Exploring assumptions and requirements for continuous modification of vehicle handling using non-linear optimal control and a new exponential tyre model

An iterative simulation-based nonlinear optimisation technique is used here to explore optimally controlled behaviour of a large RWD vehicle with rear steer and idealised differential actuators. A novel tyre model is also introduced, which uses simple analytic functions for separated calculation of lateral and longitudinal force, with both based on the combined slip and vertical load. By first considering suitable transient and steady-state targets for the yaw rate, optimal control is simulated which is effective throughout the lateral acceleration range. Interestingly this can be closely emulated under stable conditions using PID control of rear steer only, according to the yaw rate target and without the need for separate lateral velocity control. PID is no longer successful when stabilising control is considered, so future research will consider an extension to the nonlinear optimisation method for such cases

Parametric identification of vehicle handling using an extended Kalman filter

This paper considers a novel method for estimating parameters in a vehicle handling dynamic model using a recursive filter. The well known extended Kalman filter – which is widely used for real-time state estimation of vehicle dynamics – is used here in an unorthodox fashion; a model is prescribed for the sensors alone, and the state vector is replaced by a set of unknown model parameters. With the aid of two simple tuning parameters, the system self-regulates its estimates of parameter and sensor errors, and hence smoothly identifies optimal parameter choices. In a linear-in-the-parameters example, the results are shown to be comparable to least-squares identification, but the system works equally well for the more general nonlinear handling model examples, and should be well suited to any smoothly nonlinear system. Moreover, it is shown that by simple adjustment of the tuning parameters the filter can operate in a real-time capacity

Real-time characterisation of driver steering behaviour

In recent years the application of driver steering models has extended from the off-line simulation environment to autonomous vehicles research and the support of driver assistance systems. For these new environments there is a need for the model to be adaptive in real-time, so the supporting vehicle systems can react to changes in the driver, their driving style, mood and skill. This paper provides a novel means to meet these needs by combining a simple driver model with a single track vehicle handling model in a parameter estimating filter – in this case an Unscented Kalman Filter. Although the steering model is simple, a motion simulator study shows it is capable of characterising a range of driving styles and may also indicate the level of skill of the driver. The resulting filter is also efficient – comfortably operating faster than real-time – and it requires only steer and speed measurements from the vehicle in addition to reference path. Adaptation of the steer model parameters is demonstrated along with robustness of the filter to errors in initial conditions, using data from five test drivers in vehicle tests carried out on the open road

A new empirical 'exponential' tyre model

In this paper, a new and simple formula is presented for empirical modelling of tyre force data. Based on exponential functions, it is capable of matching single slip data for lateral or longitudinal forces using three parameters, which can be computed in terms of stiffness, peak and saturated force values. Through a factorial study, the three parameters are also reformulated into functions of load and slip to provide full mapping of Fx and Fy across the range of longitudinal slip, lateral slip and vertical load. Signifi cantly, the resulting model does not rely on a total slip calculation, so it retains a simple structure in force vs. slip or load derivatives. The new model is compared with two alternative simple tyre models and is shown to map forces generated from a reference Pacejka model. It is also used to fit measured tyre force data accurately

Identifying tyre models directly from vehicle test data using an extended Kalman filter

Individual tyre models are traditionally derived from component tests, with their parameters matched to force and slip measurements. They are imported into vehicle models which should, but do not always properly provide suspension geometry interaction. Recent advances in Global Positioning System (GPS)/inertia vehicle instrumentation now make full state measurement viable in test vehicles, so tyre slip behaviour is directly measurable. This paper uses an extended Kalman filter for system identification, to derive individual load-dependent tyre models directly from these test vehicle state measurements. The resulting model therefore implicitly compensates for suspension geometry and compliance. The paper looks at two variants of the tyre model, and also considers real-time adaptation of the model to road surface friction variations. Test vehicle results are used exclusively, and the results show successful tyre model identification, improved vehicle model state prediction – particularly in lateral velocity reproduction – and an effective real-time solution for road friction estimation

Linear MIMO model identification using an extended Kalman filter

Linear Multi-Input Multi-Output (MIMO) dynamic models can be identified, with no a priori knowledge of model structure or order, using a new Generalised Identifying Filter (GIF). Based on an Extended Kalman Filter, the new filter identifies the model iteratively, in a continuous modal canonical form, using only input and output time histories. The filter’s self-propagating state error covariance matrix allows easy determination of convergence and conditioning, and by progressively increasing model order, the best fitting reduced-order model can be identified. The method is shown to be resistant to noise and can easily be extended to identification of smoothly nonlinear systems

A simple realistic driver model

Many of the published driver models concentrate on algorithms which achieve accurate path following at the expense of realistic replication of the driving task itself. In this paper we consider only the most basic driving responses, to achieve a simple yet surprisingly realistic driver model. Lateral control is based on steering corrections aimed at projecting the vehicle onto a path at a single preview point on the road ahead. Only the preview time and a single proportional gain are required parameters, supported by a basic approximation of understeer gradient which becomes proressively more important as desired lateral acceleration increases. The longitudinal model regulates speed solely in proportion to an estimate of the length of road the driver can see ahead. Both aspects of the model are executed in a computationally efficient way, using the simplest possible definition of a track. The model is tested for robustness in simulation, and it gives intuitively sensible responses. Results are then given in comparison to vehicle tests, with the longitudinal parameters tuned to match the measured driving behaviour of two test subjects, while nominal lateral parameters are shown to be effective. Finally, the model is also shown to be capable of reasonable, if approximate prediction of speed variations for the same test drivers on an independent section of road

Optimisation of high-speed crash avoidance in autonomous vehicles

In the context of a future scenario of autonomous vehicle platooning, this paper considers the optimisation of a vehicle's standard brake, acceleration and steering control inputs, for collision avoidance. We consider the case where escape into the neighbouring lane is feasible. An iterative simulation-based method is used, which allows vehicle parameters to be optimised simultaneously; this also allows us to find the best vehicle handling balance for such a manoeuvre and to quantify the cost of suboptimal design. The paper also considers the relative advantages of speed reduction in conjunction with rapid lane change. The goal here is to quantify the best possible vehicle escape manoeuvre and the relative cost of alternative strategies. The paper does not provide an immediately practicable controller, but simple open-loop approximation of the optimal controls suggests a route towards future real-time solution

Structure optimisation of input layer for feed-forward NARX neural network

This paper presents an optimization method for reducing the number of input channels and the complexity of the feed-forward NARX neural network (NN) without compromising the accuracy of the NN model. By utilizing the correlation analysis method, the most significant regressors are selected to form the input layer of the NN structure. Applications of vehicle handling and ride model identification are presented in this paper to demonstrate the optimization technique. The optimal input layer structure and the optimal number of neurons for the NN models are investigated and the results show that the optimised NN model requires significantly less coefficients and training time while maintains high simulation accuracy compared with that of the unoptimised model

On-line PID tuning for engine idle-speed control using continuous action reinforcement learning automata

PID systems are widely used to apply control without the need to obtain a dynamic model. However, the performance of controllers designed using standard on-line tuning methods, such as Ziegler-Nichols, can often be significantly improved. In this paper the tuning process is automated through the use of continuous action reinforcement learning automata (CARLA). These are used to simultaneously tune the parameters of a three term controller on-line to minimise a performance objective. Here the method is demonstrated in the context of engine idle speed control; the algorithm is first applied in simulation on a nominal engine model, and this is followed by a practical study using a Ford Zetec engine in a test cell. The CARLA provides marked performance benefits over a comparable Ziegler-Nichols tuned controller in this application