Notation for the single track model, forces in the picture are expressed in the vehicles coordinate system. 

Contexts in source publication

Context 1

... a vehicle e.g. in this brakes, paper. a Further, portion of a novel the vehicles threat assessment weight is shifted approach to the is front presented and consequently in section IV and the experimental friction force results at the in front section wheels V. is increased while the force at the rear wheels decreases. Likewise weight is redistributed laterally during cornering causing the tyre forces at one side to increase while they are decreased at the other. All this affects the vehicles behaviour and the vehicle might either get into under- or oversteer. From a normal drivers point of view, the vehicle is perceived to turn less than the driver intended with his steering input in an understeer situation and more than intended in an oversteer situation. For a thorough explanation of the terms see e.g. [6]. Whether a vehicle tends to go into over- or understeer is sometimes discussed as a vehicle property. One parameter that has influence on a vehicles behaviour is e.g. whether II. L OSS OF C ONTROL In which situations a driver feels that he has lost control of his vehicle is of course highly dependant on the skills of the driver. An experienced driver in a race might e.g. intentionally create a skid and immediately correct the skid once the vehicle has performed the intended maneuver. In general however it can be stated that maneuverability of a vehicle is dramatically decreased when the vehicle is driven close to the limit of adhesion between tyre and road [4]. In such situations the relation between the drivers input and the forces generated at the tyres contact patch is highly nonlinear making the vehicles response difficult for a driver to predict [5]. In addition, the weight of a vehicle is redistributed when a vehicle undertakes a powerful maneuver. When a vehicle e.g. brakes, a portion of the vehicles weight is shifted to the front and consequently the friction force at the front wheels is increased while the force at the rear wheels decreases. Likewise weight is redistributed laterally during cornering causing the tyre forces at one side to increase while they are decreased at the other. All this affects the vehicles behaviour and the vehicle might either get into under- or oversteer. From a normal drivers point of view, the vehicle is perceived to turn less than the driver intended with his steering input in an understeer situation and more than intended in an oversteer situation. For a thorough explanation of the terms see e.g. [6]. Whether a vehicle tends to go into over- or understeer is sometimes discussed as a vehicle property. One parameter that has influence on a vehicles behaviour is e.g. whether the vehicle III. C is ONVENTIONAL driven by the Y front AW or S TABILITY the rear wheels. C ONTROL It is e.g. well Yaw known stability that with control throttle systems on, a have front been wheel commercially driven car is available more likely since to end the up 1990s, in understeer [7]. The [6]. main idea is that the nonlinear Even if behaviour the vehicle of a properties vehicle in plays highly a dynamic big role, situations also the is drivers too difficult behaviour for has a driver influence to handle on whether or understand the vehicle and goes that he into therefore under- or needs oversteer. some kind Consider of assistance a driver in in such a front situations. wheel driven car entering a curve in high speed. If the driver when realizing that he is driving too fast panics, he might e.g suddenly release the gas pedal and make a powerful turn. This will most likely put the vehicle in oversteer. Over and understeer situations is a result of vehicle states, vehicle properties and driver behaviour. When the over or understeer becomes large enough, drivers are normally disturbed. As the over or understeer grows and becomes more evident a normal driver will feel that he is not able to control his vehicle. If the vehicle is equipped with a yaw stability control system it will issue an intervention that assists the driver and helps him regain control. These situations occur when the vehicle is operated in the region where the tyre forces nonlinear characteristics become evident. Such situations, in which maneuverability of the vehicle is reduced are referred to in this paper as situations where the driver has lost control. This means that in a situation where the vehicle is driven in the nonlinear region of the tyres, the driver is considered to have lost control, even if the driver is skilled and has intentionally provoked the situation. III. C ONVENTIONAL Y AW S TABILITY C ONTROL Yaw stability control systems have been commercially available since the 1990s, [7]. The main idea is that the nonlinear behaviour of a vehicle in highly dynamic situations is too difficult for a driver to handle or understand and that he therefore needs some kind of assistance in such situations. Loss of control can be identified by e.g. considering the vehicle slip angle β . The slip angle is illustrated in figure 1 and is defined as the angle of the velocity vector in the vehicles coordinate system. If β is large, turning the steering wheel will create little or no yaw moment on the vehicle, [8][9]. The possibility to control the vehicle through the steering wheel will then be limited. One of the main tasks of a yaw stability control system is thus to make sure that the slip angle remains low. How low it needs to be depends on available friction, in general it can be said that a higher slip angle can be allowed if much friction is available. Unfortunately it is not possible to measure the slip angle with sensors available in conventional vehicles. Estimation algorithms can be good in special conditions like e.g. during full braking, however in the general case, estimation of the slip angle can be quite uncertain [8]. Another measure is therefore introduced that considers the vehicles yaw rate to identify when the driver has lost control and needs assistance [8][9]. This measure, or the threat assessment and control prin- ciple that is based on it can be viewed in different ways. In e.g. [10] the threat assessment is explained as a comparison between the vehicles actual trajectory and an interpretation of the trajectory that the driver intends to follow. If the difference between the drivers intentions and the vehicles actual movement becomes too large the system decides to assist the driver in following the intended trajectory. Interpretation of the drivers intentions is done by feeding the drivers input, i.e. steering angle through a simplified vehicle model with the assumption that it corresponds to the drivers perception of a vehicles behaviour. With this view, one can say that the control system aims at making the car follow the drivers intentions. Another perspective of the same procedure is presented in e.g. [11]. The assumption is again that the complex and nonlinear nature of a vehicle is difficult for a driver to handle. In extreme situations, a driver will therefore be unable to predict how the vehicle will respond to his inputs. By making the vehicle act according to the simplified vehicle model, it is assumed that the vehicles simplified behaviour will make the driver find it easier to predict how the vehicle will respond to his inputs. With this view one can say that the control system makes the vehicle easier to maneuver and reduces the risk that the vehicle runs of the road due to loss of control. The simplified vehicle model that is used to compute the intended- or reference trajectory is a single track model and is illustrated in figure 1, [8][10][9]. The dynamic equations of motion for the single track model ...

Context 2

... One parameter that has influence on a vehicles behaviour is e.g. whether the vehicle III. C is ONVENTIONAL driven by the Y front AW or S TABILITY the rear wheels. C ONTROL It is e.g. well Yaw known stability that with control throttle systems on, a have front been wheel commercially driven car is available more likely since to end the up 1990s, in understeer [7]. The [6]. main idea is that the nonlinear Even if behaviour the vehicle of a properties vehicle in plays highly a dynamic big role, situations also the is drivers too difficult behaviour for has a driver influence to handle on whether or understand the vehicle and goes that he into therefore under- or needs oversteer. some kind Consider of assistance a driver in in such a front situations. wheel driven car entering a curve in high speed. If the driver when realizing that he is driving too fast panics, he might e.g suddenly release the gas pedal and make a powerful turn. This will most likely put the vehicle in oversteer. Over and understeer situations is a result of vehicle states, vehicle properties and driver behaviour. When the over or understeer becomes large enough, drivers are normally disturbed. As the over or understeer grows and becomes more evident a normal driver will feel that he is not able to control his vehicle. If the vehicle is equipped with a yaw stability control system it will issue an intervention that assists the driver and helps him regain control. These situations occur when the vehicle is operated in the region where the tyre forces nonlinear characteristics become evident. Such situations, in which maneuverability of the vehicle is reduced are referred to in this paper as situations where the driver has lost control. This means that in a situation where the vehicle is driven in the nonlinear region of the tyres, the driver is considered to have lost control, even if the driver is skilled and has intentionally provoked the situation. III. C ONVENTIONAL Y AW S TABILITY C ONTROL Yaw stability control systems have been commercially available since the 1990s, [7]. The main idea is that the nonlinear behaviour of a vehicle in highly dynamic situations is too difficult for a driver to handle or understand and that he therefore needs some kind of assistance in such situations. Loss of control can be identified by e.g. considering the vehicle slip angle β . The slip angle is illustrated in figure 1 and is defined as the angle of the velocity vector in the vehicles coordinate system. If β is large, turning the steering wheel will create little or no yaw moment on the vehicle, [8][9]. The possibility to control the vehicle through the steering wheel will then be limited. One of the main tasks of a yaw stability control system is thus to make sure that the slip angle remains low. How low it needs to be depends on available friction, in general it can be said that a higher slip angle can be allowed if much friction is available. Unfortunately it is not possible to measure the slip angle with sensors available in conventional vehicles. Estimation algorithms can be good in special conditions like e.g. during full braking, however in the general case, estimation of the slip angle can be quite uncertain [8]. Another measure is therefore introduced that considers the vehicles yaw rate to identify when the driver has lost control and needs assistance [8][9]. This measure, or the threat assessment and control prin- ciple that is based on it can be viewed in different ways. In e.g. [10] the threat assessment is explained as a comparison between the vehicles actual trajectory and an interpretation of the trajectory that the driver intends to follow. If the difference between the drivers intentions and the vehicles actual movement becomes too large the system decides to assist the driver in following the intended trajectory. Interpretation of the drivers intentions is done by feeding the drivers input, i.e. steering angle through a simplified vehicle model with the assumption that it corresponds to the drivers perception of a vehicles behaviour. With this view, one can say that the control system aims at making the car follow the drivers intentions. Another perspective of the same procedure is presented in e.g. [11]. The assumption is again that the complex and nonlinear nature of a vehicle is difficult for a driver to handle. In extreme situations, a driver will therefore be unable to predict how the vehicle will respond to his inputs. By making the vehicle act according to the simplified vehicle model, it is assumed that the vehicles simplified behaviour will make the driver find it easier to predict how the vehicle will respond to his inputs. With this view one can say that the control system makes the vehicle easier to maneuver and reduces the risk that the vehicle runs of the road due to loss of control. The simplified vehicle model that is used to compute the intended- or reference trajectory is a single track model and is illustrated in figure 1, [8][10][9]. The dynamic equations of motion for the single track model ...

Context 3

... J z is the vehicles moment of inertia in the yaw direction, m is the vehicle mass and the rest of the parameters are defined in figure 1. The lateral tyre forces at each tyre are approximated to be linearly related to the tyre slip angle according ...