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The real-time simulation of multibody models on embedded systems is of particular interest for controllers and observers such as model predictive controllers and state observers, which rely on a dynamic model of the process and are customarily executed in electronic control units. This work first identifies the software techniques and tools require...
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... As a first application, we will not deal with a particular system but we focus on the feasibility of incorporating symbolic models into embedded systems that are potential candidates for implementing DTs in machines or vehicles. Among the numerous scientific works dealing with multibody models in embedded systems are those by [28] on ARM processors, [46] and [32] on an FPGA, and [13] on ROS with ROBOTRAN. ...
Symbolic generation of multibody systems equations of motion appeared in the 1980s. In addition to their computational advantage over their numerical counterparts, symbolic models can be very easily and straightforwardly interfaced with a wide range of software environments and hardware devices. These two features place this approach in a pole position to participate and intervene in the design of digital twins for systems such as vehicles, manipulators, walking robots or haptic devices.
In this context, the first goal of this paper is to highlight the interest of symbolically generated multibody models – at the root of the ROBOTRAN program – in the form of a standalone set of equations calculating the dynamic model of multibody systems, for use as a computational component within a Digital-Twin-type process. The next goal is to embed realistic and complex multibody models within processes or devices whose functioning requires a synchronized real-time computation – or analysis – of their motion.
An implementation (i) on specific hardware and (ii) on two extremely opposite but revealing applications (namely a railway vehicle and a digital piano) are presented to highlight the usefulness of symbolic models for the development of current and future multibody-based digital twins.
... The computational expenses spent by many existing multibody algorithms are high and usually do not exploit current computer hardware platforms to the extent possible [3]. The mentioned issues imply that researchers pay more and more attention to the development of parallel algorithms and formulations for modeling and analysis of MBS, including real-time simulations, e.g., [4], [5], [6], [7], [8], [9], [10]. ...
Multibody system simulations are increasingly complex for various reasons, including structural complexity, the number of bodies and joints, and many phenomena modeled using specialized formulations. In this paper, an effort is pursued toward efficiently implementing the Hamiltonian-based divide-and-conquer algorithm (HDCA), a highly-parallel algorithm for multi-rigid-body dynamics simulations modeled in terms of canonical coordinates. The algorithm is implemented and executed on a system–on–chip platform which integrates a general-purpose CPU and FPGA. The details of the LDUP factorization, which is used in the HDCA approach and accounts for significant computational load, are presented. Simple planar multibody systems with open- and closed-loop topologies are analyzed to show the correctness of the implementation. Hardware implementation details are provided, especially in the context of inherent parallelism in the HDCA algorithm and linear algebra procedures employed for calculations. The computational performance of the implementation is investigated. The final results show that the FPGA–based multibody system simulations may be executed significantly faster than the analogous calculations performed on a general–purpose CPU. This conclusion is a good premise for various model-based applications, including real-time multibody simulation and control.
... Besides, if one aims to perform an embedded simulation, the hardware is often limited. In this regard, some researches have achieved to run multibody models on other kinds of platforms, such as FPGA [20] or ARM-based systems [21]. In particular, the above-mentioned symbolic approach has been proved to be a good candidate to achieve real-time computation without having to resort to simplifications within the model [22]. ...
Multibody modeling of mechanical systems can be applied to various applications. Human-in-the-loop interfaces represent a growing research field, for which increasingly more devices include a dynamic multibody model to emulate the system physics in real-time. In this scope, reliable and highly dynamic sensors, to both validate those models and to measure in real-time the physical system behavior, have become crucial. In this paper, a multibody modeling approach in relative coordinates is proposed, based on symbolic equations of the physical system. The model is running in a ROS environment, which interacts with sensors and actuators. Two real-time applications with haptic feedback are presented: a piano key and a car simulator. In the present work, several sensors are used to characterize and validate the multibody model, but also to measure the system kinematics and dynamics within the human-in-the-loop process, and to ultimately validate the haptic device behavior. Experimental results for both developed devices confirm the interest of an embedded multibody model to enhance the haptic feedback performances. Besides, model parameters variations during the experiments illustrate the infinite possibilities that such model-based configurable haptic devices can offer.
... The size of the model is selected so that the size of the FPGA does not limit the optimization of the implementations addressed. The MB model is generated using the MBScoder presented in [40], which writes efficiently the minimal amount of code required for the simulation, in an automatic form. ...
New products in the automotive and aerospace industries must provide increased energy efficiency and exceed previous performance, safety and reliability. To meet these expectations, the role of simulation continues to grow.
Within this context, simulation models are used in real-time embedded applications such as advanced real-time control and virtual sensing. Both applications require the execution of simulation models in real-time on embedded hardware. The limited computational power of this hardware is, however, a major challenge in the adoption of model-based embedded applications.
This research explores the use of multibody models for real-time embedded applications. It describes different techniques to accelerate parts or all of the multibody computations on ARM-based and/or FPGA-based hardware.
... It may lead to MB models with more than 100 bodies, each of which needs an accurate definition of constraints, geometry, and mass properties. Although new efficient ECUs have been developed and recent studies tried to achieve real-time (RT) MB simulation of vehicle dynamics in embedded applications [26][27][28], the computation is often too expensive with respect to the limited amount of computational resources of an embedded platform, and it is not always compatible with hard RT constraints. ...
... A new simulation environment was designed and implemented using modern C++ (ISO 17), although we were inspired by an existing simulator [34]. Thanks to the modern object-oriented programming (OOP) paradigm, the proposed simulator offers a modular infrastructure, where code procedures and data are hierarchically grouped and systematically encapsulated into objects [27]. This allows a more effective representation of the increasing level of complexity required from the vehicle industry market. ...
Assessing passenger cars’ dynamic performance is a critical aspect for car industries, due to its impact on the overall vehicle safety evaluation and the subjective nature of the involved handling and comfort metrics. Accordingly, ISO standards, such as ISO 4138 and ISO 3888, define several specific driving tests to assess vehicle dynamics performance objectively. Consequently, proper evaluation of the dynamic behaviour requires measuring several physical quantities, including accelerations, speed, and linear and angular displacements obtained after instrumenting a vehicle with multiple sensors. This experimental activity is highly demanding in terms of hardware costs, and it is also significantly time-consuming. Several approaches can be considered for reducing vehicle development time. In particular, simulation software can be exploited to predict the approximate behaviour of a vehicle using virtual scenarios. Moreover, motion platforms and detail-scalable numerical vehicle models are widely implemented for the purpose. This paper focuses on a customized simulation environment developed in C++, which exploits the advantages of object-oriented programming. The presented framework strives to perform concurrent simulations of vehicles with different characteristics such as mass, tyres, engine, suspension, and transmission systems. Within the proposed simulation framework, we adopted a hierarchical and modular representation. Vehicles are modelled by a 14 degree-of-freedom (DOF) full-vehicle model, capable of capturing the dynamics and complemented by a set of scalable-detail models for the remaining sub-systems such as tyre, engine, and steering system. Furthermore, this paper proposes the usage of autonomous virtual drivers for a more objective evaluation of vehicle dynamic performances. Moreover, to further evaluate our simulator architecture’s efficiency and assess the achieved level of concurrency, we designed a benchmark able to analyse the scaling of the performances with respect to the number of different vehicles during the same simulation. Finally, the paper reports the proposed simulation environment’s scalability resulting from a set of different and varying driving scenarios.
... • An efficient code for executing MB simulations on embedded hardware is required. In [5], a library (MBScoder) for creating MB models for different platforms and programming language was presented. This thesis continues the development of this library in order to add new functionalities useful for this work, such as new MB coordinates and formulations. ...
... As Pastorino et al. presented in [5], one of the first decision is the programming language for writing the code. Although interpreted languages as Matlab or Python reduce the development time, they have low computational efficiency. ...
... In order to reduce the development time of new MB models in a compiled language, automatic programming is proposed in [5]. Automatic programming, increases the level of abstraction for the developer without compromising code efficiency, since only the minimal source code is written. ...
Simulation has become an important tool in the industry that minimizes either the
cost and time of new products development and testing. In the automotive industry,
the use of simulation is being extended to virtual sensing. Through an accurate
model of the vehicle combined with a state estimator, variables that are difficult or
costly to measure can be estimated.
The virtual sensing approach is limited by the low computational power of in-vehicle
hardware due to the strictest timing, reliability and safety requirements
imposed by automotive standards. With the new generation hardware, the computational
power of embedded platforms has increased. They are based on heterogeneous
processors, where the main processor is combined with a co-processor, such as Field
Programmable Gate Arrays (FPGAs).
This thesis explores the implementation of a state estimator based on a multibody
model of a vehicle in new generation embedded hardware. Different implementation
strategies are tested in order to explore the advantages that an FPGA can provide.
A new state-parameter-input observer is developed, providing accurate estimations.
The proposed observer is combined with an efficient multibody model of a vehicle,
achieving real-time execution.
... Accurate and efficient simulations enable considerable reductions in product development cycles, together with savings in prototyping and testing costs. The development of computing technologies in the latest decades has made it possible to extend the simulation of nontrivial engineering systems to real-time (RT) environments [1], including Hardware-in-the-Loop (HiL) and System-in-the-Loop (SITL) setups, in which computer simulations are interfaced to physical components. Such simulation processes often describe multiphysics systems of great complexity, composed by subsystems with very different behavior and physical properties. ...
... The examples included linear electric circuits, nonlinear electronics, and a thermal equivalent model of an electric motor; this last example extends the scope of the proposed testing framework to systems characterized by slow dynamics and time-varying physical properties [25]. The performance of the simulation methods was verified using conventional, off-the-shelf PCs; additionally, they were also tested in ARM processors, with limited computing power and memory, which are currently gaining importance in distributed and non-homogeneous co-simulation applications [1]. ...
Time–domain simulation of electronic and thermal circuits is required by a large array of applications, such as the design and optimization of electric vehicle powertrain components. While efficient execution is always a desirable feature of simulation codes, in certain cases like System-in-the-Loop setups, real-time performance is demanded. Whether real-time code execution can be achieved or not in a particular case depends on a series of factors, which include the mathematical formulation of the equations that govern the system dynamics, the techniques used in code implementation, and the capabilities of the hardware architecture on which the simulation is run. In this work, we present an evaluation framework of numerical methods for the simulation of electronic and thermal circuits from the point of view of their ability to deliver real-time performance. The methods were compared using a set of nontrivial benchmark problems and relevant error metrics. The computational efficiency of the simulation codes was measured under different software and hardware environments, to determine the feasibility of using them in industrial applications with reduced computational power.
... For this reason, real-time or faster-than-real-time simulation of complex closed-loop vehicle systems may not be achievable by existing commercial software packages [1,2] . Performing real-time vehicle simulation has proven to be very challenging, since it involves solving difficult dynamics problems using efficient formulations, algorithms, and system topology structures [3][4][5] . Nowadays, the vehicle real-time simulation is still very challenging in terms of full degree-of-freedom (DOF) multi-body model, affordable laptop, accurate simulation via high-order numerical integration schemes and smaller time-steps, even though the existing commercial software packages have developed their real-time simulation modules. ...
Multibody dynamics of vehicle systems can be simulated in real time using semi-recursive-based formulations and their various versions, which are normally described in terms of relative coordinates. To efficiently and accurately simulate closed-loop vehicle multibody systems, a semi-recursive formulation must be optimally combined with a numerical integration algorithm. Although a significant number of contributions has been reported in this field, there is still a need to improve accuracy and computational efficiency of real-time or faster-than-real-time simulation. This paper focuses on the loop-closure techniques that can be used when modeling vehicle systems. Consequently, a canonical tree topology is introduced to take advantage of recursive kinematics and dynamics. To this end, real-time vehicle simulations are performed based on a semi-recursive formulation and a tree-topology-oriented modeling method. The applied semi-recursive formulation makes use of double velocity transformation and independent coordinates. The introduced canonical tree topology is generated via joint-cut and rod-removal techniques. The structures of the canonical tree topologies are studied in terms of bodies, joints, constraint equations and branches. How they affect solution accuracy and computational efficiency is investigated in detail. For numerical examples, a 15-degree-of-freedom sedan vehicle model is analyzed and simulated using the semi-recursive formulation and a 4th-order Runge–Kutta algorithm in various system-tree topology cases. The results highlight the efficiency gain of the tree-topology-oriented modeling method.
... Moreover, they contain elastic and dissipative force elements with realistic nonlinear stiffness and damping properties to model real components such as shock absorbers and suspension bushings. Although recent studies tried to mitigate the computational burden of executing MB simulations of vehicle dynamics [6,7], the latter are not always compatible with the Real-Time (RT) constraints of vehicle control applications [8,9]. As an alternative, the use of concept models -usually defined by means of a lumped-parameter modelling approach -has been instrumental not only to the early stage design phases, but also as a low-cost counterparts of the corresponding high-fidelity models, especially for targeting more complex online applications such as online force estimation and control [10]. ...
Evaluation of the dynamic performance is mandatory for vehicles to ensure passengers and driver safety. Several types of tests have been defined within specific ISO standards, such as ISO 4138, to reveal key information about vehicle behaviour. These tests are done with instrumented vehicles that allow measuring different physical parameters such as accelerations, speed, angular orientations. Otherwise, complex multibody vehicle models can be used for this purpose but with high computational costs. This paper focuses on vehicle understeering and/or oversteering behaviour evaluation using a virtual Driver-in-the-Loop (vDiL) scheme. The evaluation of lateral dynamic behaviour is achieved using a Real-time (RT) simulation with an efficient 15 Degree of Freedoms (DOFs) lumped-parameter full vehicle model and an autonomous virtual driver based on two PID regulators for speed and steering control. Finally, this paper reports the results of constant steer and constant radius tests as defined by standard ISO4138 and implemented in the proposed models.
... High-fidelity models-of-the-physics are typically described as differential-and algebraic equations and are mostly numerically-intensive models. Running these numerically-intensive models on constrained embedded controllers with limited resources and computational performances can be very challenging or even impossible, especially with hard real-time constraints (Pastorino et al. 2016). Generally, the high-fidelity models need to be transformed to a simpler model which is suited for embedded controller deployment. ...
Modelling and Simulation techniques play a key role in the design of Software-Intensive and Cyber-Physical Systems. They enable not only early virtual integration of the different parts of the system but also the use of the dynamic behavior of the physical system in the control algorithms, to cope with the continuous demand for improved system control and performance. These physics-based high-fidelity models are mostly numerically-intensive that cannot be deployed on restricted embedded targets without altering the model. Altering these high-fidelity models, e.g. by performing mathematical reductions, decreases the model (re-)usability if the range-of-validity of this model is not formally captured. In this paper, we report on a framework to formally capture the range-of-validity of models-of-the-physics. The needed meta-information to grasp the range-of-validity is captured within a Validity Frame, together with the necessary experimenting and selection methods to increase re-use of physics-based system models. An academic case study is performed to demonstrate the proposed methodology.
