[Paper Review] Guaranteeing Consistency in a Motion Planning and Control Architecture Using a Kinematic Bicycle Model

Philip Polack, Florent Altché+2 more|arXiv (Cornell University)|Apr 23, 2018

Vehicle Dynamics and Control SystemsEngineering22 references20 citations

TL;DR

This paper proposes a 10Hz kinematic bicycle Model Predictive Control (MPC) motion planner combined with a 100Hz closed-loop PID controller to ensure dynamic feasibility and consistency in autonomous vehicle planning and control. By constraining the steering angle based on speed and lateral acceleration limits (≤0.5μg), the method guarantees that all planned trajectories remain valid under the kinematic model, ensuring safe and feasible tracking even in high-curvature scenarios with and without obstacles, validated in high-fidelity simulation.

ABSTRACT

This paper proposes to combine a 10Hz motion planner based on a kinematic bicycle Model Predictive Control (MPC) and a 100Hz closed-loop Proportional-Integral-Derivative (PID) controller to cope with normal driving situations. Its novelty consists in ensuring the feasibility of the computed trajectory by the motion planner through a limitation of the steering angle depending on the speed. This ensures the validity of the kinematic bicycle model at any time. The architecture is tested on a high-fidelity simulation model on a challenging track with small curve radius, with and without surrounding obstacles.

Motivation & Objective

• To address the critical safety issue of inconsistency between motion planning and control layers in autonomous vehicles.
• To ensure that trajectories planned using a kinematic bicycle model remain dynamically feasible under real vehicle dynamics.
• To maintain robustness to disturbances and modeling errors through high-frequency closed-loop control.
• To enable safe, non-conservative speed adaptation based on road geometry and friction limits without sacrificing model validity.
• To validate the architecture in high-fidelity simulation under challenging conditions, including small-radius curves and static obstacles.

Proposed method

• The motion planner uses a 10Hz kinematic bicycle MPC with a prediction horizon dependent on maximum speed and road curvature.
• A dynamic constraint limits lateral acceleration to ≤0.5μg (where μ is road friction coefficient), ensuring the kinematic model remains valid.
• The steering angle is dynamically bounded based on speed and curvature to enforce this lateral acceleration limit.
• A 100Hz closed-loop PID controller tracks the reference trajectory, improving robustness to disturbances and modeling errors.
• The system uses a heuristic local velocity planner to compute safe speeds based on curvature and friction, guiding the MPC.
• High-fidelity 9 DoF vehicle dynamics and tire friction circle models are used in PreScan simulations to validate feasibility and tracking performance.

Experimental results

Research questions

• RQ1 How can consistency between motion planning and control be guaranteed when using a simplified kinematic model?
• RQ2 What steering angle constraint ensures the kinematic bicycle model remains valid under real vehicle dynamics?
• RQ3 How does the architecture perform in high-curvature scenarios with and without obstacles?
• RQ4 To what extent does the 100Hz PID controller improve tracking robustness compared to open-loop control?
• RQ5 Can the system safely adapt speed based on road geometry without violating dynamic feasibility?

Key findings

• The motion planner consistently generated feasible trajectories by enforcing lateral acceleration ≤0.5μg, ensuring model validity at all times.
• The vehicle maintained lateral path error below 0.4 m across all test scenarios, demonstrating accurate tracking.
• The MPC computation time remained below 100 ms in all simulations, meeting real-time requirements.
• The low-level PID controller successfully prevented skidding and slipping, even in tight curves with high lateral forces.
• The system adapted speed dynamically based on curvature and friction, avoiding overly conservative behavior.
• The architecture remained robust in both obstacle-free and obstacle-encountering scenarios, with no trajectory tracking failures.