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  • 1.
    Berntorp, Karl
    et al.
    Lund University, Sweden.
    Olofsson, Bjorn
    Lund University, Sweden.
    Lundahl, Kristoffer
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Nielsen, Lars
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Models and methodology for optimal trajectory generation in safety-critical road-vehicle manoeuvres2014In: Vehicle System Dynamics, ISSN 0042-3114, E-ISSN 1744-5159, Vol. 52, no 10, p. 1304-1332Article in journal (Refereed)
    Abstract [en]

    There is currently a strongly growing interest in obtaining optimal control solutions for vehicle manoeuvres, both in order to understand optimal vehicle behaviour and, perhaps more importantly, to devise improved safety systems, either by direct deployment of the solutions or by including mimicked driving techniques of professional drivers. However, it is non-trivial to find the right combination of models, optimisation criteria, and optimisation tools to get useful results for the above purposes. Here, a platform for investigation of these aspects is developed based on a state-of-the-art optimisation tool together with adoption of existing vehicle chassis and tyre models. A minimum-time optimisation criterion is chosen for the purpose of gaining an insight into at-the-limit manoeuvres, with the overall aim of finding improved fundamental principles for future active safety systems. The proposed method to trajectory generation is evaluated in time-manoeuvres using vehicle models established in the literature. We determine the optimal control solutions for three manoeuvres using tyre and chassis models of different complexities. The results are extensively analysed and discussed. Our main conclusion is that the tyre model has a fundamental influence on the resulting control inputs. Also, for some combinations of chassis and tyre models, inherently different behaviour is obtained. However, certain variables important in vehicle safety-systems, such as the yaw moment and the body-slip angle, are similar for several of the considered model configurations in aggressive manoeuvring situations.

  • 2.
    Berntorp, Karl
    et al.
    Department of Automatic Control, Lund University, Lund, Sweden.
    Olofsson, Björn
    Department of Automatic Control, Lund University, Lund, Sweden.
    Lundahl, Kristoffer
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Bernhardsson, Bo
    Department of Automatic Control, Lund University, Lund, Sweden.
    Nielsen, Lars
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Models and Methodology for Optimal Vehicle Maneuvers Applied to a Hairpin Turn2013Conference paper (Other academic)
    Abstract [en]

    There is currently a strongly growing interest in obtaining optimal control solutions for vehicle maneuvers, both in order to understand optimal vehicle behavior and to devise improved safety systems, either by direct deployment of the solutions or by including mimicked driving techniques of professional drivers. However, it is nontrivial to find the right mix of models, formulations, and optimization tools to get useful results for the above purposes. Here, a platform is developed based on a stateof-the-art optimization tool together with adoption of existing vehicle models, where especially the tire models are in focus. A minimum-time formulation is chosen to the purpose of gaining insight in at-the-limit maneuvers, with the overall aim of possibly finding improved principles for future active safety systems. We present optimal maneuvers for different tire models with a common vehicle motion model, and the results are analyzed and discussed. Our main result is that a few-state singletrack model combined with different tire models is able to replicate the behavior of experienced drivers. Further, we show that the different tire models give quantitatively different behavior in the optimal control of the vehicle in the maneuver.

  • 3.
    Lundahl, Kristoffer
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Modeling and Optimization for Critical Vehicle Maneuvers2013Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    As development in sensor technology, situation awareness systems, and computational hardware for vehicle systems progress, an opportunity for more advanced and sophisticated vehicle safety-systems arises. With the increased level of available information---such as position on the road, road curvature and knowledge about surrounding obstacles---future systems could be seen utilizing more advanced controls, exploiting at-the-limit behavior of the vehicle. Having this in mind, optimization methods have emerged as a powerful tool for offline vehicle-performance evaluation, providing inspiration to new control strategies, and by direct implementation in on-board systems. This will, however, require a careful choice of modeling and objectives, since the solution to the optimization problem will rely on this.

    With emphasis on vehicle modeling for optimization-based maneuvering applications, a vehicle-dynamics testbed has been developed. Using this vehicle in a series of experiments, most extensively in a double lane-change maneuver, verified the functionality and capability of the equipment. Further, a comparative study was performed, considering vehicle models based on the single-track model, extended with, e.g., tire-force saturation, tire-force lag and roll dynamics. The ability to predict vehicle behavior was evaluated against measurement data from the vehicle testbed.

    A platform for solving vehicle-maneuvering optimization-problems has been developed, with state-of-the-art optimization tools, such as JModelica.org and Ipopt. This platform is utilized for studies concerning the influence different vehicle-model configurations have on the solution to critical maneuvering problems. In particular, different tire modeling approaches, as well as vehicle-chassis models of various complexity, are investigated. Also, the influence different road-surface conditions-e.g., asphalt, snow and ice-have on the solution to time-optimal maneuvers is studied.

    The results show that even for less complex models-such as a single-track model with a Magic Formula based tire-model-accurate predictions can be obtained when compared to measurement data. The general observation regarding vehicle modeling for the time-critical maneuvers is similar; even the least complex models can be seen to capture certain characteristics analogous to those of higher complexity.

    Analyzing the results from the optimization problems, it is seen that the overall dynamics, such as resultant forces and yaw moment, obtained for different model configurations, correlates very well. For different road surfaces, the solutions will of course differ due to the various levels of tire-forces being possible to realize. However, remarkably similar vehicle paths are obtained, regardless of surface. These are valuable observations, since they imply that models of less complexity could be utilized in future on-board optimization-algorithms, to generate, e.g., yaw moment and vehicle paths. In combination with additional information from enhanced situation-awareness systems, this enables more advanced safety-systems to be considered for future vehicles.

    List of papers
    1. Vehicle dynamics platform, experiments, and modeling aiming at critical maneuver handling
    Open this publication in new window or tab >>Vehicle dynamics platform, experiments, and modeling aiming at critical maneuver handling
    2013 (English)Report (Other academic)
    Abstract [en]

    For future advanced active safety systems, in road-vehicle applications, there will arise possibilities for enhanced vehicle control systems, due to refinements in, e.g., situation awareness systems. To fully utilize this, more extensive knowledge is required regarding the characteristics and dynamics of vehicle models employed in these systems. Motivated by this, an evaluative study for the lateral dynamics is performed, considering vehicle models of more simple structure. For this purpose, a platform for vehicle dynamics studies has been developed. Experimental data, gathered with this testbed, is then used for model parametrization, succeeded by evaluation for an evasive maneuver. The considered model configurations are based on the single-track model, with different additional attributes, such as tire-force saturation, tire-force lag, and roll dynamics. The results indicate that even a basic model, such as the single-track with tire-force saturation, can describe the lateral dynamics surprisingly well for this critical maneuver.

    Place, publisher, year, edition, pages
    Linköping: Linköping University Electronic Press, 2013. p. 22
    Series
    LiTH-ISY-R, ISSN 1400-3902 ; 3064
    National Category
    Engineering and Technology
    Identifiers
    urn:nbn:se:liu:diva-94203 (URN)LiTH-ISY-R-3064 (ISRN)
    Available from: 2013-06-18 Created: 2013-06-18 Last updated: 2017-01-27Bibliographically approved
    2. Models and Methodology for Optimal Vehicle Maneuvers Applied to a Hairpin Turn
    Open this publication in new window or tab >>Models and Methodology for Optimal Vehicle Maneuvers Applied to a Hairpin Turn
    Show others...
    2013 (English)Conference paper, Published paper (Other academic)
    Abstract [en]

    There is currently a strongly growing interest in obtaining optimal control solutions for vehicle maneuvers, both in order to understand optimal vehicle behavior and to devise improved safety systems, either by direct deployment of the solutions or by including mimicked driving techniques of professional drivers. However, it is nontrivial to find the right mix of models, formulations, and optimization tools to get useful results for the above purposes. Here, a platform is developed based on a stateof-the-art optimization tool together with adoption of existing vehicle models, where especially the tire models are in focus. A minimum-time formulation is chosen to the purpose of gaining insight in at-the-limit maneuvers, with the overall aim of possibly finding improved principles for future active safety systems. We present optimal maneuvers for different tire models with a common vehicle motion model, and the results are analyzed and discussed. Our main result is that a few-state singletrack model combined with different tire models is able to replicate the behavior of experienced drivers. Further, we show that the different tire models give quantitatively different behavior in the optimal control of the vehicle in the maneuver.

    National Category
    Engineering and Technology
    Identifiers
    urn:nbn:se:liu:diva-94204 (URN)
    Conference
    The 2013 American Control Conference, June 17-19, Washington, DC, USA
    Available from: 2013-06-18 Created: 2013-06-18 Last updated: 2013-06-18Bibliographically approved
    3. Studying the Influence of Roll and Pitch Dynamics in Optimal Road-Vehicle Maneuvers
    Open this publication in new window or tab >>Studying the Influence of Roll and Pitch Dynamics in Optimal Road-Vehicle Maneuvers
    Show others...
    2013 (English)Conference paper, Published paper (Other academic)
    Abstract [en]

    A comparative analysis shows how vehicle motion models of different complexity, capturing various characteristics, influence the solution when used in time-critical optimal maneuvering problems. Vehicle models with combinations of roll and pitch dynamics as well as load transfer are considered, ranging from a single-track model to a double-track model with roll and pitch dynamics and load transfer. The optimal maneuvers in a 90◦-turn and a double lane-change scenario are formulated as minimum-time optimization problems, and are solved using numerical optimization software. The results obtained with the different models show that variables potentially important for safety systems, such as the yaw rate, slip angle, and geometric path, are qualitatively the same. Moreover, the numeric differences are mostly within a few percent. The results also indicate that although input torques differ about 50–100 % for certain parts of the maneuver between the most and least complex model considered, the resulting vehicle motions obtained are similar, irrespective of the model. Our main conclusion isthat this enables the use of low-order models when designing the onboard optimization-based safety systems of the future.

    National Category
    Engineering and Technology
    Identifiers
    urn:nbn:se:liu:diva-94205 (URN)
    Conference
    The 23rd International Symposium on Dynamics of Vehicles on Roads and Tracks, 19-23 August, Qingdao, China
    Available from: 2013-06-18 Created: 2013-06-18 Last updated: 2013-06-18Bibliographically approved
    4. An Investigation of Optimal Vehicle Maneuvers for Different Road Conditions
    Open this publication in new window or tab >>An Investigation of Optimal Vehicle Maneuvers for Different Road Conditions
    2013 (English)In: IFAC Proceedings Volumes, Volume 46, Issue 21, International Federation of Automatic Control , 2013, Vol. 46, p. 66-71Conference paper, Published paper (Refereed)
    Abstract [en]

    We investigate optimal maneuvers for road-vehicles on different surfaces such as asphalt, snow, and ice. The study is motivated by the desire to find control strategies for improved future vehicle safety and driver assistance technologies. Based on earlier presented measurements for tire-force characteristics, we develop tire models corresponding to different road conditions, and determine the time-optimal maneuver in a hairpin turn for each of these. The obtained results are discussed and compared for the different road characteristics. Our main findings are that there are fundamental differences in the control strategies on the considered surfaces, and that these differences can be captured with the adopted modeling approach. Moreover, the path of the vehicle center-of-mass was found to be similar for the different cases. We believe that these findings imply that there are observed vehicle behaviors in the results, which can be utilized for developing the vehicle safety systems of tomorrow.

    Place, publisher, year, edition, pages
    International Federation of Automatic Control, 2013
    Series
    IFAC Proceedings Volumes, ISSN 1474-6670 ; Volume 47, Issue 3
    National Category
    Engineering and Technology
    Identifiers
    urn:nbn:se:liu:diva-94206 (URN)10.3182/20130904-4-JP-2042.00007 (DOI)978-3-902823-48-9 (ISBN)
    Conference
    7th IFAC Symposium on Advances in Automotive Control. The International Federation of Automatic Control, September 4-7, 2013. Tokyo, Japan
    Available from: 2013-06-18 Created: 2013-06-18 Last updated: 2016-05-25Bibliographically approved
  • 4.
    Lundahl, Kristoffer
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Models and Critical Maneuvers for Road Vehicles2016Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    As manufacturers are pushing their research and development toward more simulation based and computer aided methods, vehicle dynamics modeling and simulation become more important than ever. The challenge lies in how to utilize the new technology to its fullest, delivering the best possible performance given certain objectives and current restrictions. Here, optimization methods in different forms can be a tremendous asset. However, the solution to an optimization problem will always rely on the problem formulation, where model validity plays a crucial role. The main emphasis in this thesis lies within methodology and analysis of optimal control oriented topics for safety-critical road-vehicle maneuvers. A crucial element here is the vehicle models. This is investigated as a first study, evaluating the degree to which different model configurations can represent the lateral vehicle dynamics in critical maneuvers, where it is shown that even the low-complexity models describe the most essential vehicle characteristics surprisingly well.

    How to formulate the optimization problems and utilize optimal control tools is not obvious. Therefore, a methodology for road-vehicle maneuvering in safety-critical driving scenarios is presented, and used in evaluation studies of various vehicle model configurations and different road-surface conditions. It was found that the overall dynamics is described similarly for both the high- and low-complexity models, as well as for various road-surface conditions.

    If more information about the surroundings is available, the best control actions might differ from the ones in traditional safety systems. This is also studied, where the fundamental control strategies of classic electronic stability control is compared to the optimal strategy in a safety-critical scenario. It is concluded that the optimal braking strategy not only differs from the traditional strategies, but actually counteracts the fundamental intentions from which the traditional systems are based on.

    In contrast to passenger cars, heavy trucks experience other characteristics due to the different geometric proportions. Rollover is one example, which has to be considered in critical maneuvering. Model configurations predicting this phenomenon are investigated using optimal control methods. The results show that the simple first go-to models have to be constrained very conservatively to prevent rollover in more rapid maneuvers.

    In vehicle systems designed for path following, which has become a trending topic with the expanding area of automated driving, the requirements on vehicle modeling can be very high. These requirements ultimately depend on several various properties, where the path restrictions and path characteristics are very influential factors. The interplay between these path properties and the required model characteristics is here investigated. In situations where a smooth path is obtained, low-complexity models can suffice if path deviation tolerances are set accordingly. In more rapid and tricky maneuvers, however, vehicle properties such as yaw inertia are found to be important.

    Several of the included studies indicate that vehicle models of lower complexity can describe the overall dynamics sufficiently in critical driving scenarios, which is a valuable observation for future development.

    List of papers
    1. Vehicle dynamics platform, experiments, and modeling aiming at critical maneuver handling
    Open this publication in new window or tab >>Vehicle dynamics platform, experiments, and modeling aiming at critical maneuver handling
    2013 (English)Report (Other academic)
    Abstract [en]

    For future advanced active safety systems, in road-vehicle applications, there will arise possibilities for enhanced vehicle control systems, due to refinements in, e.g., situation awareness systems. To fully utilize this, more extensive knowledge is required regarding the characteristics and dynamics of vehicle models employed in these systems. Motivated by this, an evaluative study for the lateral dynamics is performed, considering vehicle models of more simple structure. For this purpose, a platform for vehicle dynamics studies has been developed. Experimental data, gathered with this testbed, is then used for model parametrization, succeeded by evaluation for an evasive maneuver. The considered model configurations are based on the single-track model, with different additional attributes, such as tire-force saturation, tire-force lag, and roll dynamics. The results indicate that even a basic model, such as the single-track with tire-force saturation, can describe the lateral dynamics surprisingly well for this critical maneuver.

    Place, publisher, year, edition, pages
    Linköping: Linköping University Electronic Press, 2013. p. 22
    Series
    LiTH-ISY-R, ISSN 1400-3902 ; 3064
    National Category
    Engineering and Technology
    Identifiers
    urn:nbn:se:liu:diva-94203 (URN)LiTH-ISY-R-3064 (ISRN)
    Available from: 2013-06-18 Created: 2013-06-18 Last updated: 2017-01-27Bibliographically approved
    2. Models and methodology for optimal trajectory generation in safety-critical road-vehicle manoeuvres
    Open this publication in new window or tab >>Models and methodology for optimal trajectory generation in safety-critical road-vehicle manoeuvres
    2014 (English)In: Vehicle System Dynamics, ISSN 0042-3114, E-ISSN 1744-5159, Vol. 52, no 10, p. 1304-1332Article in journal (Refereed) Published
    Abstract [en]

    There is currently a strongly growing interest in obtaining optimal control solutions for vehicle manoeuvres, both in order to understand optimal vehicle behaviour and, perhaps more importantly, to devise improved safety systems, either by direct deployment of the solutions or by including mimicked driving techniques of professional drivers. However, it is non-trivial to find the right combination of models, optimisation criteria, and optimisation tools to get useful results for the above purposes. Here, a platform for investigation of these aspects is developed based on a state-of-the-art optimisation tool together with adoption of existing vehicle chassis and tyre models. A minimum-time optimisation criterion is chosen for the purpose of gaining an insight into at-the-limit manoeuvres, with the overall aim of finding improved fundamental principles for future active safety systems. The proposed method to trajectory generation is evaluated in time-manoeuvres using vehicle models established in the literature. We determine the optimal control solutions for three manoeuvres using tyre and chassis models of different complexities. The results are extensively analysed and discussed. Our main conclusion is that the tyre model has a fundamental influence on the resulting control inputs. Also, for some combinations of chassis and tyre models, inherently different behaviour is obtained. However, certain variables important in vehicle safety-systems, such as the yaw moment and the body-slip angle, are similar for several of the considered model configurations in aggressive manoeuvring situations.

    Place, publisher, year, edition, pages
    Taylor andamp; Francis: STM, Behavioural Science and Public Health Titles, 2014
    Keywords
    optimal manoeuvres; time-optimal trajectory generation; road vehicles; chassis and tyre modelling
    National Category
    Electrical Engineering, Electronic Engineering, Information Engineering
    Identifiers
    urn:nbn:se:liu:diva-111629 (URN)10.1080/00423114.2014.939094 (DOI)000342291200005 ()
    Note

    Funding Agencies|ELLIIT, the Strategic Area for ICT research - Swedish Government; Swedish Research Council

    Available from: 2014-10-27 Created: 2014-10-27 Last updated: 2017-12-05
    3. An Investigation of Optimal Vehicle Maneuvers for Different Road Conditions
    Open this publication in new window or tab >>An Investigation of Optimal Vehicle Maneuvers for Different Road Conditions
    2013 (English)In: IFAC Proceedings Volumes, Volume 46, Issue 21, International Federation of Automatic Control , 2013, Vol. 46, p. 66-71Conference paper, Published paper (Refereed)
    Abstract [en]

    We investigate optimal maneuvers for road-vehicles on different surfaces such as asphalt, snow, and ice. The study is motivated by the desire to find control strategies for improved future vehicle safety and driver assistance technologies. Based on earlier presented measurements for tire-force characteristics, we develop tire models corresponding to different road conditions, and determine the time-optimal maneuver in a hairpin turn for each of these. The obtained results are discussed and compared for the different road characteristics. Our main findings are that there are fundamental differences in the control strategies on the considered surfaces, and that these differences can be captured with the adopted modeling approach. Moreover, the path of the vehicle center-of-mass was found to be similar for the different cases. We believe that these findings imply that there are observed vehicle behaviors in the results, which can be utilized for developing the vehicle safety systems of tomorrow.

    Place, publisher, year, edition, pages
    International Federation of Automatic Control, 2013
    Series
    IFAC Proceedings Volumes, ISSN 1474-6670 ; Volume 47, Issue 3
    National Category
    Engineering and Technology
    Identifiers
    urn:nbn:se:liu:diva-94206 (URN)10.3182/20130904-4-JP-2042.00007 (DOI)978-3-902823-48-9 (ISBN)
    Conference
    7th IFAC Symposium on Advances in Automotive Control. The International Federation of Automatic Control, September 4-7, 2013. Tokyo, Japan
    Available from: 2013-06-18 Created: 2013-06-18 Last updated: 2016-05-25Bibliographically approved
    4. Towards Lane-Keeping Electronic Stability Control for Road-Vehicles
    Open this publication in new window or tab >>Towards Lane-Keeping Electronic Stability Control for Road-Vehicles
    Show others...
    2014 (English)In: Proceedings of the 19th IFAC World Congress, 2014 / [ed] Boje, Edward, Xia, Xiaohua, International Federation of Automatic Control , 2014, Vol. 19, p. 6319-6325Conference paper, Published paper (Refereed)
    Abstract [en]

    The emerging new idea of lane-keeping electronic stability control is investigated. In a critical situation, such as entering a road curve at excessive speed, the optimal behavior may differ from the behavior of traditional ESC, for example, by prioritizing braking over steering response. The important question that naturally arises is if this has a significant effect on safety. The main contribution here is to give a method for some first quantitative measures of this. It is based on optimal control, applied to a double-track chassis model with wheel dynamics and high-fidelity tire-force modeling. The severity of accidents grows with the square of the kinetic energy for high velocities, so using kinetic energy as a measure will at least not overestimate the usefulness of the new safety system principle. The main result is that the safety gain is significant compared to traditional approaches based on yaw rotation, for several situations and different road-condition parameters.

    Place, publisher, year, edition, pages
    International Federation of Automatic Control, 2014
    Series
    World Congress, ISSN 1474-6670 ; Volume 19, Issue 1
    National Category
    Vehicle Engineering
    Identifiers
    urn:nbn:se:liu:diva-127795 (URN)10.3182/20140824-6-ZA-1003.02578 (DOI)
    Conference
    19th IFAC World Congress, August 24-28, Cape Town, South Africa
    Available from: 2016-05-12 Created: 2016-05-12 Last updated: 2016-05-25Bibliographically approved
    5. Analyzing Rollover Indices for Critical Truck Maneuvers
    Open this publication in new window or tab >>Analyzing Rollover Indices for Critical Truck Maneuvers
    2015 (English)In: SAE International Journal of Commercial Vehicles, ISSN 1946-391X, E-ISSN 1946-3928, Vol. 8, no 1, p. 189-196Article in journal (Refereed) Published
    Abstract [en]

    Rollover has for long been a major safety concern for trucks, and will be even more so as automated driving is envisaged to becoming a key element of future mobility. A natural way to address rollover is to extend the capabilities of current active-safety systems with a system that intervenes by steering or braking actuation when there is a risk of rollover. Assessing and predicting the rollover is usually performed using rollover indices calculated either from lateral acceleration or lateral load transfer. Since these indices are evaluated based on different physical observations it is not obvious how they can be compared or how well they reflect rollover events in different situations.

    In this paper we investigate the implication of the above mentioned rollover indices in different critical maneuvers for a heavy 8×4 twin-steer truck. The analysis is based on optimal control applied to a five degrees of freedom chassis model with individual wheel dynamics and high-fidelity tire-force modeling. Driving scenarios prone to rollover accidents are considered, with a circular-shaped turn and a slalom maneuver being studied in-depth. The optimization objective for the considered maneuvers are formulated as minimum-time and maximum entry-speed problems, both triggering critical maneuvers and forcing the vehicle to operate on the limit of its physical capabilities. The implication of the rollover indices on the optimal trajectories is investigated by constraining the optimal maneuvers with different rollover indices, thus limiting the vehicle's maneuvering envelope with respect to each rollover index. The resulting optimal trajectories constrained by different rollover indices are compared and analyzed in detail. Additionally, the conservativeness of the indices for assessing the risk of rollovers are discussed.

    Place, publisher, year, edition, pages
    SAE International, 2015
    National Category
    Control Engineering
    Identifiers
    urn:nbn:se:liu:diva-127796 (URN)10.4271/2015-01-1595 (DOI)
    Available from: 2016-05-12 Created: 2016-05-12 Last updated: 2017-11-30Bibliographically approved
    6. Implications of Path Tolerance and Path Characteristics on Critical Vehicle Maneuvers
    Open this publication in new window or tab >>Implications of Path Tolerance and Path Characteristics on Critical Vehicle Maneuvers
    (English)Manuscript (preprint) (Other academic)
    Abstract [en]

    Path planning and path following are core components in safe autonomous driving. Typically a path planner provides a path with sometolerance on how tightly the path should be followed. Based on that, and other path characteristics, for example sharpness of curves, a speed profile needs to be assigned so that the vehicle can stay within the given tolerance without going unnecessarily slow. Here, such trajectory planning is based on optimal control formulations where critical cases arises as on-the-limit solutions. Several results are obtained on required model complexity depending on path characteristics, for example quantification of required path tolerance for a simple model to be sufficient, quantification of when yaw inertia needs to be considered in more detail, and how the curvature rate of change of curvature interplays with available friction. Overall, in situations where the path planner, due to the type of vehicle operation ranging from good transport roads to more tricky maneuvering, give paths with a wide range of tolerances and characteristics, then the results provided give the basis for real-time path following with reasonably high speed.

    National Category
    Vehicle Engineering Control Engineering
    Identifiers
    urn:nbn:se:liu:diva-127797 (URN)
    Available from: 2016-05-12 Created: 2016-05-12 Last updated: 2016-05-25Bibliographically approved
  • 5.
    Lundahl, Kristoffer
    et al.
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Berntorp, Karl
    Department of Automatic Control, Lund University, Lund, Sweden.
    Olofsson, Björn
    Department of Automatic Control, Lund University, Lund, Sweden.
    Åslund, Jan
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Nielsen, Lars
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Studying the Influence of Roll and Pitch Dynamics in Optimal Road-Vehicle Maneuvers2013Conference paper (Other academic)
    Abstract [en]

    A comparative analysis shows how vehicle motion models of different complexity, capturing various characteristics, influence the solution when used in time-critical optimal maneuvering problems. Vehicle models with combinations of roll and pitch dynamics as well as load transfer are considered, ranging from a single-track model to a double-track model with roll and pitch dynamics and load transfer. The optimal maneuvers in a 90◦-turn and a double lane-change scenario are formulated as minimum-time optimization problems, and are solved using numerical optimization software. The results obtained with the different models show that variables potentially important for safety systems, such as the yaw rate, slip angle, and geometric path, are qualitatively the same. Moreover, the numeric differences are mostly within a few percent. The results also indicate that although input torques differ about 50–100 % for certain parts of the maneuver between the most and least complex model considered, the resulting vehicle motions obtained are similar, irrespective of the model. Our main conclusion isthat this enables the use of low-order models when designing the onboard optimization-based safety systems of the future.

  • 6.
    Lundahl, Kristoffer
    et al.
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Frisk, Erik
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Nielsen, Lars
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Implications of Path Tolerance and Path Characteristics on Critical Vehicle ManeuversManuscript (preprint) (Other academic)
    Abstract [en]

    Path planning and path following are core components in safe autonomous driving. Typically a path planner provides a path with sometolerance on how tightly the path should be followed. Based on that, and other path characteristics, for example sharpness of curves, a speed profile needs to be assigned so that the vehicle can stay within the given tolerance without going unnecessarily slow. Here, such trajectory planning is based on optimal control formulations where critical cases arises as on-the-limit solutions. Several results are obtained on required model complexity depending on path characteristics, for example quantification of required path tolerance for a simple model to be sufficient, quantification of when yaw inertia needs to be considered in more detail, and how the curvature rate of change of curvature interplays with available friction. Overall, in situations where the path planner, due to the type of vehicle operation ranging from good transport roads to more tricky maneuvering, give paths with a wide range of tolerances and characteristics, then the results provided give the basis for real-time path following with reasonably high speed.

  • 7.
    Lundahl, Kristoffer
    et al.
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Lee, Chih Feng
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Frisk, Erik
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Nielsen, Lars
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Analyzing Rollover Indices for Critical Truck Maneuvers2015In: SAE International Journal of Commercial Vehicles, ISSN 1946-391X, E-ISSN 1946-3928, Vol. 8, no 1, p. 189-196Article in journal (Refereed)
    Abstract [en]

    Rollover has for long been a major safety concern for trucks, and will be even more so as automated driving is envisaged to becoming a key element of future mobility. A natural way to address rollover is to extend the capabilities of current active-safety systems with a system that intervenes by steering or braking actuation when there is a risk of rollover. Assessing and predicting the rollover is usually performed using rollover indices calculated either from lateral acceleration or lateral load transfer. Since these indices are evaluated based on different physical observations it is not obvious how they can be compared or how well they reflect rollover events in different situations.

    In this paper we investigate the implication of the above mentioned rollover indices in different critical maneuvers for a heavy 8×4 twin-steer truck. The analysis is based on optimal control applied to a five degrees of freedom chassis model with individual wheel dynamics and high-fidelity tire-force modeling. Driving scenarios prone to rollover accidents are considered, with a circular-shaped turn and a slalom maneuver being studied in-depth. The optimization objective for the considered maneuvers are formulated as minimum-time and maximum entry-speed problems, both triggering critical maneuvers and forcing the vehicle to operate on the limit of its physical capabilities. The implication of the rollover indices on the optimal trajectories is investigated by constraining the optimal maneuvers with different rollover indices, thus limiting the vehicle's maneuvering envelope with respect to each rollover index. The resulting optimal trajectories constrained by different rollover indices are compared and analyzed in detail. Additionally, the conservativeness of the indices for assessing the risk of rollovers are discussed.

  • 8.
    Lundahl, Kristoffer
    et al.
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Olofsson, Björn
    Department of Automatic Control, Lund University.
    Berntorp, Karl
    Department of Automatic Control, Lund University.
    Åslund, Jan
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Nielsen, Lars
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Towards Lane-Keeping Electronic Stability Control for Road-Vehicles2014In: Proceedings of the 19th IFAC World Congress, 2014 / [ed] Boje, Edward, Xia, Xiaohua, International Federation of Automatic Control , 2014, Vol. 19, p. 6319-6325Conference paper (Refereed)
    Abstract [en]

    The emerging new idea of lane-keeping electronic stability control is investigated. In a critical situation, such as entering a road curve at excessive speed, the optimal behavior may differ from the behavior of traditional ESC, for example, by prioritizing braking over steering response. The important question that naturally arises is if this has a significant effect on safety. The main contribution here is to give a method for some first quantitative measures of this. It is based on optimal control, applied to a double-track chassis model with wheel dynamics and high-fidelity tire-force modeling. The severity of accidents grows with the square of the kinetic energy for high velocities, so using kinetic energy as a measure will at least not overestimate the usefulness of the new safety system principle. The main result is that the safety gain is significant compared to traditional approaches based on yaw rotation, for several situations and different road-condition parameters.

  • 9.
    Lundahl, Kristoffer
    et al.
    Linköping University, Department of Electrical Engineering. Linköping University, The Institute of Technology.
    Åslund, Jan
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Nielsen, Lars
    Linköping University, Department of Electrical Engineering. Linköping University, The Institute of Technology.
    Investigating Vehicle Model Detail for Close to Limit Maneuvers Aiming at Optimal Control2011Conference paper (Other academic)
    Abstract [en]

    In advanced road vehicle safety systems it is imperative to have a model describing the vehicle motions and behaviors with sufficient precision. Often a model incorporating a higher level of complexity generates more accurate data, with the disadvantage of demanding additional calculation power. This study will therefore focus on investigating how models of different detail level represents the vehicle behavior, for maneuvers going from moderate to more aggressive. The characteristics in particular investigated are tire saturation, tire force lag and the effect of load transfers. A vehicle testbed has also been developed, making model validations towards experimental data available.

  • 10.
    Lundahl, Kristoffer
    et al.
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Åslund, Jan
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Nielsen, Lars
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Vehicle dynamics platform, experiments, and modeling aiming at critical maneuver handling2013Report (Other academic)
    Abstract [en]

    For future advanced active safety systems, in road-vehicle applications, there will arise possibilities for enhanced vehicle control systems, due to refinements in, e.g., situation awareness systems. To fully utilize this, more extensive knowledge is required regarding the characteristics and dynamics of vehicle models employed in these systems. Motivated by this, an evaluative study for the lateral dynamics is performed, considering vehicle models of more simple structure. For this purpose, a platform for vehicle dynamics studies has been developed. Experimental data, gathered with this testbed, is then used for model parametrization, succeeded by evaluation for an evasive maneuver. The considered model configurations are based on the single-track model, with different additional attributes, such as tire-force saturation, tire-force lag, and roll dynamics. The results indicate that even a basic model, such as the single-track with tire-force saturation, can describe the lateral dynamics surprisingly well for this critical maneuver.

  • 11.
    Olofsson, Björn
    et al.
    Department of Automatic Control, Lund University, Lund, Sweden.
    Lundahl, Kristoffer
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Berntorp, Karl
    Department of Automatic Control, Lund University, Lund, Sweden.
    Nielsen, Lars
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    An Investigation of Optimal Vehicle Maneuvers for Different Road Conditions2013In: IFAC Proceedings Volumes, Volume 46, Issue 21, International Federation of Automatic Control , 2013, Vol. 46, p. 66-71Conference paper (Refereed)
    Abstract [en]

    We investigate optimal maneuvers for road-vehicles on different surfaces such as asphalt, snow, and ice. The study is motivated by the desire to find control strategies for improved future vehicle safety and driver assistance technologies. Based on earlier presented measurements for tire-force characteristics, we develop tire models corresponding to different road conditions, and determine the time-optimal maneuver in a hairpin turn for each of these. The obtained results are discussed and compared for the different road characteristics. Our main findings are that there are fundamental differences in the control strategies on the considered surfaces, and that these differences can be captured with the adopted modeling approach. Moreover, the path of the vehicle center-of-mass was found to be similar for the different cases. We believe that these findings imply that there are observed vehicle behaviors in the results, which can be utilized for developing the vehicle safety systems of tomorrow.

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