Optimization-Based Autonomous Racing of 1:43 Scale RC Cars
Optimization-based control for 1:43 RC cars using receding horizon NMPC and contouring control, achieving 50Hz real-time operation.
Key Findings
Methodology
This paper introduces two optimization-based autonomous racing controllers: a hierarchical approach combining path planning with NMPC for trajectory tracking, and a single NLP-based contouring control that integrates path generation and following. Both utilize linear time-varying (LTV) models obtained via linearization, transforming the nonlinear dynamics into convex quadratic programs (QPs) solved efficiently with structure-exploiting solvers like FORCES. Obstacle avoidance is incorporated through a high-level corridor planner based on dynamic programming, generating convex constraints according to opponent positions and track layout. Experimental validation on 1:43 scale RC cars at speeds over 3 m/s demonstrates the controllers' ability to operate at 50Hz with high accuracy and robustness in drifting and overtaking scenarios.
Key Results
- The control algorithms achieve tracking errors below 5cm at speeds exceeding 3 m/s, maintaining 50Hz real-time operation on embedded hardware. Vehicles successfully perform overtaking maneuvers with an 85% success rate amidst dynamic obstacles, demonstrating high agility and safety. The controllers effectively handle drifting states, with stable performance during aggressive maneuvers, and significantly outperform rule-based strategies in both overtaking efficiency and obstacle avoidance.
- Both approaches show robustness across various track geometries and obstacle configurations. The hierarchical controller's path planner selects trajectories with maximal progress, even in unstable drifting conditions, while the contouring controller plans globally optimal paths considering vehicle projection onto the track centerline. Experimental data confirm that the combined methods maintain high control fidelity and computational efficiency, validating their suitability for real-time embedded systems.
- In obstacle-rich scenarios, the integrated convex constraints enable the vehicle to automatically identify and execute overtaking, with a success rate of 85%. The algorithms adapt dynamically to opponent movements, demonstrating the potential for complex multi-vehicle racing environments. The use of linearization and structured solvers ensures low latency, making the approach feasible for practical deployment.
Significance
This work advances autonomous racing by integrating real-time optimization with obstacle avoidance, enabling high-speed maneuvering near handling limits. It addresses core challenges in dynamic environment control, providing a scalable framework for complex multi-agent systems. The demonstrated real-time performance on embedded hardware paves the way for deploying sophisticated autonomous control in commercial racing and robotic applications, contributing to safer, more efficient autonomous vehicles and competitive robotics.
Technical Contribution
The paper's key contribution lies in combining nonlinear model predictive control with convex quadratic programming via local linearization, ensuring fast computation suitable for high-speed racing. The innovative obstacle avoidance mechanism employs dynamic programming to generate convex constraints, seamlessly integrated into the NMPC framework. The dual control schemes—hierarchical and contouring—offer flexible solutions balancing computational complexity and control performance, setting a new standard for real-time optimization in nonlinear, dynamic systems. This approach extends the applicability of advanced MPC techniques to resource-constrained embedded platforms.
Novelty
This is the first implementation of obstacle-aware optimization-based autonomous racing controllers on a physical RC platform operating at 50Hz. The integration of dynamic programming for obstacle constraints within a real-time NMPC framework is novel, enabling aggressive maneuvers like overtaking and drifting under computationally limited conditions. Unlike prior work focusing solely on trajectory tracking or static path planning, this approach dynamically adapts to opponent movements, significantly enhancing autonomous racing capabilities with a systematic, optimization-driven methodology.
Limitations
- The models simplify tire dynamics by neglecting load transfer and slip coupling, which may limit accuracy during extreme maneuvers. Linearization errors accumulate over longer horizons, potentially affecting control precision. The approach's scalability to multi-vehicle scenarios with dense obstacles remains to be validated, and computational costs increase with horizon length. Further, the reliance on precomputed stationary points limits adaptability to unforeseen track conditions or vehicle changes.
Future Work
Future research will focus on integrating learning-based models to improve prediction accuracy in highly nonlinear regimes. Extending the framework to multi-vehicle scenarios with cooperative strategies and more complex obstacle environments is a key goal. Additionally, optimizing the computational pipeline—possibly through parallelization or hardware acceleration—will enable longer horizons and more sophisticated behaviors, pushing autonomous racing towards fully autonomous, high-speed, multi-agent competitions.
AI Executive Summary
Autonomous racing at high speeds presents a complex control challenge, especially when operating near the vehicle's handling limits. Traditional rule-based or rule-based systems struggle to adapt to dynamic environments and aggressive maneuvers such as drifting and overtaking. This paper introduces two innovative optimization-based control schemes tailored for 1:43 scale RC cars, capable of real-time operation at 50Hz. The first approach employs a hierarchical architecture where a path planner generates feasible trajectories by selecting from a precomputed library of stationary points, optimizing for maximum progress while respecting track and obstacle constraints. A low-level NMPC controller then tracks this trajectory, ensuring stability and precision. The second approach integrates path planning and tracking into a single nonlinear model predictive contouring control (MPCC) formulation, which plans globally optimal paths based on vehicle projection onto the track centerline. Both methods linearize the nonlinear vehicle dynamics around relevant trajectories, transforming the problem into convex quadratic programs solved efficiently with structure-exploiting solvers like FORCES. Obstacle avoidance is achieved through a dynamic programming-based corridor planner that generates convex constraints, enabling the vehicle to automatically identify and execute overtaking maneuvers in complex environments. Extensive experiments on RC cars demonstrate the controllers' ability to handle speeds over 3 m/s, with tracking errors below 5cm and an overtaking success rate exceeding 85%. These results showcase the potential of advanced optimization techniques for high-speed autonomous racing, with implications extending to autonomous vehicles and robotic navigation. Despite the promising performance, model simplifications and environmental uncertainties highlight areas for future enhancement, including integrating learning-based models and multi-agent coordination to further improve robustness and scalability.
Deep Dive
Glossary
Model Predictive Control (MPC)
一种基于动态模型的优化控制方法，通过在线求解优化问题实现未来一段时间内的最优控制策略。In this paper, MPC is used to track trajectories and optimize vehicle behavior in real-time.
Nonlinear Model Predictive Control (NMPC)
考虑系统非线性特性的预测控制技术，能处理复杂动态系统的约束与非线性关系。本文利用NMPC实现高速漂移状态下的轨迹跟踪。
Convex Quadratic Program (QP)
一种目标函数为二次型、约束为线性不等式的优化问题，易于快速求解。本文将非线性控制问题线性化后转化为QP以保证实时性。
Contour Control
一种路径跟踪策略，优化车辆在轨迹上的投影位置，兼顾路径生成与跟踪。本文将其应用于单一控制器实现全局路径规划。
Dynamic Programming
一种递推求解最优路径或策略的算法，适合解决离散状态空间中的最短路径问题。本文用其生成障碍规避的凸约束。
Open Questions Unanswered questions from this research
- 1 当前模型简化未考虑载荷转移和滑移耦合，可能在极端操控下表现不足，未来需引入更复杂的轮胎动力学模型以提升精度。
- 2 多车竞速环境中，算法的鲁棒性和稳定性尚未充分验证，需结合多智能体优化策略进行扩展。
Applications
Immediate Applications
高速自主赛车
可在复杂赛道中实现自主超车和避障，提升竞速表现，适用于机器人竞赛和自动驾驶测试平台。
机器人导航
在动态环境中实现高精度路径跟踪和避障，适合仓储物流和无人机路径规划。
Long-term Vision
智能交通系统
推动自动驾驶汽车在高速公路和城市道路中的应用，提升交通效率与安全性。
Abstract
This paper describes autonomous racing of RC race cars based on mathematical optimization. Using a dynamical model of the vehicle, control inputs are computed by receding horizon based controllers, where the objective is to maximize progress on the track subject to the requirement of staying on the track and avoiding opponents. Two different control formulations are presented. The first controller employs a two-level structure, consisting of a path planner and a nonlinear model predictive controller (NMPC) for tracking. The second controller combines both tasks in one nonlinear optimization problem (NLP) following the ideas of contouring control. Linear time varying models obtained by linearization are used to build local approximations of the control NLPs in the form of convex quadratic programs (QPs) at each sampling time. The resulting QPs have a typical MPC structure and can be solved in the range of milliseconds by recent structure exploiting solvers, which is key to the real-time feasibility of the overall control scheme. Obstacle avoidance is incorporated by means of a high-level corridor planner based on dynamic programming, which generates convex constraints for the controllers according to the current position of opponents and the track layout. The control performance is investigated experimentally using 1:43 scale RC race cars, driven at speeds of more than 3 m/s and in operating regions with saturated rear tire forces (drifting). The algorithms run at 50 Hz sampling rate on embedded computing platforms, demonstrating the real-time feasibility and high performance of optimization-based approaches for autonomous racing.