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Single-track vehicle model.
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In this work we derive steady-state cornering conditions for a single-track vehicle model without restricting the operation of the tires to their linear region (i.e. allowing the vehicle to drift). For each steady-state equilibrium we calculate the corresponding tire friction forces at the front and rear tires, as well as the required front steerin...
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During vehicle driving process, the tyre security is very important, but the blow-out is inevitable sometimes, so it is very necessary to control the vehicle stability in order to avoid serious traffic accidents caused by the blow-out. In this paper, with the tyre brush model and the seven degree of freedom vehicle model, the vehicle driving system...
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... The drifting movement of the racing car can be controlled by the drifting controller, which realizes the target drifting motion analyzed based on the three-of-freedom vehicle dynamics model when tires reach the maximum in [16]. The regular-size vehicle drifting motion parameters, including velocity, sideslip angle, yaw rate, and steering angle can be calculated and obtained by analyzing the steady-state vehicle dynamics expressions in the adhesion limit [17], and the drifting controllers of a regular-size vehicle are designed based on the linear quadratic regulator theory [17][18][19], the model predictive control theory [20,21], and the adaptive control theory [22]. There is reinforcement learning [18], and neural networks [23] are applied to the vehicle drifting control based on existing vehicle drifting motion parameters. ...
... The drifting movement of the racing car can be controlled by the drifting controller, which realizes the target drifting motion analyzed based on the three-of-freedom vehicle dynamics model when tires reach the maximum in [16]. The regular-size vehicle drifting motion parameters, including velocity, sideslip angle, yaw rate, and steering angle can be calculated and obtained by analyzing the steady-state vehicle dynamics expressions in the adhesion limit [17], and the drifting controllers of a regular-size vehicle are designed based on the linear quadratic regulator theory [17][18][19], the model predictive control theory [20,21], and the adaptive control theory [22]. There is reinforcement learning [18], and neural networks [23] are applied to the vehicle drifting control based on existing vehicle drifting motion parameters. ...
The narrow tilting vehicle receives extensive public attention because of traffic congestion and environmental pollution, and the active rolling motion control is a traffic safety precaution that reduces the rollover risk caused by the structure size of the narrow vehicle. The drifting motion control reflects the relatively updated attentive research of the regular-size vehicle, which can take full advantage of the vehicle’s dynamic performance and improve driving safety, especially when tires reach their limits. The narrow tilting vehicle drifting control is worthy of research to improve the driving safety of the narrow tilting vehicle, especially when tires reach the limit. The nonlinear narrow tilting vehicle dynamic model is established with the UniTire model to describe the vehicle motion characteristics and is simplified to reduce the computation of the drifting controller design. The narrow tilting vehicle drifting controller is designed based on the robust theory with uncertain external disturbances. The controller has a wide application, validity, and robustness and whose performance is verified by realizing different drifting motions with different initial driving motions. The narrow tilting vehicle drifting robust control has some practical and theoretical significance for more research.
... ]. Drift equilibrium[Velenis et al. (2009)] and various other techniques have been proposed to sustain drift motion, including feedback linearization[Voser et al. (2010)], model inversion;Goh et al. (2018)], model predictive control[Acosta et al. (2018); Arab and Yi ...
Expert human drivers can execute emergency steering actions to avoid sudden events like a deer crossing the road. However, justifying beyond-the-limit emergency maneuvering for automated driving systems is exceptionally challenging. Emergency maneuvering often requires non-linear control policies without stability guarantees. Liability concerns, ethics, lack of safety guarantees, and non-linear system dynamics convolute an already complicated problem. Against this backdrop, we propose a principled approach to justify a particular type of emergency steering in safety-critical situations. A limit-handling controller is justified and deployed to execute the emergency maneuver upon a conventional controller's formally verified incapability to handle. We claim this check justifies the execution of the emergency maneuver as we show failure is mathematically inevitable otherwise. The simulation-based experimental validation shows that using backward reachability analysis, the proposed approach can determine emergencies. The validation justifies using limit-handling controllers for collision avoidance in a scenario where the baseline controllers fail catastrophically.
... The environment consists of a racetrack, shown in figure 1, which is a simplified version of the track from [4], and a dynamical model of the race car. The car is modelled using a bicycle model, as done in [24] and [25], where the car is considered a two-wheeled rigid body with mass m and inertia I z around the centre of gravity (CoG). The friction forces between the wheels and road are modelled using a simplified Pacejka Tire Model [26]. ...
... This manuscript describes drift maneuvers using equilibrium points as stated in [8,9]. It was shown in [10] that a three-state bicycle model with a nonlinear tire model could be used for steady-state drift control design. ...
Electronic vehicle dynamics systems are expected to evolve in the future as more and more automobile manufacturers mark fully automated vehicles as their main path of development. State-of-the-art electronic stability control programs aim to limit the vehicle motion within the stable region of the vehicle dynamics, thereby preventing drifting. On the contrary, in this paper, the authors suggest its use as an optimal cornering technique in emergency situations and on certain road conditions. Achieving the automated initiation and stabilization of vehicle drift motion (also known as powerslide) on varying road surfaces means a high level of controllability over the vehicle. This article proposes a novel approach to realize automated vehicle drifting in multiple operation points on different road surfaces. A three-state nonlinear vehicle and tire model was selected for control-oriented purposes. Model predictive control (MPC) was chosen with an online updating strategy to initiate and maintain the drift even in changing conditions. Parameter identification was conducted on a test vehicle. Equilibrium analysis was a key tool to identify steady-state drift states, and successive linearization was used as an updating strategy. The authors show that the proposed controller is capable of initiating and maintaining steady-state drifting. In the first test scenario, the reaching of a single drifting equilibrium point with −27.5° sideslip angle and 10 m/s longitudinal speed is presented, which resulted in −20° roadwheel angle. In the second demonstration, the setpoints were altered across three different operating points with sideslip angles ranging from −27.5° to −35°. In the third test case, a wet to dry road transition is presented with 0.8 and 0.95 road grip values, respectively.
... It makes use a well-known slip-based tire model as in (Pacejka 2005). The original model without suspension dynamics from (Velenis, Frazzoli, and Tsiotras 2009), on which our model is based, focusses on stability of cornering maneuvers, whereas we needed a more general purpose model. So we chose an alternative set of dynamic states u u u for our NLSTM: ...
During the process of modelling an existing dynamic physical system, it may be hard to capture some of the phenomena exactly on the basis of only textbook-equations. With measurement data from the real system, approximators like artificial neural networks can help improve the models. However, simulation and machine learning are usually done in different software applications. A unified environment for modeling, simulation and optimization would be highly valuable. We here present a framework within the Julia programming language that encompasses tools for acausal modeling, automatic differentiation rsp. sensitivity analysis involving solvers for differential equations. We use it to build and evaluate an easily interpretable model based on both physics and data.
... The drift circle motion is the first and important step of the vehicle drift study. Velenis obtained the main state parameters including the vehicle velocity and the sideslip angle and yaw rate by analyzing the steady-state cornering based on a three-state model in drift conditions in [6]. Hindiyeh analyzed the drift equilibrium of the vehicle phase portrait based on the three-state bicycle model, presented a controller framework for autonomous drifting of a rear-wheel-drive vehicle, and achieved the drift motion in [7,8]. ...
... Most theory-based controllers are designed based on the optimizing control theory. Velenis in [6], Huang in [10], and Park in [11] all designed controllers based on the LQR (linear quadratic regulator) theory. Wachter designed an optimal controller based on the SDRE (state dependent Riccati equation) technique and implemented the controller in a test vehicle in [12]. ...
Professor drivers, including racing drivers, can drive cars to achieve drift motions by taking control of the steering angle in high tire slip ratios, which provides a way to improve the driving safety of autonomous vehicles. The existing studies can be divided into two kinds based on analysis methods, and the theory-based is chosen in this study. Because the recent theory based is most applied for planar models with neglect of the rollover accident risk, the nonlinear vehicle model is established by considering longitudinal, lateral, roll, and yaw motions and rolling safety with the nonlinear tire model UniTire. The drift motion mechanism is analyzed in steady and transient states to obtain drift motion conditions, including the velocity limitation and the relationship between sideslip angle and yaw rate, and vehicle main status parameters including the velocity, side-slip angle and yaw rate in drift conditions. The state-feedback controller is designed based on robust theory and LMI (linear matrix inequation) with uncertain disturbances to realize circle motions in drift conditions. The designed controller in simulations realizes drift circle motions aiming at analyzed status target values by matching the front-wheel steering angle with saturated tire forces, which satisfies the Lyapunov stability with robustness. Robust control in drift conditions solves the problem of how to control vehicles to perform drift motions with uncertain disturbances and improves the driving safety of autonomous vehicles.
... The possibility of steady-state drifting has been studied by Velenis et al. (2009);, using a bicycle model with nonlinear tyre model. The required longitudinal tyre forces at front and rear are calculated, which enable steady-state drifting at a constant steering angle. ...
This study looks into the handling limit condition from a rather innovative perspective, by making use of an assumption, namely the independent wheel actuation. This assumption is recently becoming more relevant to the vehicle dynamics, as the electrified vehicles with in-wheel motors are getting a more common type of passenger vehicles. The focus of this research is on passenger vehicles moving at high-speed around the handling limit. Handling limit refers to the condition where the tyre forces reach their maximum value in a particular direction. This conditions is well-observed in the practice of drifting, as performed by highly-skilled drivers, which narrows down the focus of this work to those manoeuvres. The ultimate goal of this study is providing the analysis and guidelines on how the vehicle behaviour changes with different slips under the tyres when the vehicle starts to slide. First, a thorough planar motion analysis is performed, using a simplified vehicle model and the general behaviour of the vehicle is evaluated. An effective method for path-tracking control of the vehicle is studied and further developed. A qualitative metric to measure the amount of drifting in vehicle is suggested in a mathematical form, based on the quantitative descriptions about drifting. In the next stage, a four-wheel model with 7 degrees of freedom is introduced and validated for use in vehicle sliding analysis. To capture the nonlinear behaviour of the tyre forces, an elliptic tyre model is introduced for the combined-slip conditions. The model is then used to analyse the drifting manoeuvres. Drifting is studied in detail, in terms of dynamic equilibria and stability. The four-wheel vehicle model is used to calculate the dynamic equilibria in planar motion, numerically, by introducing an assumption on constant longitudinal tyre slips. This assumption enables studying the system effectively with three state variables. Other than the unstable drifting points that were reported by previous researchers, a new pair of drifting equilibria are identified and the difference of the two types is studied. The phase portrait approach is used to identify the type of these equilibria. The two-by-two phase portraits reveal the type of instability in the primary and the secondary drifting points and provide control suggestions to stabilise the drifting equilibria. Finally, general remarks on using the primary drifting for path-tracking during drifting are stated.
Full-text available at: https://researchrepository.rmit.edu.au/discovery/delivery?vid=61RMIT_INST:ResearchRepository&repId=12268692140001341#13268692130001341
... In [6], the powerslide motion was evaluated, authors focused on the importance of limited-slip differentials and the authority of the steering and traction force in control. In [7], [8], [9] the authors described drift maneuver using equilibrium points. In [7] a sliding mode controller coupled with independent traction and brake torque inputs at the front and rear axles was able to stabilize the vehicle at steady-state drifting, using fixed steering angle. ...
... In [7], [8], [9] the authors described drift maneuver using equilibrium points. In [7] a sliding mode controller coupled with independent traction and brake torque inputs at the front and rear axles was able to stabilize the vehicle at steady-state drifting, using fixed steering angle. In [9] the lateral and longitudinal control of the vehicle was separated. ...
... The previous analyses on vehicle stability at the limits of handling led to the elaboration of the first high body slip stability control systems. In [132,133], the authors introduced a preliminary "drift" control system adopting a torque control formulation based on Slid- ...
Official Final version: https://www.db-thueringen.de/receive/dbt_mods_00040620
... Among other, steady-state analysis and handling capabilities issues are very related to vehicle safe trajectory and steering behavior. Many researches were devoted to study the steady-state handling for cars, see (Pacejka, 1973;Velenis, Frazzoli, and Tsiotras, 2009;Grigorievich, Igorevich, and Nikolayevich, 2018;Wasiwitono, Sutantra, and Triwinarno, 2015), either to define the analytical handling criteria or the critical dynamic variables by which the divergent loss of handling occurs. The analysis of the properties of handling highlights certain dynamic aspects that are important to define dangerous/safe stability threshold conditions (Evangelou, 2004), as the neutral, overturning or underturning behavior (Glaser, Mammar, and Sentouh, 2010;Velenis, Frazzoli, and Tsiotras, 2010;Evangelou, 2004;Grigorievich, Igorevich, and Nikolayevich, 2018;Wasiwitono, Sutantra, and Triwinarno, 2015). ...
Nowadays, PTWV are an increasingly popular means of transport in daily urban and rural displacements, especially for the possibilities it offers to avoid traffic congestion. However, riders are considered as the most vulnerable road users. In fact, the unstable nature of the PTWV makes them more susceptible to loss of control. This problem is even more complex during emergency braking or on cornering. As matter of fact, passive and active safety systems such as Anti-Lock Braking (ABS), Electronic Stability Control (ESP), seat
belts, airbags developed in favour of passenger vehicles have largely contributed to the reduction of risks on the road. However, the delay in the development of security systems for motorcycles is clear. Moreover, despite some existing systems, motorcycle riders use them badly or they don’t at all. Therefore, it is not trivial that this delay, in the development of Advanced Rider Assistance Systems (ARAS), coming from a delay in the development of theoretical and research tools.
