[Paper Review] Local NMPC on Global Optimised Path for Autonomous Racing

Dvij Kalaria, Parv Maheshwari+5 more|arXiv (Cornell University)|Sep 15, 2021

Robotic Path Planning Algorithms12 references6 citations

TL;DR

This paper proposes a two-stage control framework for autonomous racing: first computing a global optimal racing line using trajectory optimization, then employing a local nonlinear model predictive controller (NMPC) that uses this line as a reference to simultaneously maximize progress, avoid collisions with opponents, and leverage drafting. The method significantly improves lap time and stability compared to centerline-based NMPC, with validation in simulation showing superior performance in overtaking and high-speed cornering.

ABSTRACT

The paper presents a strategy for the control of anautonomous racing car on a pre-mapped track. Using a dynamic model of the vehicle, the optimal racing line is computed, taking track boundaries into account. With the optimal racing line as areference, a local nonlinear model predictive controller (NMPC) is proposed, which takes into account multiple local objectives like making more progress along the race line, avoiding collision with opponent vehicles, and use of drafting to achieve more progress.

Motivation & Objective

• To develop a control strategy for autonomous racing cars that outperforms conventional centerline-based approaches by using a globally optimized racing line as a reference.
• To address the challenge of high-speed vehicle dynamics by incorporating a dynamic, high-fidelity tire force model at elevated speeds.
• To enable effective multi-agent racing by integrating a drafting effect model into the NMPC controller for strategic overtaking.
• To improve local trajectory tracking by merging with the optimal racing line at turns, maximizing progress and minimizing deviation.
• To validate the controller in a simulated multi-agent racing environment with realistic dynamics and opponent behavior.

Proposed method

• A global optimal racing line is computed via numerical optimization of a minimum-time trajectory, constrained by track boundaries and vehicle dynamics.
• The local NMPC controller uses the optimal racing line as a reference path, with a cost function that prioritizes progress along the line over contouring error.
• A modified Pacejka tire model captures nonlinear, high-speed tire forces, improving dynamic accuracy under extreme conditions.
• A drafting effect model is embedded in the cost function, encouraging the ego vehicle to position behind opponents to reduce drag and increase speed.
• Overtaking decisions are made dynamically: if an opponent is detected within a critical proximity, the controller selects a preferred overtaking direction (left/right) based on prior decisions to avoid oscillation.
• The NMPC is solved in real time using IPOPT, with a 1-second prediction horizon, and the first control action is executed at each time step.

Experimental results

Research questions

• RQ1 Can using a globally optimized racing line as a reference in local NMPC improve lap time and trajectory tracking compared to centerline-based approaches?
• RQ2 How does incorporating a dynamic tire force model affect the accuracy and stability of high-speed vehicle control?
• RQ3 To what extent can a drafting-aware cost function in NMPC enhance speed and overtaking performance in multi-agent racing?
• RQ4 How does dynamic overtaking direction selection prevent oscillatory behavior and improve robustness in close-proximity scenarios?
• RQ5 What is the computational feasibility of real-time NMPC with a nonlinear, high-fidelity model in a simulated multi-agent racing environment?

Key findings

• The proposed NMPC with the optimal racing line reference reduced trajectory deviation and improved progress along the track compared to contouring error-based methods.
• The inclusion of a dynamic tire model enabled accurate simulation of high-speed cornering and longitudinal dynamics, essential for realistic control performance.
• The drafting cost term led to measurable speed gains during straightaways when following a lead vehicle, with trajectories showing strategic positioning behind opponents.
• The algorithm successfully executed overtaking maneuvers with consistent direction selection, avoiding oscillation due to symmetric cost conditions.
• The controller achieved stable, high-speed performance in a 5-lap simulation of a multi-agent racing scenario, demonstrating robustness in head-to-head conditions.
• Despite satisfactory performance, the controller ran at approximately 5 FPS in real time due to the computational load of solving the nonlinear optimization with IPOPT, indicating a need for future acceleration via linearization or iterative LQR.