In Kalman filter design, the filter algorithm and prediction model design are the most discussed topics in research. Another fundamental but less investigated issue is the careful selection of measurands and their contribution to the estimation problem. This is often done purely on the basis of empirical values or by experiments. This paper presents a novel holistic method to design and assess Kalman filters in an automated way and to perform their analysis based on quantifiable parameters. The optimal filter parameters are computed with the help of a nonlinear optimization algorithm. To determine and analyze an optimal filter design, two novel quantitative nonlinear observability measures are presented along with a method to quantify the dominance contribution of a measurand to an estimate. As a result, different filter configurations can be specifically investigated and compared with respect to the selection of measurands and their influence on the estimation. An unscented Kalman filter algorithm is used to demonstrate the method’s capabilities to design and analyze the estimation problem parameters. For this purpose, an example of a vehicle state estimation with a focus on the tire-road friction coefficient is used, which represents a challenging problem for classical analysis and filter parameterization.
High-level modeling languages facilitate system modeling and the development of control systems. This is mainly achieved by the automated handling of differential algebraic equations which describe the dynamics of the modeled systems across different physical domains. A wide selection of model libraries provides additional support to the modeling process. Nevertheless, deployment on embedded targets poses a challenge and usually requires manual modification and reimplementation of the control system. The novel proposed eFMI Standard (Functional Mock-up Interface for embedded systems) introduces a workflow and an automated toolchain to simplify the deployment of model-based control systems on embedded targets. This contribution describes the application and verification of the eFMI workflow using a vertical dynamics control problem with an automotive application as an example. The workflow is exemplified by a control system design process which is supported by the a-causal, multi-physical, high-level modeling language Modelica. In this process, the eFMI toolchain is applied to a model-based controller for semi-active dampers and demonstrated using an eFMI-based nonlinear prediction model within a nonlinear Kalman filter. The generated code was successfully tested in different validation steps on the dedicated embedded system. Additionally, tests with a low-volume production electronic control unit (ECU) in a series-produced car demonstrated the correct execution of the controller code under real-world conditions. The novelty of our approach is that it automatically derives an embedded software solution from a high-level multi-physical model with standardized eFMI methodology and tooling. We present one of the first full application scenarios (covering all aspects ranging from multi-physical modeling up to embedded target deployment) of the new eFMI tooling.
Having knowledge about the states of a system is an important component in most control systems. However, an exact measurement of the states cannot always be provided because it is either not technically possible or only possible with a significant effort. Therefore, state estimation plays an important role in control applications. The well-known and widely used Kalman filter is often employed for this purpose. This paper describes the implementation of nonlinear Kalman filter algorithms, the extended and the unscented Kalman filter with square-rooting, in the programming language C, that are suitable for the use on embedded systems. The implementations deal with single or double precision data types depending on the application. The newly implemented filters are demonstrated in the context of semi-active vehicle damper control and the estimation of the tire–road friction coefficient as application examples, providing real-time capability. Their per-formances were evaluated in tests on an electronic control unit and a rapid-prototyping platform.
AI-For-Mobility (AFM) is the new research platform to investigate and implement novel control methods based on Artificial Intelligence (AI) within the Department of Vehicle System Dynamics at the German Aerospace Center (DLR). A production hybrid vehicle serves as a base platform. Since AI-based methods are data-driven, the vehicle is equipped with manifold sensors to provide the required data. They measure the vehicle’s state holistically and perceive the surrounding environment, while high performance on-board CPUs and GPUs handle the sensor data. A full by-wire control system enables the vehicle to be used for applications in the field of automated driving. Despite all modifications, it is approved for public road use and meets the driving dynamics properties of a standard road vehicle. This makes it an attractive research and test platform, both for automotive applications and technology demonstrations in other scientific fields (e.g., robotics, aviation, etc.). This paper presents the vehicle’s design and architecture in a detailed manner and shows a promising application potential of AFM in the context of AI-based control methods.
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