Pub Date : 2019-08-01DOI: 10.1109/MMAR.2019.8864708
Edmond Skeli, Dimitri Harder, Dirk Weidemann, K. Panreck
For model-based control and/or diagnosing purposes it is necessary to determine mathematical models that are sufficiently precise on the one hand, but do not require too much computational effort on the other. In this regard, reduction of a model describing the processing of a highly-viscous, non-isothermal fluid with a free-surface is examined. The behaviour of the fluid is given by a system of partial differential equations containing the two dimensional Navier-Stokes equations and the thermal energy equation. Using perturbation theory it can be shown that the behaviour of the velocity and the temperature can be described sufficiently precise by two simpler submodels. The first submodel is used to calculate the flow dynamics and the second submodel to calculate the thermal behaviour with simultaneous adaptation of the flow dynamics to the current thermal conditions. In addition, the Marker and Cell method is used to determine the temporal development of the free-surface. Finally, the spatial discretisation is done with a curved grid, resulting in a smaller model size than the use of a rectangular grid.
{"title":"Modelling of a highly-viscous, non-isothermal Fluid with free Surface using Model Reduction","authors":"Edmond Skeli, Dimitri Harder, Dirk Weidemann, K. Panreck","doi":"10.1109/MMAR.2019.8864708","DOIUrl":"https://doi.org/10.1109/MMAR.2019.8864708","url":null,"abstract":"For model-based control and/or diagnosing purposes it is necessary to determine mathematical models that are sufficiently precise on the one hand, but do not require too much computational effort on the other. In this regard, reduction of a model describing the processing of a highly-viscous, non-isothermal fluid with a free-surface is examined. The behaviour of the fluid is given by a system of partial differential equations containing the two dimensional Navier-Stokes equations and the thermal energy equation. Using perturbation theory it can be shown that the behaviour of the velocity and the temperature can be described sufficiently precise by two simpler submodels. The first submodel is used to calculate the flow dynamics and the second submodel to calculate the thermal behaviour with simultaneous adaptation of the flow dynamics to the current thermal conditions. In addition, the Marker and Cell method is used to determine the temporal development of the free-surface. Finally, the spatial discretisation is done with a curved grid, resulting in a smaller model size than the use of a rectangular grid.","PeriodicalId":392498,"journal":{"name":"2019 24th International Conference on Methods and Models in Automation and Robotics (MMAR)","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125293474","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-08-01DOI: 10.1109/MMAR.2019.8864656
T. Sulkowski, Paulina Bugiel, J. Izydorczyk
This paper describes the use of Lattice Boltzmann Method for dynamic autonomous driving trajectory planning. By simulating fluid flow on roads as a two-dimensional tubes in a small area around ego car, a vector map is created which can be used as a direct basis for driving trajectory. To tailor the phenomena of fluid flow for legal driving trajectory, the simulated fluid source is placed at an offset angle while dynamically following target car and road borders generate additional potential field. Experiments have shown that fluid simulation needs to propagate relatively to car driven distance for the algorithm to be feasible. During evaluation such ratio has been found and approximated.
{"title":"Dynamic Trajectory Planning for Autonomous Driving Based on Fluid Simulation","authors":"T. Sulkowski, Paulina Bugiel, J. Izydorczyk","doi":"10.1109/MMAR.2019.8864656","DOIUrl":"https://doi.org/10.1109/MMAR.2019.8864656","url":null,"abstract":"This paper describes the use of Lattice Boltzmann Method for dynamic autonomous driving trajectory planning. By simulating fluid flow on roads as a two-dimensional tubes in a small area around ego car, a vector map is created which can be used as a direct basis for driving trajectory. To tailor the phenomena of fluid flow for legal driving trajectory, the simulated fluid source is placed at an offset angle while dynamically following target car and road borders generate additional potential field. Experiments have shown that fluid simulation needs to propagate relatively to car driven distance for the algorithm to be feasible. During evaluation such ratio has been found and approximated.","PeriodicalId":392498,"journal":{"name":"2019 24th International Conference on Methods and Models in Automation and Robotics (MMAR)","volume":"104 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127639826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-08-01DOI: 10.1109/MMAR.2019.8864673
Julia Kersten, A. Rauh, H. Aschemann
Dynamical systems are often subject to uncertainties, whether it be parameter uncertainties or the interpretation of state dependencies in quasi-linear state-space representations as some kind of time-varying uncertain parameters. The first group of uncertainties arises from mathematical model simplifications, manufacturing tolerances, and imperfect measurements. Here, uncertainties can be represented in different forms like probability distributions in the stochastic case or interval representations in a bounded error framework. On the one hand, there exist numerous techniques to handle stochastic uncertainty, for example Monte-Carlo methods, but those do not allow for the computation of worst-case bounds of the sets of reachable states. On the other hand, approaches based on interval analysis are capable of the latter aspect. This paper deals with those methods from the perspective of an application scenario in the form of a guaranteed robust stabilization of an inverted pendulum by using constant controller gains. Here, we assume an interval representation for the bounded influence of state dependencies in the system matrices by a polytopic uncertainty model. When dealing with interval uncertainty, the rigorous computation of guaranteed state enclosures is a difficult task. Due to conservatism and/or the wrapping effect, overestimation is a common problem. This paper discusses different approaches to perform a verified reachability analysis by means of interval enclosures to be interfaced with the controller parameterization and gives guidelines on which available technique to use in a real-life robust control task.
{"title":"Application-Based Discussion of Verified Simulations of Interval Enclosure Techniques","authors":"Julia Kersten, A. Rauh, H. Aschemann","doi":"10.1109/MMAR.2019.8864673","DOIUrl":"https://doi.org/10.1109/MMAR.2019.8864673","url":null,"abstract":"Dynamical systems are often subject to uncertainties, whether it be parameter uncertainties or the interpretation of state dependencies in quasi-linear state-space representations as some kind of time-varying uncertain parameters. The first group of uncertainties arises from mathematical model simplifications, manufacturing tolerances, and imperfect measurements. Here, uncertainties can be represented in different forms like probability distributions in the stochastic case or interval representations in a bounded error framework. On the one hand, there exist numerous techniques to handle stochastic uncertainty, for example Monte-Carlo methods, but those do not allow for the computation of worst-case bounds of the sets of reachable states. On the other hand, approaches based on interval analysis are capable of the latter aspect. This paper deals with those methods from the perspective of an application scenario in the form of a guaranteed robust stabilization of an inverted pendulum by using constant controller gains. Here, we assume an interval representation for the bounded influence of state dependencies in the system matrices by a polytopic uncertainty model. When dealing with interval uncertainty, the rigorous computation of guaranteed state enclosures is a difficult task. Due to conservatism and/or the wrapping effect, overestimation is a common problem. This paper discusses different approaches to perform a verified reachability analysis by means of interval enclosures to be interfaced with the controller parameterization and gives guidelines on which available technique to use in a real-life robust control task.","PeriodicalId":392498,"journal":{"name":"2019 24th International Conference on Methods and Models in Automation and Robotics (MMAR)","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126338282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-08-01DOI: 10.1109/MMAR.2019.8864648
A. Rauh, Julia Kersten, H. Aschemann
Quasi-linear continuous-time state-space representations are common for a large variety of dynamic systems described by ordinary differential equations (ODEs) with continuously differentiable smooth right-hand sides. Such models arise, for example, after representing technical systems by the use of first-principle techniques and subsequently factoring out the state vectors so that a set of ODEs is obtained that has a structure similar to linear dynamics. However, in the case of quasi-linear ODEs, the system matrix (as well as the corresponding input matrix) are explicit functions of the state variables. Thus, analytic solutions to corresponding initial value problems (IVPs) are, even in cases of a-priori defined closed-form control inputs, hardly available. Therefore, this paper aims at giving an overview of interval-based techniques which allow for determining outer enclosures of the reachable states by either numerical iteration procedures or by similarity transformations of the state equations.
{"title":"Techniques for Verified Reachability Analysis of Quasi-Linear Continuous-Time Systems","authors":"A. Rauh, Julia Kersten, H. Aschemann","doi":"10.1109/MMAR.2019.8864648","DOIUrl":"https://doi.org/10.1109/MMAR.2019.8864648","url":null,"abstract":"Quasi-linear continuous-time state-space representations are common for a large variety of dynamic systems described by ordinary differential equations (ODEs) with continuously differentiable smooth right-hand sides. Such models arise, for example, after representing technical systems by the use of first-principle techniques and subsequently factoring out the state vectors so that a set of ODEs is obtained that has a structure similar to linear dynamics. However, in the case of quasi-linear ODEs, the system matrix (as well as the corresponding input matrix) are explicit functions of the state variables. Thus, analytic solutions to corresponding initial value problems (IVPs) are, even in cases of a-priori defined closed-form control inputs, hardly available. Therefore, this paper aims at giving an overview of interval-based techniques which allow for determining outer enclosures of the reachable states by either numerical iteration procedures or by similarity transformations of the state equations.","PeriodicalId":392498,"journal":{"name":"2019 24th International Conference on Methods and Models in Automation and Robotics (MMAR)","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126059186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-08-01DOI: 10.1109/MMAR.2019.8864647
C. Wernik, G. Ulacha
In this paper the lossless block encoder application using the adaptive Golomb code and asymmetric inter-channel dependencies are presented. Using the sets of settings obtained from the study of inter-channel dependencies, the lowest bit averages were found within the channels. In the next step the algorithm was improved by adaptation within the blocks, what allowed to improving the degree of compression.
{"title":"Application of an adaptive Golomb block code using asymmetric inter-channel dependencies","authors":"C. Wernik, G. Ulacha","doi":"10.1109/MMAR.2019.8864647","DOIUrl":"https://doi.org/10.1109/MMAR.2019.8864647","url":null,"abstract":"In this paper the lossless block encoder application using the adaptive Golomb code and asymmetric inter-channel dependencies are presented. Using the sets of settings obtained from the study of inter-channel dependencies, the lowest bit averages were found within the channels. In the next step the algorithm was improved by adaptation within the blocks, what allowed to improving the degree of compression.","PeriodicalId":392498,"journal":{"name":"2019 24th International Conference on Methods and Models in Automation and Robotics (MMAR)","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128126724","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-08-01DOI: 10.1109/MMAR.2019.8864665
M. Galek, R. Stanisławski, Marek Rydel, K. Latawiec, M. Lukaniszyn
This paper presents a new concept for modeling of linear fractional-order dynamical systems. The proposed model is based on specific basis functions, the so called Fractional-order Difference Basis Functions, which are a generalization of the delayed filters used in the FIR model. In the paper, we show elementary properties of the model and present a method for model implementation. Simulation example shows that the model can be effective in modeling of a class of dynamical systems.
{"title":"Fractional-order Difference Basis Functions - a new modeling concept for dynamical systems","authors":"M. Galek, R. Stanisławski, Marek Rydel, K. Latawiec, M. Lukaniszyn","doi":"10.1109/MMAR.2019.8864665","DOIUrl":"https://doi.org/10.1109/MMAR.2019.8864665","url":null,"abstract":"This paper presents a new concept for modeling of linear fractional-order dynamical systems. The proposed model is based on specific basis functions, the so called Fractional-order Difference Basis Functions, which are a generalization of the delayed filters used in the FIR model. In the paper, we show elementary properties of the model and present a method for model implementation. Simulation example shows that the model can be effective in modeling of a class of dynamical systems.","PeriodicalId":392498,"journal":{"name":"2019 24th International Conference on Methods and Models in Automation and Robotics (MMAR)","volume":"110 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127988944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-08-01DOI: 10.1109/MMAR.2019.8864645
K. Bartecki
The paper discusses an approximation model developed for linear hyperbolic DPS with two state variables and two collocated boundary inputs, expressed in classical, finite-dimensional state-space framework. Using the method of lines approach with the backward difference scheme, the original PDEs are transformed into a set of ODEs and expressed in the form of the state-space equations with matrix-valued state, input and output operators. The eigenvalues and the steady-state solutions of the approximation model are analyzed. The considerations are illustrated with a parallel-flow double-pipe heat exchanger. Steady-state and frequency-domain responses obtained from its original PDE model are compared with those calculated from its ODE approximations of different orders.
{"title":"Approximation state-space model for 2×2 hyperbolic systems with collocated boundary inputs","authors":"K. Bartecki","doi":"10.1109/MMAR.2019.8864645","DOIUrl":"https://doi.org/10.1109/MMAR.2019.8864645","url":null,"abstract":"The paper discusses an approximation model developed for linear hyperbolic DPS with two state variables and two collocated boundary inputs, expressed in classical, finite-dimensional state-space framework. Using the method of lines approach with the backward difference scheme, the original PDEs are transformed into a set of ODEs and expressed in the form of the state-space equations with matrix-valued state, input and output operators. The eigenvalues and the steady-state solutions of the approximation model are analyzed. The considerations are illustrated with a parallel-flow double-pipe heat exchanger. Steady-state and frequency-domain responses obtained from its original PDE model are compared with those calculated from its ODE approximations of different orders.","PeriodicalId":392498,"journal":{"name":"2019 24th International Conference on Methods and Models in Automation and Robotics (MMAR)","volume":"477 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133808777","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-08-01DOI: 10.1109/MMAR.2019.8864619
Ahmed E. Al-Tarras, M. Yacoub, M. Asfoor, A. M. Sharaf
FastSLAM algorithm is commonly used in Unmanned Ground Vehicles (UGVs) recently. One of the main problems under research is the computation cost of this probabilistic algorithm. Since the speed of the UGV is limited by the latency of the algorithm, the computation complexity and its effect on the step time of the FastSLAM needs to be investigated. The present work addresses the effects of the number of particles and number of map features on the computation complexity of the FastSLAM algorithm. The study included the prediction, the observation, data association and resampling phase's complexities. Also, the correlation between the uncertainty of the UGV location and the number of particles was addressed. The simulation study was validated experimentally using hardware in the loop (HIL) setup. The analysis showed that when there is a prior knowledge of the average number of map features, an optimum number of particle filters could be set for that UGV in the given environment while maintaining an improved performance of the algorithm.
{"title":"Computation Complexity Evaluation of FastSLAM Algorithm for Unmanned Ground Vehicles","authors":"Ahmed E. Al-Tarras, M. Yacoub, M. Asfoor, A. M. Sharaf","doi":"10.1109/MMAR.2019.8864619","DOIUrl":"https://doi.org/10.1109/MMAR.2019.8864619","url":null,"abstract":"FastSLAM algorithm is commonly used in Unmanned Ground Vehicles (UGVs) recently. One of the main problems under research is the computation cost of this probabilistic algorithm. Since the speed of the UGV is limited by the latency of the algorithm, the computation complexity and its effect on the step time of the FastSLAM needs to be investigated. The present work addresses the effects of the number of particles and number of map features on the computation complexity of the FastSLAM algorithm. The study included the prediction, the observation, data association and resampling phase's complexities. Also, the correlation between the uncertainty of the UGV location and the number of particles was addressed. The simulation study was validated experimentally using hardware in the loop (HIL) setup. The analysis showed that when there is a prior knowledge of the average number of map features, an optimum number of particle filters could be set for that UGV in the given environment while maintaining an improved performance of the algorithm.","PeriodicalId":392498,"journal":{"name":"2019 24th International Conference on Methods and Models in Automation and Robotics (MMAR)","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134259228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-08-01DOI: 10.1109/MMAR.2019.8864655
F. Baker, S. Thennadil
Kalman filtering can produce unrealistic values and can prevent accurate convergence as the technique does not naturally include safeguards that exclude unphysical states. It can be demonstrated that without implementing constraints, or even some existing constraint strategies, that the filter could converge incorrectly. Currently available approaches to constraining the estimated state variables are arbitrary. For example, a simple way to constrain a violating state variable, is to reset its value to the constraint limit, the effect of which is a reduction of the importance of the measurement. The proposed constraining method attempts to preserve the importance of the observation/measurement in the fused estimate. This method compensates the changes in the constrained state variables by adjusting the non-constrained state variables in order to force the net change in measurement estimate to zero. The approach is implemented for the extended Kalman filters. The method is using a gas phase reaction in a Continuously Stirred Tank Reactor, with the state variables consisting of three species concentrations and the measurement is a pressure measurement with a known relationship to the state variables. The performance of the method is compared to currently available constraining techniques.
{"title":"Constrained Kalman Filtering: Improving Fused Information Retention During Constraining","authors":"F. Baker, S. Thennadil","doi":"10.1109/MMAR.2019.8864655","DOIUrl":"https://doi.org/10.1109/MMAR.2019.8864655","url":null,"abstract":"Kalman filtering can produce unrealistic values and can prevent accurate convergence as the technique does not naturally include safeguards that exclude unphysical states. It can be demonstrated that without implementing constraints, or even some existing constraint strategies, that the filter could converge incorrectly. Currently available approaches to constraining the estimated state variables are arbitrary. For example, a simple way to constrain a violating state variable, is to reset its value to the constraint limit, the effect of which is a reduction of the importance of the measurement. The proposed constraining method attempts to preserve the importance of the observation/measurement in the fused estimate. This method compensates the changes in the constrained state variables by adjusting the non-constrained state variables in order to force the net change in measurement estimate to zero. The approach is implemented for the extended Kalman filters. The method is using a gas phase reaction in a Continuously Stirred Tank Reactor, with the state variables consisting of three species concentrations and the measurement is a pressure measurement with a known relationship to the state variables. The performance of the method is compared to currently available constraining techniques.","PeriodicalId":392498,"journal":{"name":"2019 24th International Conference on Methods and Models in Automation and Robotics (MMAR)","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133256459","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-08-01DOI: 10.1109/MMAR.2019.8864644
A. Świerniak, Michal Krzeslak, D. Borys
We propose to endow evolutionary game models with changes of the phenotypes adjustment during the transient generations performed by the parameters in the payoff matrix which determine the fitness resulting from different interactions between players. These changes represent alteration of access to external resources which, in turn, may describe control actions for the populations. For non-spatial games it leads to time-varying reproduction dynamics and the same to time-varying asymptotics. In the case of spatial games, these functions are represented by an additional lattice where another and parallel game based on cellular automata is performed. The main assumption of the spatial games is that each cell on the lattice is represented by a player following only one strategy. We propose to consider cells on the spatial lattice as heterogeneous (instead of homogeneous), so that each particular player may contain mixed phenotypes. Spatial games of the type, proposed by us, are called multidimensional spatial evolutionary games (MSEG). It may happen that within the population, all of the players have diverse phenotypes (which probably better describes biological phenomena). The additional lattice representing the evolution of resources increases only the dimension of the lattice in the MSEG.
{"title":"Games with resources and their use in modeling control processes in heterogeneous populations","authors":"A. Świerniak, Michal Krzeslak, D. Borys","doi":"10.1109/MMAR.2019.8864644","DOIUrl":"https://doi.org/10.1109/MMAR.2019.8864644","url":null,"abstract":"We propose to endow evolutionary game models with changes of the phenotypes adjustment during the transient generations performed by the parameters in the payoff matrix which determine the fitness resulting from different interactions between players. These changes represent alteration of access to external resources which, in turn, may describe control actions for the populations. For non-spatial games it leads to time-varying reproduction dynamics and the same to time-varying asymptotics. In the case of spatial games, these functions are represented by an additional lattice where another and parallel game based on cellular automata is performed. The main assumption of the spatial games is that each cell on the lattice is represented by a player following only one strategy. We propose to consider cells on the spatial lattice as heterogeneous (instead of homogeneous), so that each particular player may contain mixed phenotypes. Spatial games of the type, proposed by us, are called multidimensional spatial evolutionary games (MSEG). It may happen that within the population, all of the players have diverse phenotypes (which probably better describes biological phenomena). The additional lattice representing the evolution of resources increases only the dimension of the lattice in the MSEG.","PeriodicalId":392498,"journal":{"name":"2019 24th International Conference on Methods and Models in Automation and Robotics (MMAR)","volume":"119 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115599493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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