Over the years, complex control approaches have been developed to control the motion of a bicycle. Reinforcement Learning (RL), a branch of machine learning, promises to be an automated approach for solving optimal control problems. By interacting with and observing an environment, a so-called agent is trained, ultimately leading to a learned controller. The present work introduces a pure RL approach to do path following with a virtual bicycle model while simultaneously stabilizing it laterally. The bicycle, modeled using the Whipple benchmark model and multibody system dynamics, has no stabilization aids. The observation of the environment consists of the minimal positional and velocity coordinates of the bicycle, as well as of information about the path ahead of the bicycle provided by moving preview points. Both path following and stabilization of the bicycle model are achieved exclusively by controlling the steering angle setpoint of the bicycle. Curriculum learning is applied as a state-of-the-art training strategy. Different settings for the RL approach are investigated and compared. The ability of the learned controllers to do path following and stabilization of the bicycle model traveling between 2 m/s and 7 m/s along complex paths including full circles, slalom maneuvers, and lane changes is demonstrated. Explanatory methods for machine learning are used to analyze the learned controller and identify connections to research in bicycle dynamics.

Falls due to disturbances are a common cause of serious cycling injuries, yet evaluation approaches to systematically evaluate interventions aimed at improving balance recovery are lacking. Current ex-post evaluations are hindered by sparse crash data, and existing ex-ante approaches often lack generalizability or rely on surrogate measures that are not validated against fall risk. This study introduces the Maximum Allowable Handlebar Disturbance (MAHD), a novel performance indicator that quantifies the largest handlebar disturbance a cyclist can recover from without falling. The MAHD captures the cyclist’s resilience to disturbances and provides a direct, interpretable measure of intervention effectiveness. We propose two methods for determining MAHD: (1) controlled treadmill experiments with induced handlebar disturbances and safe fall conditions and (2) simulations using bicycle dynamics and cyclist control models. Together, these methods allow quantitative ex-ante evaluation and systematic comparison of interventions targeting cyclist control, bicycle design, and infrastructure features such as curbs and road shoulders. With further validation, the MAHD offers practical value for researchers, engineers, and policymakers seeking to design safer bicycles, training programs, and road environments and improve evidence-based resource allocation. In the future, this could reduce fall-related cycling injuries.

Falls are a significant cause of injury among cyclists, highlighting the need for effective fall prevention interventions. However, ex-ante evaluation of such interventions remains challenging for engineers designing safer infrastructure and bicycles, as well as for safety professionals developing training programs. This study proposes the Maximum Allowable Handlebar Disturbance (MAHD) — the largest external handlebar disturbance a cyclist can recover from — as a performance indicator for evaluating fall prevention interventions. While bicycle dynamics and cyclist control models have the potential to determine this indicator and simulate interventions, their application is currently limited by a lack of validation in predicting the MAHD and the narrow range of interventions that can be incorporated into existing cyclist control models. To address these limitations, we conducted controlled experiments with 24 participants of varying ages and skill levels, exposing them to impulse-like handlebar disturbances that resulted in both recoveries and falls. This dataset, which includes recorded cyclist falls, supports future validation of bicycle dynamics and control models in predicting the MAHD. In addition, using Bayesian Model Averaging, we identified key cyclist factors influencing the MAHD, with forward speed and cyclist balancing skill being critical predictors. Incorporating these predictors into cyclist control models can substantially improve their practical application. These insights were then used to develop a Bayesian multilevel logistic regression model to predict the MAHD for different types of cyclists. Our findings improve the potential for bicycle dynamics and control models to proactively evaluate cyclist fall prevention methods, contributing to safer cycling environments.

Shape-morphing structures have the ability to adapt to various target shapes, offering significant advantages for many applications. However, predicting their behavior presents challenges. Here, we present a method to assess the shape-matching behavior of shape-morphing structures using a multibody systems approach wherein the structure is represented by a collection of nodes and their associated constraints. This representation preserves the kinematic properties of the original structure while allowing for a rigorous treatment of the shape-morphing behavior of the underlying metamaterial. We assessed the utility of the proposed method by applying it to a wide range of 2D/3D sample shape-morphing structures. A modular system of joints and links was also 3D printed for the experimental realization of the systems under study. Both our simulations and the experiments confirmed the ability of the presented technique to capture the true shape-morphing behavior of complex shape-morphing metamaterials.

Bicycle simulators have been the subject of considerable research, however, few of these attempts have integrated direct balance control and realistic freedom of motion to deliver a real-world dynamic cycling experience. This study presents the BIKE (Bicycle Intrinsic Kinematics Emulator) system, a kinematic bicycle simulator, developed with the purpose of letting its users experience realistic steer, roll, yaw and sway motions. Motion is provided with Carvallo–Whipple bicycle model-based control of sway and yaw combined with passive steer and roll. This study validates the BIKE simulator by comparing cycling behaviour and subjective evaluation for the simulator with and without motion to outdoor tests with an instrumented bicycle. 15 participants of varying age and mass, performed straight-line cycling, at low ((Formula presented.)) to high ((Formula presented.)) velocities and zig-zag manoeuvres. Results show that users can successfully rely on existing cycling skills to use the simulator with motion. Objectively, in the kinematic sense, the simulator with motion performs similarly to an outdoor bicycle. Subjectively, the simulator performs better with motion and is experienced by riders as close to real outdoor cycling.

Experiments and human rider models were used to investigate bicycle balance and steering using visuo/vestibular motion and proprioceptive feedback taking into account sensory delays. An instrumented steer-by-wire bicycle designed and built at the TU Delft bicycle laboratory was used to investigate rider responses with and with reduced steering torque feedback. Steering responses and bicycle motions were measured perturbing balance with impulsive forces at the seat post. The rider was commanded to follow a straight lane at unstable (2.6 and 3.7 ms ^-1) and stable speeds (4.5 and 5.6 ms ^-1). Bicycle speed was controlled with an electric drive and cruise control. Balance and steering responses could well be captured by linear impulse response functions which were consistent across participants. The impulse response functions were used to develop neuromuscular control models capturing rider–bicycle interaction. The Carvallo–Whipple bicycle model was extended with rider inertia and an additional degree of freedom for the steer-by-wire system. Rider behaviour was modelled as a balance and heading controller. This controller used visuo/vestibular motion feedback of roll angle and roll rate, heading angle and heading rate, and proprioceptive feedback of steering angle, velocity and torque. Results showed that the rider model followed the necessary stability condition of steer into the fall and was capable of stabilising the bicycle. Sensory delays had a negative effect on the model fit, which was resolved with an internal model and prediction algorithm. A model without steer angle and steer velocity feedback could not well capture the human response at the highest speeds and the absence of torque feedback had similar effects for all speeds, supporting the relevance of steer angle and torque feedback in bicycle control.

The objective of this study was to identify the dynamic response of the bicycle rider’s body during translational perturbations, in an effort to improve two-wheeler safety and comfort. A bicycle mock-up was equipped with sensors measuring three-dimensional seat and trunk accelerations and rider’s force responses at the seat, handlebars, and footpegs. The bicycle mock-up was driven by a hexapod motion platform that generated random noise perturbations in the range of 0–10 Hz. Twenty-four healthy male adults participated in this study. Responses are represented as frequency response functions capturing three-dimensional force interactions of the rider’s body at the seat, handlebars and footpegs in terms of apparent mass, and rider’s trunk motion (one-dimensional) as function of seat motion as seat-to-sternum transmissibility. Results showed that the vertical and longitudinal apparent mass for most of the bicycle interfaces followed the resonance of the seat-to-sternum transmissibility. A twice as high magnitude was observed at the resonance, although a more heavily damped system was apparent in the seat-to-sternum transmissibility. Resonant frequencies were considerably higher in the vertical direction compared to the longitudinal direction. Different dynamics were observed for the lateral measurements, where all magnitudes decreased after the base frequency, and no resonance was observed.

With the resurgence in bicycle ridership in the last decade and the continuous increase of electric bicycles in the streets a better understanding of bicycle rider behaviour is imperative to improve bicycle safety. Unfortunately, these studies are dangerous for the rider, given that the bicycle is a laterally unstable vehicle and most of the time in need for rider balance control. Moreover, the bicycle rider is very vulnerable and not easily protected against impact injuries. A bicycle simulator, on which the rider can balance and manoeuvre a bicycle within a simulated environment and interact with other simulated road users, would solve most of these issues. In this paper, we present a description of a recently build bicycle simulator at TU Delft, were mechanical and mechatronics aspects are discussed in detail.

Measuring the roll angle of single-track vehicles has always been a challenging task; however, accurate and reliable measurements of this magnitude are paramount for controlling the stability of these vehicles, both for autonomous riding and for safety reasons. A roll angle estimation is also useful in other situations, such as tests to perform the identification of the parameters of the rider control. In this work, a new algorithm is presented for estimating the roll angle of bicycles. This estimator, based on the well-known Kalman filter, employs a wheel speed sensor to approximate the speed of the vehicle, and three angular rate sensors, which are currently small and affordable sensors. The proposed method was implemented in a microcontroller and tested in a bicycle and the results were compared with measurements obtained with optical sensors, showing a good correlation. Although it has not been tested in motorcycles, comparable results are expected.