Bicycle Stability Research Articles

Unmanned Bicycle Balance Control Based on Tunicate Swarm Algorithm Optimized BP Neural Network PID

In this study, the authors introduce a novel approach that leverages the tunicate swarm algorithm (TSA) to optimize proportional-integral-derivative (PID) controller based on a back propagation (BP) neural network. The core objective of the approach is to manage and counteract uncertainties and disturbance that may jeopardize the balance and stability of self-driving bicycles in operation. By using the self-learning capabilities of BP neural networks, the controller can dynamically adjust PID parameters in real time. This enables an enhanced robustness and reliability during operation. Further bolstering the efficiency of our controller, the authors use the TSA to optimize the initial weights of a neural network. This effectively mitigates the commonly associated with slow convergence and being entrapped in local minima. Through simulation and experimentation, the findings reveal that the TSA-optimized BP neural network PID controller dramatically improves dynamic performance and robustness. It also proficiently manages changes in the environment such as wind and ground bumps. Therefore, the proposed controller design offers an effective solution to the balancing problem of self-driving bicycles and paves the way for a promising future in designing versatile controllers with broad application potential.

A General Multibody Approach for the Linear and Nonlinear Stability Analysis of Bicycle Systems. Part II: Application to the Whipple-Carvallo Bicycle Model

This paper represents the second contribution of a two-part research work presenting the application of the proposed multibody analysis approach to bicycle systems and the relative numerical results found. In this work, a nonlinear multibody model of a bicycle system is developed and implemented to perform a parametric analysis to understand the influence of the variation of the principal model parameters on the system stability under investigation. To demonstrate the effectiveness of the proposed approach, the case study considered in this paper is the dynamic analysis of the Whipple-Carvallo bicycle model. Considering the combined use of a robust numerical technique for nonlinear dynamical simulations with a specifically devised linearization procedure, the effects of the different geometric parameters and inertial properties on the bicycle stability are investigated. The numerical results obtained in this work using the proposed multibody techniques are useful to gain insight information about the dynamic behavior of the bicycle system in a straight motion. The proposed multibody methodology also demonstrated a high potential for analyzing complex multibody mechanical systems in virtue of the generality of the analytical and computational approaches adopted.

A design sensitivity analysis of bicycle stability and experimental validation

In this study, the sensitivities of weave and capsize speeds with respect to design parameters were calculated on the basis of the linear forms of uncontrolled-bicycle dynamic equations. The significance of the design parameters and the way in which the stable speed range is changed were determined by analyzing the sensitivity curves. Among the seven important parameters (out of 25), head angle was found to be the most dominant, followed by the diameter of front wheel, mass, and moment of inertia, demonstrating the importance of front side design to bicycle stability. The procedure for predicting the stable speed range using sensitivity information was also investigated. When a single parameter was changed, the stable range was determined by that parameter, whereas when multiple parameters were changed, the stable range was determined by summing all the contributions from each parameter. The weave speeds in the nominal and changed configurations yielding the lowest values were measured using an experimental bicycle of variable configuration. A comparison of the measured and predicted values of weave speeds showed a good correlation, demonstrating the validity of the sensitivity-based stability analysis. This study used a novel procedure for predicting the stable speed range through the sensitivity analysis of design parameters related to bicycle stability and validation of the stable speed range with experiment.

Stability analysis for the Whipple bicycle dynamics

It has been known that bicycle stability is closely linked to a pair of ordinary differential equations (ODEs). The linearization technique used to derive these ODEs, nevertheless, has yet to be thoroughly examined. For this purpose, we conduct an analysis of the dynamics of the Whipple bicycle, starting with the contact kinematics, using the Gibbs–Appell method. The effort results in a complete nonlinear model with minimal dimensions, from which equilibrium points during the bicycle’s straight and circular motions can be determined. The model can be linearized around these points via a perturbation analysis under no additional assumptions. Given the non-hyperbolic nature of the equilibria, we apply the center manifold theorem to analyze their stability, offering a rigorous derivation of the (well-know) exponential stability of the bicycle in its leaning and steering motions. Finally, a dimensionless index is defined to characterize the influence of physical parameters on the bicycle stability.

Correction to: A robust two-stage active disturbance rejection control for the stabilization of a riderless bicycle

Correction to: Multibody Syst Dyn (2019) 45:7–35 In the original publication the affiliation of author John Cortes-Romero was given in its translated form (National University of Colombia). It is a legal requirement of this university that its name be given in the original Spanish in publications (Universidad Nacional de Colombia) and this correction article is published to amend this.

Stabilization of bicycle which equips inertia rotor

Stabilization of bicycle which equips inertia rotor

A robust two-stage active disturbance rejection control for the stabilization of a riderless bicycle

In this work we propose a two-stage observer-based feedback control approach to automatically stabilizing a riderless bicycle in its upright position when moving forward at a constant speed. Our strategy uses a modern control approach called Active Disturbance Rejection Control (ADRC), based on Generalized Proportional Integral (GPI) extended observers, to estimate a unified signal that groups all the discrepancies between an adopted linear model and the actual behavior of the plant. These estimations are used in the feedback controller as an additive, close cancellation and terms devising proper output feedback control laws that linearly regulate the lean angle with respect to its upright position. From a control-design perspective, the bicycle is a perturbed, uncertain system with an unstable and non-linear behavior that is strongly forward speed dependent. The ADRC scheme allows one to solve this problem easily by using a control strategy based on an acceptable mathematical model derived from lumped-parameter analysis, and its effectiveness has been validated by the successful results from real implementation experiments on an instrumented bicycle prototype. A detailed description of all the stages of the mechatronics process design is included for a proper reference.

On the influence of tyre and structural properties on the stability of bicycles

ABSTRACTIn recent years the Whipple Carvallo Bicycle Model has been extended to analyse high speed stability of bicycles. Various researchers have developed models taking into account the effects of front frame compliance and tyre properties, nonetheless, a systematic analysis has not been yet carried out. This paper aims at analysing parametrically the influence of front frame compliance and tyre properties on the open loop stability of bicycles. Some indexes based on the eigenvalues of the dynamic system are defined to evaluate quantitatively bicycle stability. The parametric analysis is carried out with a factorial design approach to determine the most influential parameters. A commuting and a racing bicycle are considered and numerical results show different effects of the various parameters on each bicycle. In the commuting bicycle, the tyre properties have greater influence than front frame compliance, and the weave mode has the main effect on stability. Conversely, in the racing bicycle, the front frame compliance parameters have greater influence than tyre properties, and the wobble mode has the main effect on stability.

Gain-scheduled linear quadratic regulator applied to the stabilization of a riderless bicycle

In this article, a gain-scheduling control is designed to achieve the stabilization of a riderless bicycle. The main contribution is the design of a stabilizing control system including integral ac...

The bicycle problem that nearly broke mathematics.

The bicycle problem that nearly broke mathematics.

The co-contraction index of the upper limb for young and old adult cyclists

Bicycling is a popular and convenient means of transportation amongst the elderly in the Netherlands. However, the uptake of the electric bicycle resulted in an increase of single-sided bicycle accidents amongst the elderly (Veiligheid, 2010). Since elderly are prone to severe injuries, bicycle stability is currently a popular research topic. Three main balance strategies have been proposed in former studies: steering as the primary balance strategy and trunk −and lateral knee movement as secondary balance strategies (Moore et al., 2011; Cain, 2013). Since steering is the primary strategy for bicycle stability, the stiffness of the arms plays an important role in active stability during cycling. It has been shown that the arm stiffness of a passive rider is an important factor on the stability of a bicycle (Doria and Tognazzo, 2014). In the study presented here, the co-contraction index (CCI) of the upper limb for young and old adult cyclist is studied. Data is collected during experiments based on the setup described in (Kiewiet et al., 2014), wherein contact forces, muscle activities and motions of the rider and bicycle are measured for 15 young adult (mean±sd: 25.3±2.8 yrs) and 15 old adult (mean±sd: 58.1±2.1 yrs) subjects during unperturbed and perturbed cycling. The arm stiffness is defined as a co-contraction ratio between muscle activity of the m. Biceps Brachii and m. Triceps Lateralis. Results suggest that older adult cyclists use more co-contraction of their arm muscles during cycling, compared to young cyclists. The inter-subject variability of the found CCI was higher for the old adult subject group, compared to the young group. The results support the initial hypothesis that the increase in co-contraction of the upper limb for older cyclists is higher during perturbed cycling compared to unperturbed cycling than for younger cyclists. The findings might give direction towards solutions for increasing the safety and stability for elderly cyclists.

The effect of tyre and rider properties on the stability of a bicycle

To work towards an advanced model of the bicycle-rider-environment system, an open-loop bicycle-rider model was developed in the commercial multibody dynamics software ADAMS. The main contribution of this article to bicycle dynamics is the analysis of tyre and rider properties that influence bicycle stability. A system identification method is used to extract linear stability properties from time domain analysis. The weave and capsize eigenmodes of the bicycle-rider system are analysed. The effect of tyre properties is studied using the tyre’s forces and torques that have been measured in several operating conditions. The main result is that extending simplified models with a realistic tyre model leads to a notable decrease in the weave stability and a stabilization of the capsize mode. This effect is mainly caused by the twisting torque. Different tyres and tyre inflation pressures have little effect on the bicycle’s stability, in the case of riding straight at a constant forward speed. On the other hand, the tyre load does have a large effect on bicycle stability. The sensitivity study of rider properties shows that body stiffness and damping have a small effect on the weave and capsize mode, whereas arm stiffness destabilizes the capsize mode and arm damping destabilizes the weave mode.

Influence of tire side forces on bicycle self-stability

Lateral forces are known to be important in motorcycle stability. These forces also affect the stability of bicycles. In this study, we focus on the influence of tire lateral forces on bicycle self-stability. On the basis of the work of Whipple, we develop a linear bicycle model, including front and rear wheel lateral forces, in symbolic equations of motion. Modal analysis and dynamic simulation of the bicycle model are conducted and used to examine self-stability. The lateral stability of a bicycle is characterized by two oscillatory vibration modes, namely, wobble and weave, and one non-oscillatory capsize mode. Tire sideslip force modeling reveals the wobble mode, and relaxation modeling reveals the rear wobble mode. At low speed, the unstable capsize mode dominates. At medium speed, the weave mode vibratory motion dominates. At high speed, the wobble mode dominates. The influence of lateral forces on self-stability is identified using the developed model. A nonlinear multibody bicycle model is used to confirm the results of the linear analysis.

Analysis of stability differences in road and time trial bicycles with instantaneous and delayed control

Bicycle stability has been of interest to dynamicists and athletes since before J. W. Whipple described the canonical model for bicycle motion in 1899. Since then, the subject has fascinated many who sought to find a simple way to describe the essence of stability for a hands-free bicycle at a prescribed forward speed. Caster and gyroscopic effects have been shown to be helpful, but not necessary for there to exist a stable range of forward speeds. This work focuses on showing how using the eigenvalues of the linearized equations for roll and steer (with and without an instantaneous or delayed steering torque) can illuminate the stabilizing and destabilizing effects of changing bicycle geometry and rider position. The results of altering aspects of the control law and bicycle geometry are demonstrated, and a primary cause of the decreased stability a cyclist on a time trial bike experiences when in the aerodynamic position, as opposed to riding with hands on the brake hoods or bull horns, is proposed.

The influence of the dynamic response of the rider’s body on the open-loop stability of a bicycle

The passive response of the rider’s body to bicycle oscillations is experimentally studied by means of laboratory tests. Lumped element models of the rider’s body are developed and the relevant stiffness and damping parameters are identified from experimental results. The biomechanical model of the rider is coupled with the benchmark model of the bicycle and open-loop stability analysis is carried out. Results show that the stiffness and damping parameters of the waist do not strongly affect bicycle stability. Uncontrolled arm stiffness has a very detrimental effect on stability and destroys the self-stabilization mechanism. Arm damping has a more complex effect and reduces the self-stability region.

Identification of the mechanical properties of bicycle tyres for modelling of bicycle dynamics

Advanced simulation of the stability and handling properties of bicycles requires detailed road–tyre contact models. In order to develop these models, in this study, four bicycle tyres are tested by means of a rotating disc machine with the aim of measuring the components of tyre forces and torques that influence the safety and handling of bicycles. The effect of inflation pressure and tyre load is analysed. The measured properties of bicycle tyres are compared with those of motorcycle tyres.

Bicycle steering and roll responses

This article investigates the effects of different steering geometries on the steering response, system stability and frequency response of bicycles. A computer model was developed using Simulink™. The model simulates different bicycle designs allowing several different steering geometries to be quantified in terms of performance. It was validated by data available in literature and from an experimental investigation conducted with a bicycle fitted with steering and roll sensors. Three key variables were examined in detail: the head tube angle, front fork rake and bicycle speed. Their actual importance was determined by systematically changing each key variable one at a time while keeping all other terms constant. Large variations in roll and yaw responses show how sensitive bicycles are to small changes in head tube angles and rake dimensions. At higher speeds, the observed steering responses support the common observation that bicycles are more stable and easier to ride at higher speeds. These simulations show the importance of correctly designing a bicycle’s steering geometry in order to optimise steering performance and the sensitivity of bicycles to small changes in geometry.

On the stability of a bicycle on rollers

Riding a bicycle on the newest form of indoor training, rollers, presents a unique experiment on bicycle stability. The stability factors eliminated by riding on rollers are discussed in terms of refined handling and control of the centre of mass on a bicycle. This paper is intended for undergraduate physics majors as well as any other general readership interested in the dynamics of bicycle stability.

Bicycle Stability Revisited

Bicycle Stability Revisited

Science Podcast

The show includes budgeting for science, an ethical framework for biofuels, re-exploring bicycle stability, and more.