Dynamics and Control of Two-Wheeled Vehicles

The dynamics of two-wheeled vehicles encompass the complex interplay between wheel–ground interactions, rider inputs and vehicle geometry. Stability modes such as weave and capsize emerge from the combined effects of tyre forces, steering kinematics and gyroscopic torques. Tyre characteristics—including lateral stiffness, self-aligning torque and camber angle—critically influence handling and stability margins. The rider or control system must modulate steering angle and lean to maintain balance, especially during low-speed manoeuvres or sudden perturbations. Modern control approaches span classical feedback schemes, robust H₂/H∞ designs and advanced predictive strategies that anticipate future vehicle states. Sensor integration via inertial measurement units and state estimation algorithms provides real-time awareness of roll and yaw dynamics. Recent trends explore active stabilisation using gyroscopic flywheels, adaptive control for energy efficiency and machine-learning-based frameworks for autonomous balancing. Practical applications range from enhanced safety systems on motorcycles to self-driving bicycles and robotic assistive transport. Continued progress in multibody modelling, tyre-road contact representation and embedded control implementation drives both theoretical understanding and real-world performance of single-track vehicles.

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Dynamics and Control of Two-Wheeled Vehicles publication trend

The graph below shows the total number of articles in dynamics and control of two-wheeled vehicles across all publications each year (not limited to Nature Index journals).

Technical terms

Self-aligning torque: Torque that aligns a rotating tyre with its direction of travel.

Camber angle: Angle between the wheel plane and vertical, affecting tyre contact patch.

Gyroscopic effect: Stabilising torque from a spinning mass resisting changes in its rotational axis.

Model predictive control (MPC): Control method optimising future inputs based on a predictive system model.

Extended Kalman Filter (EKF): State estimator that linearises a nonlinear system for real-time sensor fusion.

Inertial measurement unit (IMU): Sensor combining accelerometers and gyroscopes to measure motion and orientation.

References

1. Twisting torque – A simplified theoretical model for bicycle tyres. Measurement (2023).
2. Balancing Control of Bicyrobo by Particle Swarm Optimization-Based Structure-Specified Mixed H2/H∞ Control. International Journal of Advanced Robotic Systems (2008).
3. Modeling and Control of an Active Stabilizing Assistant System for a Bicycle. Sensors (2019).
4. A new application of the Extended Kalman Filter to the estimation of roll angles of a motorcycle with Inertial Measurement Unit. FME Transaction (2020).
5. Improving Energy Efficiency of an Autonomous Bicycle with Adaptive Controller Design. Sustainability (2017).
6. Toward Self-Driving Bicycles Using State-of-the-Art Deep Reinforcement Learning Algorithms. Symmetry (2019).