Pub Date : 2006-08-01DOI: 10.5220/0001207503260333
D. Merad, S. Metz, S. Miguet
Our work focuses on the interdisciplinary field of detailed analysis of behaviors exhibited by individuals during sessions of distributed collaboration. With a particular focus on ergonomics, we propose new mechanisms to be integrated into existing tools to enable increased productivity in distributed learning and working. Our technique is to record ocular movements (eye tracking) to analyze various scenarios of distributed collaboration in the context of computer-based training. In this article, we present a low-cost oculometric device that is capable of making ocular measurements without interfering with the natural behavior of the subject. We expect that this device could be employed anywhere that a natural, non-intrusive method of observation is required, and its low-cost permits it to be readily integrated into existing popular tools, particularly E-learning campus.
{"title":"Eye and gaze tracking algorithm for collaborative learning system","authors":"D. Merad, S. Metz, S. Miguet","doi":"10.5220/0001207503260333","DOIUrl":"https://doi.org/10.5220/0001207503260333","url":null,"abstract":"Our work focuses on the interdisciplinary field of detailed analysis of behaviors exhibited by individuals during sessions of distributed collaboration. With a particular focus on ergonomics, we propose new mechanisms to be integrated into existing tools to enable increased productivity in distributed learning and working. Our technique is to record ocular movements (eye tracking) to analyze various scenarios of distributed collaboration in the context of computer-based training. In this article, we present a low-cost oculometric device that is capable of making ocular measurements without interfering with the natural behavior of the subject. We expect that this device could be employed anywhere that a natural, non-intrusive method of observation is required, and its low-cost permits it to be readily integrated into existing popular tools, particularly E-learning campus.","PeriodicalId":302311,"journal":{"name":"ICINCO-RA","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127943344","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 : 2006-08-01DOI: 10.5220/0001207400740081
D. Merad, Jean-Yves Didier
In this paper we describe an original method for the 3D free form object tracking in monocular vision. The main contribution of this article is the use of the skeleton of an object in order to recognize, locate and track this object in real time. Indeed, the use of this kind of representation made it possible to avoid difficulties related to the absence of prominent elements in free form objects (which makes the matching process easier). The skeleton is a lower dimension representation of the object, it is homotopic and it has a graph structure. This allowed us to use powerful tools of the graph theory in order to perform matching between scene objects and models (recognition step). Thereafter, we used skeleton extremities as interest points for the tracking.
{"title":"Toward 3D free form object tracking using skeleton","authors":"D. Merad, Jean-Yves Didier","doi":"10.5220/0001207400740081","DOIUrl":"https://doi.org/10.5220/0001207400740081","url":null,"abstract":"In this paper we describe an original method for the 3D free form object tracking in monocular vision. The main contribution of this article is the use of the skeleton of an object in order to recognize, locate and track this object in real time. Indeed, the use of this kind of representation made it possible to avoid difficulties related to the absence of prominent elements in free form objects (which makes the matching process easier). The skeleton is a lower dimension representation of the object, it is homotopic and it has a graph structure. This allowed us to use powerful tools of the graph theory in order to perform matching between scene objects and models (recognition step). Thereafter, we used skeleton extremities as interest points for the tracking.","PeriodicalId":302311,"journal":{"name":"ICINCO-RA","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121565041","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 : 2006-08-01DOI: 10.5220/0001210701540161
J. Albus, R. Bostelman, T. Hong, Tommy Chang, W. Shackleford, M. Shneier
The National Institute of Standards and Technology's (NIST) Intelligent Systems Division (ISD) is a par- ticipant in the Defense Advanced Research Project Agency (DARPA) LAGR (Learning Applied to Ground Robots) Project. The NIST team's objective for the LAGR Project is to insert learning algorithms into the modules that make up the 4D/RCS (Four Dimensional/Real-Time Control System), the standard reference model architecture to which ISD has applied to many intelligent systems. This paper describes the 4D/RCS structure, its application to the LAGR project, and the learning and mobility control methods used by the NIST team's vehicle.
{"title":"The lagr project - integrating learning into the 4D/RCS control hierarchy","authors":"J. Albus, R. Bostelman, T. Hong, Tommy Chang, W. Shackleford, M. Shneier","doi":"10.5220/0001210701540161","DOIUrl":"https://doi.org/10.5220/0001210701540161","url":null,"abstract":"The National Institute of Standards and Technology's (NIST) Intelligent Systems Division (ISD) is a par- ticipant in the Defense Advanced Research Project Agency (DARPA) LAGR (Learning Applied to Ground Robots) Project. The NIST team's objective for the LAGR Project is to insert learning algorithms into the modules that make up the 4D/RCS (Four Dimensional/Real-Time Control System), the standard reference model architecture to which ISD has applied to many intelligent systems. This paper describes the 4D/RCS structure, its application to the LAGR project, and the learning and mobility control methods used by the NIST team's vehicle.","PeriodicalId":302311,"journal":{"name":"ICINCO-RA","volume":"207 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133871345","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 : 2006-08-01DOI: 10.5220/0001218103980403
F. Marchese
In this paper is described a fast Path-Planner for Multi-robot composed by mobile robots having generic shapes and sizes (user defined) and different kinematics. We have developed an algorithm that computes the shortest collision-free path for each robot, from the starting pose to the goal pose, while considering their real shapes, avoiding the collisions with the static obstacles and the other robots. It is based on a directional (anisotropic) propagation of attracting potential values in a 4D Space-Time, using a Multilayered Cellular Automata (MCA) architecture. This algorithm makes a search for all the optimal collision-free trajectories following the minimum valley of a potential hypersurface embedded in a 5D space.
{"title":"Multiple mobile robots motion-planning: An approach with space-time MCA","authors":"F. Marchese","doi":"10.5220/0001218103980403","DOIUrl":"https://doi.org/10.5220/0001218103980403","url":null,"abstract":"In this paper is described a fast Path-Planner for Multi-robot composed by mobile robots having generic shapes and sizes (user defined) and different kinematics. We have developed an algorithm that computes the shortest collision-free path for each robot, from the starting pose to the goal pose, while considering their real shapes, avoiding the collisions with the static obstacles and the other robots. It is based on a directional (anisotropic) propagation of attracting potential values in a 4D Space-Time, using a Multilayered Cellular Automata (MCA) architecture. This algorithm makes a search for all the optimal collision-free trajectories following the minimum valley of a potential hypersurface embedded in a 5D space.","PeriodicalId":302311,"journal":{"name":"ICINCO-RA","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114709824","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 : 2006-08-01DOI: 10.5220/0001206704940499
Loic Plassart, P. L. Parc, Frank Singhoff, L. Marcé
This paper presents an original performance analysis applied to a flow-shop system driven by a set of local command units and a central controller. The performance evaluation is done with a timed coloured Petri net model. Simulation results show needs for bounding the controller response time in order to meet production targets.
{"title":"Performance evaluation of a controlled flow-shop system with a timed petri net model","authors":"Loic Plassart, P. L. Parc, Frank Singhoff, L. Marcé","doi":"10.5220/0001206704940499","DOIUrl":"https://doi.org/10.5220/0001206704940499","url":null,"abstract":"This paper presents an original performance analysis applied to a flow-shop system driven by a set of local command units and a central controller. The performance evaluation is done with a timed coloured Petri net model. Simulation results show needs for bounding the controller response time in order to meet production targets.","PeriodicalId":302311,"journal":{"name":"ICINCO-RA","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124665212","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 : 2006-08-01DOI: 10.5220/0001213505160522
H. Moreno, José Alfonso Pámanes García, P. Wenger, D. Chablat
In this paper the trajectory planning problem is solved for a 2PRR parallel manipulator which works in cooperation with a 1 degree-of-freedom (dof) platform. The whole kinematic chain is considered as a redundant 3-dof manipulator, and an algorithm is presented to solve the redundancy by using the joint velocities in the null space of the jacobian matrix. The internal motion of the assisted manipulator allows globally optimize the condition number of the jacobian matrix during the accomplishment of a desired task. Consequently, the accuracy of the manipulator is maximized and singular or degenerate poses are avoided. A case of study is presented to show the effectiveness of our approach.
{"title":"Global optimization of performance of a 2PRR parallel manipulator for cooperative tasks","authors":"H. Moreno, José Alfonso Pámanes García, P. Wenger, D. Chablat","doi":"10.5220/0001213505160522","DOIUrl":"https://doi.org/10.5220/0001213505160522","url":null,"abstract":"In this paper the trajectory planning problem is solved for a 2PRR parallel manipulator which works in cooperation with a 1 degree-of-freedom (dof) platform. The whole kinematic chain is considered as a redundant 3-dof manipulator, and an algorithm is presented to solve the redundancy by using the joint velocities in the null space of the jacobian matrix. The internal motion of the assisted manipulator allows globally optimize the condition number of the jacobian matrix during the accomplishment of a desired task. Consequently, the accuracy of the manipulator is maximized and singular or degenerate poses are avoided. A case of study is presented to show the effectiveness of our approach.","PeriodicalId":302311,"journal":{"name":"ICINCO-RA","volume":"143 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128764615","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 : 2006-08-01DOI: 10.5220/0001211604380444
G. Blanc, Y. Mezouar, P. Martinet
This paper presents an obstacle avoidance module dedicated to non-holonomic wheeled mobile robots. Chained system theory and deformable virtual zone principle are coupled to design an original framework based on path following formalism. The proposed strategy allows to correct the control output provided by a navigation module to preserve the robot security while assuring the navigation task. First, local paths and control inputs are derived from the interaction between virtual zones surrounding the robot and obstacles to efficiently prevent from collisions. The resulting control inputs and the ones provided by the navigation module are then adequately merged to ensure the success of the navigation task. Experimental results using a cart-like mobile robot equipped with a sonar sensors belt confirm the relevance of the approach.
{"title":"A path planning strategy for obstacle avoidance","authors":"G. Blanc, Y. Mezouar, P. Martinet","doi":"10.5220/0001211604380444","DOIUrl":"https://doi.org/10.5220/0001211604380444","url":null,"abstract":"This paper presents an obstacle avoidance module dedicated to non-holonomic wheeled mobile robots. Chained system theory and deformable virtual zone principle are coupled to design an original framework based on path following formalism. The proposed strategy allows to correct the control output provided by a navigation module to preserve the robot security while assuring the navigation task. First, local paths and control inputs are derived from the interaction between virtual zones surrounding the robot and obstacles to efficiently prevent from collisions. The resulting control inputs and the ones provided by the navigation module are then adequately merged to ensure the success of the navigation task. Experimental results using a cart-like mobile robot equipped with a sonar sensors belt confirm the relevance of the approach.","PeriodicalId":302311,"journal":{"name":"ICINCO-RA","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133857390","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 : 1900-01-01DOI: 10.5220/0001498401690174
Ricardo S. Britto, A. M. Santana, A. Souza, A. Medeiros, P. Alsina
In this paper, we introduce a hardware-software architecture for controlling the autonomous mobile robot Kapeck. The Kapeck robot is composed of a set of sensors and actuators organized in a CAN bus. Two embedded computers and eigth microcontroller-based boards are used in the system. One of the computers hosts the vision system, due to the significant processing needs of this kind of system. The other computer is used to coordinate and access the CAN bus and to accomplish the other activities of the robot. The microcontrollerbased boards are used with the sensors and actuators. The robot has this distributed configuration in order to exhibit a good real-time behavior, where the response time and the temporal predictability of the system is important. We adopted the hybrid deliberative-reactive paradigm in the proposed architecture to conciliate the reactive behavior of the sensors-actuators net and the deliberative activities required to accomplish more complex tasks.
{"title":"A Distributed Hardware-software Architecture for Control an Autonomous Mobile Robot","authors":"Ricardo S. Britto, A. M. Santana, A. Souza, A. Medeiros, P. Alsina","doi":"10.5220/0001498401690174","DOIUrl":"https://doi.org/10.5220/0001498401690174","url":null,"abstract":"In this paper, we introduce a hardware-software architecture for controlling the autonomous mobile robot Kapeck. The Kapeck robot is composed of a set of sensors and actuators organized in a CAN bus. Two embedded computers and eigth microcontroller-based boards are used in the system. One of the computers hosts the vision system, due to the significant processing needs of this kind of system. The other computer is used to coordinate and access the CAN bus and to accomplish the other activities of the robot. The microcontrollerbased boards are used with the sensors and actuators. The robot has this distributed configuration in order to exhibit a good real-time behavior, where the response time and the temporal predictability of the system is important. We adopted the hybrid deliberative-reactive paradigm in the proposed architecture to conciliate the reactive behavior of the sensors-actuators net and the deliberative activities required to accomplish more complex tasks.","PeriodicalId":302311,"journal":{"name":"ICINCO-RA","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123044740","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 : 1900-01-01DOI: 10.5220/0001642200670075
I. Nikolos, N. Tsourveloudis
We suggest an evolutionary based off-line/on-line path planner for cooperating Unmanned Aerial Vehicles (UAVs) that takes into account the environment characteristics and the flight envelope and mission constraints of the cooperating UAVs. The scenario under consideration is the following: a number of UAVs are launched from the same or different known initial locations. The main issue is to produce 3-D trajectories that ensure a collision free operation with respect to mission constraints. The path planner produces curved routes that are represented by 3-D B-Spline curves. Two types of planner are discussed: The off-line planner generates collision free paths in environments with known characteristics and flight restrictions. The on-line planner, which is based on the off-line one, generates collision free paths in unknown static environments, by using acquired information from the UAV’s on-board sensors. This information is exchanged between the cooperating UAVs in order to maximize the knowledge of the environment. Both off-line and on-line path planning problems are formulated as optimization problems, with a Differential Evolution algorithm to serve as the optimizer.
{"title":"Evolutionary path planning for unmanned aerial vehicles cooperation","authors":"I. Nikolos, N. Tsourveloudis","doi":"10.5220/0001642200670075","DOIUrl":"https://doi.org/10.5220/0001642200670075","url":null,"abstract":"We suggest an evolutionary based off-line/on-line path planner for cooperating Unmanned Aerial Vehicles (UAVs) that takes into account the environment characteristics and the flight envelope and mission constraints of the cooperating UAVs. The scenario under consideration is the following: a number of UAVs are launched from the same or different known initial locations. The main issue is to produce 3-D trajectories that ensure a collision free operation with respect to mission constraints. The path planner produces curved routes that are represented by 3-D B-Spline curves. Two types of planner are discussed: The off-line planner generates collision free paths in environments with known characteristics and flight restrictions. The on-line planner, which is based on the off-line one, generates collision free paths in unknown static environments, by using acquired information from the UAV’s on-board sensors. This information is exchanged between the cooperating UAVs in order to maximize the knowledge of the environment. Both off-line and on-line path planning problems are formulated as optimization problems, with a Differential Evolution algorithm to serve as the optimizer.","PeriodicalId":302311,"journal":{"name":"ICINCO-RA","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116699265","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 : 1900-01-01DOI: 10.5220/0001645200980102
R. Pepy, Eric Pierre
Nowadays, path planning for mobile robots has taken a new dimension. Due to many failures when experimenting the following of geometrical paths, determined by the first generation of planners (Latombe, 1991), with real robots, searchers concluded that those too simple paths were no longer enough. Planning method must now guarantee that the paths proposed are safe, i.e. that the robot will be able to follow a path without any risk of failure, or at least in warranting a high success rate. To achieve this goal, some parameters must be considered : uncertainties of the model used (not-so-perfect mapping, inaccuracy of the sensors, slipping of the robot on the floor, etc.). Collision detection is very important in mobile robotic and furthermore when trying to find a safe path in an uncertain-configuration space. Thus, searchers tend to integrate evolved collision detection in their planners. Thus, after having used circular disk to approximate the shape taken by the mobile robot, more and more searchers use elliptic disks as they offer a better accuracy. Used in the context of safepath planning (Pierre and Lambert, 2006; Lozano-Pérez and Wesley, 1979; Gonzalez and Stentz, 2005; Pepy and Lambert, 2006), ellipsoids allow to approximate the shape of the set of positions where the mobile could be(ellipsoids thus take the mobile robot’s geometry and the uncertainties on its position into account). The the Safe A* with Towers of Uncertainty (SATU*) planner (Pierre and Lambert, 2006) is one of those safe path planner that use ellipsoid to approximate the shape of the set of positions where the mobile could be. Ellipsoids are used in the SATU* to perform collision detection between the mobile robot and its environment. However, the authors of the SATU* have also proposed a new mean of organising the performing of the planner so that the ellipsoids can be used to detect very early beginning of useless paths. In order to achieve this goal, inclusion detection must be performed between two ellipsoids (that correspond to two different ways to come to the same position). In this paper, we are going to present an algebraic method using the resultant of Sylvester (Lang, 1984) to solve this problem. The SATU* algorithm (Alg. 1) has already been presented in (Pierre and Lambert, 2006) and three tests of inclusion of uncertainties (lines 7, 26 and 36) are used. However the authors did not explain how they implemented those tests nor give the algorithms used. As the model of uncertainties used in the SATU* corresponds to an ellipsoid in 3 dimensions, this test of inclusion of uncertainties can be seen as a test of inclusion of ellipsoids. In the present paper, we are going to propose an algorithm of test of inclusion of ellipsoids. In a first part, the uncertain configuration space will be described. Then, Sylvester’s resultant will be used to defined a ready for use inclusion detection test.
目前，移动机器人的路径规划已经进入了一个新的阶段。由于第一代规划者(Latombe, 1991)在用真正的机器人试验以下几何路径时多次失败，研究人员得出结论，那些过于简单的路径已经不够了。规划方法现在必须保证所提出的路径是安全的，即机器人将能够沿着没有任何失败风险的路径，或者至少保证高成功率。为了实现这一目标，必须考虑一些参数:所使用模型的不确定性(不太完美的映射，传感器的不准确性，机器人在地板上滑动等)。碰撞检测在移动机器人中是非常重要的，尤其是在不确定空间中寻找安全路径时。因此，搜索者倾向于将进化的碰撞检测集成到他们的计划中。因此，在使用圆形圆盘来近似移动机器人的形状之后，越来越多的搜索者使用椭圆圆盘，因为它们提供了更好的精度。用于安全路径规划(Pierre and Lambert, 2006;lozano - psamez and Wesley, 1979;Gonzalez and Stentz, 2005;Pepy和Lambert, 2006)，椭球体可以近似移动机器人所在位置的形状(椭球体因此考虑了移动机器人的几何形状和位置的不确定性)。安全A* with Towers of Uncertainty (SATU*)规划器(Pierre and Lambert, 2006)是一种使用椭球体来近似移动设备可能所在位置的安全路径规划器。在SATU*中使用椭球体来执行移动机器人与其环境之间的碰撞检测。然而，SATU*的作者也提出了一种新的方法来组织规划器的执行，这样椭球体就可以用来检测无用路径的早期开始。为了实现这一目标，必须在两个椭球体之间进行包含检测(对应于到达同一位置的两种不同方式)。在本文中，我们将使用Sylvester (Lang, 1984)的结式来提出一种代数方法来解决这个问题。SATU*算法(Alg. 1)已经在(Pierre and Lambert, 2006)中提出，并使用了包含不确定性的三个测试(第7、26和36行)。然而，作者没有解释他们是如何实现这些测试的，也没有给出使用的算法。由于SATU*中使用的不确定度模型对应于三维的椭球，所以这个不确定度的包含检验可以看作是椭球的包含检验。在本文中，我们将提出一种椭球包含检验算法。在第一部分中，将描述不确定构型空间。然后，Sylvester的结果将被用来定义一个现成的包含检测测试。
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