# Numerically Stable Dynamic Bicycle Model for Discrete-time Control

arXiv: https://arxiv.org/abs/2011.09612 · HTML: https://mlsanity.com/paper/2011.09612/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Nov 2020.

## Built on by (most cited first, 15 of 15)

- [Model-based Constrained Reinforcement Learning using Generalized Control Barrier Function](https://mlsanity.com/paper/2103.01556/) (2021)
- [Integrated Decision and Control: Towards Interpretable and Computationally Efficient Driving Intelligence](https://mlsanity.com/paper/2103.10290/) (2021)
- [Self-learned Intelligence for Integrated Decision and Control of Automated Vehicles at Signalized Intersections](https://mlsanity.com/paper/2110.12359/) (2021)
- [Enhance Planning with Physics-informed Safety Controller for End-to-end Autonomous Driving](https://mlsanity.com/paper/2405.00316/) (2024)
- [Integrated Decision and Control at Multi-Lane Intersections with Mixed Traffic Flow](https://mlsanity.com/paper/2108.13038/) (2021)
- [Learn Zero-Constraint-Violation Policy in Model-Free Constrained Reinforcement Learning](https://mlsanity.com/paper/2111.12953/) (2021)
- [Improve Generalization of Driving Policy at Signalized Intersections with Adversarial Learning](https://mlsanity.com/paper/2204.04403/) (2022)
- [Risk-Aware Reinforcement Learning for Autonomous Driving: Improving Safety When Driving through Intersection](https://mlsanity.com/paper/2503.19690/) (2025)
- [VLM-UDMC: VLM-Enhanced Unified Decision-Making and Motion Control for Urban Autonomous Driving](https://mlsanity.com/paper/2507.15266/) (2025)
- [Zeroth-Order Actor-Critic: An Evolutionary Framework for Sequential Decision Problems](https://mlsanity.com/paper/2201.12518/) (2022)
- [Safe Reinforcement Learning with Probabilistic Control Barrier Functions for Ramp Merging](https://mlsanity.com/paper/2212.00618/) (2022)
- [Policy Bifurcation in Safe Reinforcement Learning](https://mlsanity.com/paper/2403.12847/) (2024)
- [Performance-Driven Controller Tuning via Derivative-Free Reinforcement Learning](https://mlsanity.com/paper/2209.04854/) (2022)
- [Integrated Decision and Control for High-Level Automated Vehicles by Mixed Policy Gradient and Its Experiment Verification](https://mlsanity.com/paper/2210.10613/) (2022)
- [Steady-State Error Compensation for Reinforcement Learning with Quadratic Rewards](https://mlsanity.com/paper/2402.09075/) (2024)

## Abstract (arXiv)

Dynamic/kinematic model is of great significance in decision and control of intelligent vehicles. However, due to the singularity of dynamic models at low speed, kinematic models have been the only choice under many driving scenarios. This paper presents a discrete dynamic bicycle model feasible at any low speed utilizing the concept of backward Euler method. We further give a sufficient condition, based on which the numerical stability is proved. Simulation verifies that (1) the proposed model is numerically stable while the forward-Euler discretized dynamic model diverges; (2) the model reduces forecast error by up to 49% compared to the kinematic model. As far as we know, it is the first time that a dynamic bicycle model is qualified for urban driving scenarios involving stop-and-go tasks.