Structure (13 sections, 23 equations, 5 figures, 1 table, 1 algorithm)

This paper contains 13 sections, 23 equations, 5 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Methodology
  3. Vehicle Dynamics and Linearize Non-holonomic Constraints
  4. Vehicle Dynamics
  5. Linearize Non-honolomic Constraints
  6. MIQP Objective Function, Constraints, and Algorithm
  7. MIQP Objective Function
  8. Speed Bump Negotiation Mimicking Human Driving Behavior Constraints
  9. MIQP-MPC Algorithm
  10. Experimental Results
  11. Experimental Setup
  12. Results and Discussion
  13. Conclusion

Figures (5)

  • Figure 1: Motion planning control
  • Figure 2: The result with bumper width of 2m- no steering to reduce jerk
  • Figure 3: The result with human behavior steering
  • Figure 4: The result with bumper 2m, longer run to converge to reference speed
  • Figure 5: The result handling high-speed over bumper