Matt C. Best

An Extended Adaptive Kalman Filter for Real-time State Estimation of Vehicle Handling Dynamics

This paper considers a method for estimating vehicle handling dynamic states in real-time, using a reduced sensor set; the information is essential for vehicle handling stability control and is also valuable in chassis design evaluation. An extended (nonlinear) Kalman filter is designed to estimate the rapidly varying handling state vector. This employs a low order (4 DOF) handling model which is augmented to include adaptive states (cornering stiffnesses) to compensate for tyre force nonlinearities. The adaptation is driven by steer-induced variations in the longitudinal vehicle acceleration. The observer is compared with an equivalent linear, model-invariant Kalman filter. Both filters are designed and tested against data from a high order source model which simulates six degrees of freedom for the vehicle body, and employs a combined-slip Pacejka tyre model. A performance comparison is presented, which shows promising results for the extended filter, given a sensor set comprising three accelerometers only. The study also presents an insight into the effect of correlated error sources in this application, and it concludes with a discussion of the new observers practical viability.

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

Abstract 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.

A comparison of braking and differential control of road vehicle yaw-sideslip dynamics

Abstract Two actuation mechanisms are considered for the comparison of performance capabilities in improving the yaw-sideslip handling characteristics of a road vehicle. Yaw moments are generated either by the use of single-wheel braking or via driveline torque distribution using an overdriven active rear differential. For consistency, a fixed reference vehicle system is used, and the two controllers are synthesized via a single design methodology. Performance measures relate to both open-loop and closed-loop driving demands, and include both on-centre and limit handling manoeuvres.

AN AUTOMATED DRIVER BASED ON CONVERGENT VECTOR FIELDS

Abstract This paper describes a new general framework for the action of an automated driver (or driver model) to provide the control of longitudinal and lateral dynamics of a road vehicle. The context of the problem is assumed to be in high-speed competitive driving, as in motor racing, where the requirement is for maximum possible speed along a track, making use of a reference path (racing line) but with the capacity for obstacle avoidance and recovery from large excursions. While not necessarily representative of a human driver, the analysis provides worthwhile insight into the nature of the driving task and offers a new approach for vehicle lateral and longitudinal control; it also has applications in less demanding applications such as Advanced Cruise Control systems. As is common in the literature, the driving task is broken down into two distinct subtasks: path planning and local feedback control. In the first of these tasks, an essentially geometric approach is taken here, which makes use of a vector field analysis. At each location x the automated driver is to prescribe a vector w for the desired vehicle mass centre velocity; the spatial distribution and global properties of w(x) provide essential information for stability analysis, as well as control reference. The resulting vector field is considered in the context of limited friction and limited mass centre accelerations, leading to constraints on ∇w. Provided such constraints are satisfied, and using suitable adaptation of w(x) when required, it is shown that feedback control can be applied to guarantee stable asymptotic tracking of a reference path, even under limit handling conditions. A specific implementation of the method is included, using dual non-linear SISO (single-input single-output) controllers.

Yaw motion control via active differentials

The majority of vehicle dynamics control systems currently in production utilize some form of brake or throttle intervention to generate a yaw moment and control wheel slip. Such control systems can be both intrusive and inefficient. The use of active driveline technology is therefore an attractive alternative and recent advances in controlled differential technology have served to make it a potentially viable one. Using simulation results, this paper will demonstrate the power of these devices to influence vehicle dynamics by first proposing a suitable control strategy. This is then used to illustrate how, with perfect actuation, a vehicles handling characteristics may be modified. The actuator limitations imposed by the two main classes of contemporary controlled differentials are then discussed and imposed on the simulation model. Using the ideal results as a benchmark, the relative merits of each type are then assessed.

The identifying extended Kalman filter: parametric system identification of a vehicle handling model

Abstract This article 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. The method makes one contentious assumption that vehicle lateral velocity (or body sideslip angle) is available as a measurement, along with the more conventionally available yaw velocity state. However, the article demonstrates that by using the new generation of combined GPS/inertial body motion measurement systems, a suitable lateral velocity signal is indeed measurable. The system identification is thus demonstrated in simulation, and also proved by successful parametrization of a model, using test vehicle data. The identifying extended Kalman filter has applications in model validation - for example, acting as a reference between vehicle behaviour and higher-order multi-body models - and it could also be operated in a real-time capacity to adapt parameters in model-based vehicle control applications.

A parameter identifying a Kalman filter observer for vehicle handling dynamics

Abstract The paper presents a method for designing a non-linear (i.e. extended) Kalman filter that is also parameter adaptive and hence capable of online identification of its model. The filter model is deliberately simple in structure and low order, yet includes non-linear, load-varying tyre force calculations to ensure accuracy over a range of test conditions. Shape parameters within the (Pacejka) tyre model are adapted rapidly in real time, to maintain excellent state reconstruction accuracy, and provide valuable real-time lateral and vertical tyre force information. The filter is tested in both simulated and test vehicle environments and provides good results. The paper also provides an illustration of the importance of good Kalman filter design practice in terms of selection and tuning of the noise matrices, particularly in terms of the influence of model/sensor error cross-correlations.

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.

Comparison between Kalman Filter and Robust Filter for Vehicle Handling Dynamics State Estimation

This paper explores design methods for a vehicle handling dynamics state estimator based on a linear vehicle model. The state estimator is needed because there are some states of the vehicle that cannot be measured directly, such as sideslip velocity, and also some which are relatively expensive to measure, such as roll and yaw rates. Information about the vehicle states is essential for vehicle handling stability control and is also valuable in chassis design evaluation. The aim of this study is to compare the performance of a Kalman filter with that of a robust filter, under conditions which would be realistic and viable for a production vehicle. Both filters are thus designed and tested with reference to a higher order source model which incorporates nonlinear saturating tyre force characteristics. Also, both filters rely solely on accelerometer sensors, which are simulated with expected noise characteristics in terms of amplitude and spectra. As is widely known, the Kalman filter is a stochastic filter whose design depends on the nominal vehicle model and statistical information of process and measurement noises. By contrast, the robust filter is deterministic, formulated in terms of model parameter uncertainties and the expected gain of process and measurement noises. The objective of both filter designs is to minimise the variance of the estimation error. Both filters are designed to compensate the vehicle model non-linearities, parameter uncertainties and other modeling errors, which are represented in terms of process and measurement noise covariances in Kalman filter design and in terms of additive model uncertainties in robust filter design. The study shows that the robust filter offers higher performance potential. The work concludes with a discussion on the practical realisation of each method, and gives recommendations for further research into a single design methodology which combines the benefits of both approaches.

Model predictive driving simulator motion cueing algorithm with actuator-based constraints

The simulator motion cueing problem has been considered extensively in the literature; approaches based on linear filtering and optimal control have been presented and shown to perform reasonably well. More recently, model predictive control (MPC) has been considered as a variant of the optimal control approach; MPC is perhaps an obvious candidate for motion cueing due to its ability to deal with constraints, in this case the platform workspace boundary. This paper presents an MPC-based cueing algorithm that, unlike other algorithms, uses the actuator positions and velocities as the constraints. The result is a cueing algorithm that can make better use of the platform workspace whilst ensuring that its bounds are never exceeded. The algorithm is shown to perform well against the classical cueing algorithm and an algorithm previously proposed by the authors, both in simulation and in tests with human drivers.