# Real-Time Control for Autonomous Racing Based on Viability Theory

arXiv: https://arxiv.org/abs/1701.08735 · HTML: https://mlsanity.com/paper/1701.08735/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2017.

## Built on by (most cited first, 8 of 8)

- [Autonomous Vehicles on the Edge: A Survey on Autonomous Vehicle Racing](https://mlsanity.com/paper/2202.07008/) (2022)
- [Deep Latent Competition: Learning to Race Using Visual Control Policies in Latent Space](https://mlsanity.com/paper/2102.09812/) (2021)
- [Learning Interactive Driving Policies via Data-driven Simulation](https://mlsanity.com/paper/2111.12137/) (2021)
- [Motion Planning and Control for Multi Vehicle Autonomous Racing at High Speeds](https://mlsanity.com/paper/2207.11136/) (2022)
- [Autonomous Driving Small-Scale Cars: A Survey of Recent Development](https://mlsanity.com/paper/2404.06229/) (2024)
- [Learning Autonomous Race Driving with Action Mapping Reinforcement Learning](https://mlsanity.com/paper/2406.14934/) (2024)
- [Attainment Regions in Feature-Parameter Space for High-Level Debugging in Autonomous Robots](https://mlsanity.com/paper/2108.03150/) (2021)
- [Modelling, Positioning, and Deep Reinforcement Learning Path Tracking Control of Scaled Robotic Vehicles: Design and Experimental Validation](https://mlsanity.com/paper/2401.05194/) (2024)

## Abstract (arXiv)

In this paper we consider autonomous driving of miniature race cars. The viability kernel is used to efficiently generate finite look-ahead trajectories that maximize progress while remaining recursively feasible with respect to static obstacles (e.g., stay inside the track). Together with a low-level model predictive controller, this method makes real-time autonomous racing possible. The viability kernel computation is based on space discretization. To make the calculation robust against discretization errors, we propose a novel numerical scheme based on game theoretical methods, in particular the discriminating kernel. We show that the resulting algorithm provides an inner approximation of the viability kernel and guarantees that, for all states in the cell surrounding a viable grid point, there exists a control that keeps the system within the kernel. The performance of the proposed control method is studied in simulation where we determine the effects of various design choices and parameters and in experiments on an autonomous racing set-up maintained at the Automatic Control Laboratory of ETH Zurich. Both simulation and experimental results suggest that the more conservative approximation using the discriminating kernel results in safer driving style at the cost of a small increase in lap time.