# Reduced Dynamics and Control for an Autonomous Bicycle

arXiv: https://arxiv.org/abs/2103.16051 · HTML: https://mlsanity.com/paper/2103.16051/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Mar 2021.

## Built on by (most cited first, 1 of 1)

- [Lightweight Temporal Transformer Decomposition for Federated Autonomous Driving](https://mlsanity.com/paper/2506.23523/) (2025)

## Abstract (arXiv)

In this paper, we propose the reduced model for the full dynamics of a bicycle and analyze its nonlinear behavior under a proportional control law for steering. Based on the Gibbs-Appell equations for the Whipple bicycle, we obtain a second-order nonlinear ordinary differential equation (ODE) that governs the bicycle's controlled motion. Two types of equilibrium points for the governing equation are found, which correspond to the bicycle's uniform straight forward and circular motions, respectively. By applying the Hurwitz criterion to the linearized equation, we find that the steer coefficient must be negative, consistent with the human's intuition of turning toward a fall. Under this condition, a critical angular velocity of the rear wheel exists, above which the uniform straight forward motion is stable, and slightly below which a pair of symmetrical stable uniform circular motions will occur. These theoretical findings are verified by both numerical simulations and experiments performed on a powered autonomous bicycle.