Motorbike Modeling and Control (original) (raw)
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Control of An Autonomous Motorbike
2012
The work in this paper aims at developing a control system for an autonomous motorbike using Model Predictive Control (MPC) and Proportional Integral Derivative (PID) control strategies. The mathematical modelling of the motorbike is based on kinematics and dynamics and is inspired in the literature. These non linear models were linearized to use with a MPC toolbox developed at TU Delft. The paper also reviews the racing problem. The racing problem addresses the time it takes to do one lap of a closed circuit. The proposed control system was validated by two simulations in a closed circuit, one using the kinematics of the motorbike as reference model and the other using the dynamics model. The results obtained are compatible with those of a real motorbike driven by a human rider.
A Motorcycle Model for Stability and Control Analysis
2001
The observed dynamic behaviour of motorcycles suggests that interesting and significant motions occur that are not currently understood. The most elaborate modelling exercise completed so far has produced results that need confirmation and extension. The construction of these models necessitates the use of automated methods and one such modelling methodology is described. The automated model building platform that was used here is AutoSim. This code was used to generate a variety of linear and nonlinear models in symbolic form. The relatively complex geometry of the steering system and the front tyre force system is discussed in detail and a new method of checking the self-consistency of the model is described and exploited. Sample results in the form of root-locus plots for small perturbations from straight running and cornering equilibrium states are presented. These are used to reproduce important findings from the literature. Conclusions are drawn on the basis of the results presented.
2021
The use of computer simulations in motorcycle engineering makes it possible both to reduce designing time and costs and to avoid the risks and dangers associated with experiments and tests. The multi-body model for computer simulations can be built either by developing a mathematical model of the vehicle or by using commercial software for vehicle system dynamics. Even though the first method is more difficult and timeconsuming than the second, maximum flexibility in the description of the features of the model can be obtained only by using an analytical model. Moreover, mathematical modelling has a high computation efficiency, whereas multi-body software requires a lot of time to carry out simulations. For the reasons above, the aim of this work was to develop a mathematical model of a motorcycle.
Advances in the Modelling of Motorcycle Dynamics
Starting from an existing advanced motorcycle dynamics model, which allows simulation of reasonably general motions and stability, modal and response computations for small perturbations from any trim condition, improvements are described. These concern (a) tyre/road contact geometry, (b) tyre shear force and moment descriptions, as functions of load, slip and camber, (c) tyre relaxation properties, (d) a new analytic treatment of the monoshock rear suspension mechanism with sample results, (e) parameter values describing a contemporary high performance machine and rider, (f) steady-state equilibrium and power checking and (g) steering control. In particular, the " Magic Formula " motorcycle tyre model is utilised and complete sets of parameter values for contemporary tyres are derived by identification methods. The new model is used for steady turning, stability, design parameter sensitivity and response to road forcing calculations. The results show the predictions of the model to be in general agreement with observations of motorcycle behaviour from the field and they suggest that frame flexibility remains an important design and analysis area, despite improvements in frame designs over recent years. Motorcycle rider parameters have significant influences on the behaviour, with results consistent with a commonly held view, that lightweight riders are more likely to suffer oscillation problems than heavyweight ones.
Modelling, Control System Design and Simulation of an Autonomous Bicycle
Modelling, Identification and Control, 2014
This paper presents the mathematical modelling and control system design of an autonomous bicycle. The nonlinear equations of motion have been derived and the proposed control system has been used in the simulation of the dynamical behaviour of the bicycle. With the assumption of rolling without slipping condition for the wheels-ground interaction, the system is constrained by nonholonomic equations, and the equations of motion are highly nonlinear. Unlike many other approaches present in related literature, the dynamical model is preserved in simulations in its original nonlinear form without any simplifying assumptions and linearization. Numerical results of the simulations show that the proposed closedloop control system is achievable. Design of the experimental system has been based on a commercially available bicycle. The mechanical modifications and control system hardware have been designed according to the simulation results.
An efficient Newton method for general motorcycle kinematics
Vehicle System Dynamics, 2009
This paper presents a detailed study of the kinematics of single track vehicles, with a special emphasis on motorcycles. We consider a general class of tire profiles as well as rather general vehicle geometry. We show that the kinematic problem may be reduced to the problem of finding the zero of a (single) nonlinear equation in the pitch angle which may then be solved using a safeguarded Newton method, providing rapid convergence. Special care, enabled by the systematic use of rotation matrices, is taken to understand the range of pitch angles for which all quantities in the equation are well defined. The paper provides a fast and numerically reliable algorithm that can be used within analysis tools such as those involving numerical integration of system dynamics.
A nonlinear mathematical model for a bicycle
This paper concerns the mathematical modelling of a bicycle taking account of the presence of a trail. It is well known that the bicycle is a classical example of a nonholonomic system. First we consider the kinematics of rolling of a bicycle and we derive the full Lagrangian for a bicycle with trail. Then we write the equation of motion for a simplified model with zero caster angle, following the constrained Lagrangian point of view.
The Motor Cycle and Rider-Modeling and Analysis of the Control System
2012
− A motorcycle and a rider may be modeled as an automatic control system. The eyes of the rider act as the sensor to gather information about the world map around him. This information is carried by the sensory nerves to the brain acting as the central processing unit. The signal is processed here and fed back to the hands and legs which exercise the steering, starting, braking and other control functions. In this paper, a motor cycle and a rider combination has been mathematically modeled. The experience of the rider has been taken into consideration by inserting a zero of variable location in the transfer function. The system gain has been adjusted with reference to the root locus to get acceptably good performance in steering control. Both time-domain and frequency-domain analysis have been made using MATLAB7.1 and the results have been displayed.
Modeling of a Motorcycle using Multi-Body Dynamics and Its Stabilization Control
2010
In this paper, a new rider-motorcycle system including front and rear suspensions [1], [2], [3] is modeled using multi-body dynamics, and then the stabilization control system is designed based on the multi-body dynamics model. We have already modeled the rider-motorcycle system taking into account of the lean angle of the rider’s upper torso [4], [5], however, including the front and rear suspensions will be necessary for dynamical analysis of a motorcycle during braking in a turn or straight running. A dynamical model of the nonlinear twelve-degree of freedom rider-motorcycle system derived as shown in Figure 1. In addition to the lean motion of the rider’s upper torso: θwx rotating around the x-axis of the rear frame of the motorcycle, the steering angle: δ and the rotation of the front and the rear wheel, this model includes the compression length of the front suspension: lUD and the compression angle of the rear suspension: ψ, which are restrained with a spring and a dumper res...
Motorcycle Dynamic Model Synthesis for Two Wheeled Driving Simulator
2007 IEEE Intelligent Transportation Systems Conference, 2007
This paper presents the development of motorcycle dynamics model. The considered vehicle contains six bodies linked with simple joints and parametrised by 11 degrees of freedom (DOF). The motorcycle model is to be used as a component in driving simulator application. It serves to investigate the influence of using a complete motorcycle dynamics model in inertial cues realism. The choice of the modeling method is based on the algorithmic Lagrange equation representation. This method makes the implementation of the dynamic model very easy. In addition, the principal external forces affecting the motorcycle behavior are considered (pneumatic forces, driver actions, brakes ... etc). At the end of this article, some simulation results are presented in the case of street line motion.