EP1728182A2 - Procede et dispositif de simulation interactive du contact entre objets - Google Patents
Procede et dispositif de simulation interactive du contact entre objetsInfo
- Publication number
- EP1728182A2 EP1728182A2 EP05741914A EP05741914A EP1728182A2 EP 1728182 A2 EP1728182 A2 EP 1728182A2 EP 05741914 A EP05741914 A EP 05741914A EP 05741914 A EP05741914 A EP 05741914A EP 1728182 A2 EP1728182 A2 EP 1728182A2
- Authority
- EP
- European Patent Office
- Prior art keywords
- objects
- contact
- forces
- time
- triangle
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Withdrawn
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Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T19/00—Manipulating 3D models or images for computer graphics
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T13/00—Animation
- G06T13/20—3D [Three Dimensional] animation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2210/00—Indexing scheme for image generation or computer graphics
- G06T2210/21—Collision detection, intersection
Definitions
- the present invention relates to a method and a device for interactive simulation of the contact between at least a first deformable object and at least a second object with a predetermined sampling time step of a simulated model. It has already been proposed to carry out a simulation of interpenetration measurements between a rigid object and a deformable object from volume or distance estimates, in particular for virtual surgery applications where a rigid virtual surgery tool cooperates with an organ. deformable virtual body.
- the relation between the measurement of interpenetration and the reaction contact forces have no physical basis and artificial forces can be applied to nodes of the meshes of the objects which are not in contact, this which affects reliability, or the contact forces do not meet the conditions of the Signorini problem.
- the present invention aims to remedy the aforementioned drawbacks and to make it possible to carry out an interactive simulation in real time of contact between objects, at least some of which are deformable, in a simplified and economical manner while respecting the constraints of the physical laws which govern contacts. , in such a way that the simulated contacts between objects are reliable and thus the stability of the simulation is guaranteed.
- These aims are achieved by an interactive simulation process of the contact between at least a first deformable object and at least a second object with a predetermined sampling time step of a simulated model, characterized in that: (a) we calculates beforehand the parameters describing the physical characteristics of each of the objects, such as the geometry and the mechanics of the materials of each of the objects, and these parameters are stored in a memory,
- each sampling time step of the simulated model we analyze in real time, at the level of a global scene comprising the objects likely to come into contact, pairs of objects which are detected at intersection, and we establishes a list of collision groups which contains a chain of colliding objects and a description of the collisions, (d) at each sampling time step of the simulated model, each group of collisions is brought back in real time parameters representing the physical characteristics of the objects and the description of the collisions, so as to determine, for each case, the solution to the Signorini problem which governs the contact between two objects in the case of a pure relative slip,
- step a) of preliminary calculation of the parameters describing the physical characteristics of each of the objects one uses for the parameters describing the mechanics of the materials a description of the deformations of the finite element type, with the filling and the inversion of matrices, solving equation systems and storing data in memory.
- each object is described in a configuration at rest as a set of triangles reproducing its surface and a set of tetrahedrons describing the interior of the object.
- each triangle is described by three points, placed in an order which makes it possible to calculate normals which are invariably directed towards the outside of the object.
- the deformations of the objects are interpolated by the finite element method using a linear tetrahedral mesh.
- the explicit forces applied to the object which are already known at the start of the computation step, are integrated during step b) at the level of an object, so as to define the movement that they create on the object, while the value of the implicit contact forces, which themselves depend on the movement of the objects in the step of time of computation, is determined during the stage d) of research at the level d 'a global scene, of the solution to Signorini's problem.
- step c) of analysis at the level of a global scene the existing intersections between the objects of the scene are geometrically detected in order to extract pairs of elements of intersecting objects, a length and a direction of interpenetration between the two elements of a couple of object elements.
- step c) of analysis at the level of a global scene to extract pairs of elements of intersecting objects, a length and a direction of interpenetration between the two elements d 'a couple of object elements, we also take into account an intermediate movement of objects between the previous calculation step and the current calculation step, to calculate a preferred direction of interference between these objects.
- step d) during step d) of finding the solution to the Signorini problem, in the case of a segment-segment intersection of two objects in triangle, the two points chosen to constitute the extreme points of application of the contact force between the two objects subjected to a collision are located at the intersection of each of the two segments with the plane formed by the face of the triangle in intersection.
- a first point chosen to constitute an extreme point of application of the contact force between the two objects subjected to a collision is the point of the intersection while the second extreme point of application of the contact force between the two objects subjected to a collision is the projection of the first extreme point on the face of the intersecting triangle.
- the barycentric coordinates are used to distribute the displacements and the forces of the points of application of the contact force between the extreme points of application of the contact force by performing a linear interpolation for a finite element modeling.
- one can calculate the interpenetration distance ⁇ between the two extreme points of application of the contact force in the case of a segment-segment contact between a first segment and a second segment of a second triangle from the following equation: N v ⁇ [a, b, c [a 1 - a] w, - [ ⁇ i - ⁇ ] V, (D
- ⁇ and 1- ⁇ are the barycentric coordinates on the first segment
- ⁇ and 1- ⁇ are the barycentric coordinates on the second segment
- ai bj q are the coordinates of the direction or interpenetration
- Wi and W 2 are the coordinates of the first segment
- Vi and V 2 are the coordinates of the second segment.
- ⁇ [a j bj c (2)
- ⁇ , ⁇ and ⁇ are the barycentric coordinates on the first triangle
- ai bj q are the coordinates of the direction or interpenetration
- Wi, W 2 , W 3 are the coordinates of the first triangle
- Vi represents the coordinates of the point of contact constituted by a vertex of the second triangle.
- step d) we consider the mass and inertia of an object in a global manner, at its center of gravity and an instantaneous relationship is established between the contact forces f c in the direction of the contact, the accelerations ⁇ " c due to constraints in the same direction and the free accelerations ⁇ " Ubre in the same direction known during step c) at the level of a global scene, according to the following equation:
- J c is a Jacobian matrix m * 6n which transfers the instantaneous linear and angular motion in the contact space
- 3 C T is the transposed matrix of J c
- M is a diagonal block matrix corresponding to the mass and the inertia of n objects in the contact group.
- N e is a passage matrix from the displacement space of the mesh to the displacement space at the contacts.
- ' c is a matrix of passage from the space of displacements of the mesh towards the space of displacements of contacts
- N 1 is the transposed matrix of N' c
- A is a matrix making it possible to define the deformation of l object at the local level, so that if U k represents the displacement vector in the local coordinate system of the object at the current time and U k -i represents the displacement vector in the local coordinate system of the object at no previous calculation whose instantaneous values are known at the start of the current calculation step, we have:
- UK A (Uk-i) F k + b (U k - ⁇ ) (7)
- F is a vector representing the external forces applied to the object expressed in the local coordinate system
- b is a vector which has a value in the space of displacements and which depends on the deformation model of the object.
- J c is a Jacobian matrix m * 6n which transfers the instantaneous linear and angular motion in the contact space
- c is the transposed matrix of J c 'M is a diagonal block matrix corresponding to the mass and inertia of n objects of the contact group
- ⁇ is a constant depending on the integration method in time
- N ' c is a passage matrix from the displacement space of the mesh to the contact displacement space
- (N ⁇ ) ⁇ is the transposed matrix ûe W c
- A is a matrix allowing to define the deformation of the object at the local level, so that if U k represents the vector of displacement in the local coordinate system of the object at the moment current and U k -i represents the displacement vector in the local coordinate system of the object at the previous calculation step, the instantaneous values of which are known at the start of the current calculation step, we have:
- the method according to the invention further comprises a step of coupling with a haptic interface module to produce a feedback of haptic sensation on a mechanical device by which an operator manipulates the objects in a virtual scene.
- the invention also relates to a device for interactive simulation of the contact between at least a first deformable object and at least a second object with a predetermined sampling time step of a simulated model, characterized in that it comprises:
- a coupling module with a user interface comprising a mechanical device held by a user allowing him to virtually exert forces on said objects in a scene of the simulated model
- a display screen for viewing said objects represented in the form of meshes
- a central processing unit associated with input means, comprising at least el) an object analysis module for analyzing in time real at the level of each object the proper behavior of the object to predict the positions, speeds and accelerations of this object according to a free movement which does not take account of possible subsequent contacts, e2) a model of analysis of a scene global including objects likely to come into contact, to analyze in real time pairs of objects which are detected in interaction and establish a list of collision groups which contains a chain of collision objects and a description of the collisions, e3) a real-time repatriation module, for each group of collisions, parameters representing the physical characteristics of the objects and the description of the collisions to determine, for each case, the solution to the Signorini problem which governs the contact between two objects in the case of a pure relative slip, e4) a processing module for each object to allow in real time at the level of each object a visualization in real time of the proper behavior of the object following
- the device comprises means for producing a haptic sensation feedback on the user interface.
- the calculation step corresponds to a frequency equal to or greater than approximately 500 Hz.
- FIG. 8 schematically illustrates an example of a device making it possible to implement the invention and to carry out the interactive simulation in real time of the contact between objects while allowing in particular to have a feedback of haptic sensation.
- a central processing unit 100 which can be constituted from a conventional computer, makes it possible to carry out the various calculations necessary to carry out a simulation.
- a display screen 107 connected to the computer 100 by a graphical interface allows the display of objects represented in the form of a mesh comprising nodes or vertices connecting segments or edges.
- Information can be supplied to the computer 100 from a conventional user interface 103 which may include a keyboard and for example a mouse and constituting input means.
- a specific mechanical device 104 held by a user connected by a coupling module 101 to the computer 100 may also be provided to allow the user to virtually exert forces on the objects in a scene of a simulated model.
- Such a mechanical device 104 and the coupling module 101 constitute a haptic interface which allows the user to exert a stress on the virtual objects of the scene and receive in return a haptic simulation which is a response provided by the simulation of contact between objects.
- the computer 100 conventionally comprises at least one processor, a permanent memory for storing programs and data and a working memory cooperating with the processor.
- a first module located at the level of each object and describing its own behavior, makes it possible to develop the position and the shape of the object according to the forces and the places of the forces exerted.
- This module is called at the start of the calculation step to predict the positions, speeds and accelerations of the objects without taking account of the contact then will be again mobilized to take account of the forces calculated in a third module called "contact processing”.
- a second module located at the level of the global scene establishes pairs of objects which are detected at intersection.
- This module can create intermediate movements between the simulation steps to know when and how the objects entered at intersection.
- This module is governed above all by optimized geometric laws which make it possible to speed up the calculation in order to obtain a chain of colliding objects and a description of the collisions.
- a collision group is thus a set of objects linked together by at least one collision.
- An object enters a group if it collides with at least one of the objects in the group.
- a collision is necessarily described by the pair of objects in collision and by the location of the collision using either the basic geometric elements (for example two triangles or two surfaces) at intersection, or by a segment connecting the two points which are locally the most interpenetrated.
- a third module called “contact processing” is called by the "collision detection” module and calls back to the "mechanical” module.
- the contact processing module brings together the physical characteristics of the objects and the description of the collisions.
- the module is able to determine, for each case, the solution to the Signorini problem which governs the contact between two objects in the case of pure sliding.
- the invention allows for interactive simulation.
- a simulation is defined by the sampling time step of the simulated model and by the calculation time step of this model.
- the method according to the invention implements a computation time step which is always less than the time step chosen for the sampling, which makes it possible to have an interactive simulation where the user will be able to intervene directly during the simulation.
- Figure 1 summarizes the main steps of the method according to the invention which implements a simulation loop using the three aforementioned main modules installed in the computer 100 of Figure 8.
- FIG. 2 illustrates the different levels of processing between objects in during the different stages of the simulation process.
- a first processing step 130 uses the so-called "mechanical” module and is located at the level of each object (object level 3). The information is provided through a coupling module 120 from the user interface 110 or haptic interface which determines the position and the shape of each object (information 135 developed in step 130).
- a modeling 13 takes into account each object or tool 201, 202, 203 individually without taking account of any subsequent interactions and makes it possible to change the position and the shape of the object according to the forces and the places of the forces exerted from the user interface 110.
- a second step of the processing 140 uses the so-called "collision detection" module and is situated at the level of a global scene (scene level 4).
- the information 135 produced in step 130 is used in step 140 to establish pairs of objects which are detected at intersection.
- a list of collision groups (information 145) is produced containing a chain of colliding objects and a description of the collisions.
- a modeling 14 thus takes into account a pair of intersecting objects such as the objects 201, 202 at the level of a global scene.
- a third processing step 150 uses the module called "contact processing" and is located at the level of a global scene (scene level 5).
- the information 145 produced in step 140 as well as the information 135 produced in step 130 are used to determine for each case the solution to the Signorini problem which governs the contact between two objects in the case of pure sliding (information 155).
- a modeling 15 thus takes into account the interaction between two objects such as the objects 201, 202 at the level of a global scene, the physical characteristics of the objects and the description of the collisions being retrieved for each group of collisions by the "contact processing" module.
- the third processing step 150 provides information 155 concerning forces and locations which are transmitted to the first "mechanical" module during a fourth processing step 160 which is again located at the object level (object level 6).
- the result of the simulation processing in real time can simply be normalized in a viewing step 170 or can be transmitted back through the coupling 120 to the user interface 110 to give the user feedback. haptic sensation.
- a modeling 16 thus again takes into account each object or tool 201, 202, 203 individually while having taken into account the contacts previously simulated.
- the object is described as a set of triangles reproducing its surface and a set of tetrahedra to describe its interior, all in a resting configuration. This configuration corresponds to the shape of the object when no force is applied to it.
- the triangles are described by three points, placed in an order which allows the calculation of the normals to be invariably directed towards the outside of the object.
- the surfaces of objects are closed so that you can distinguish an exterior from an interior.
- the deformations of the objects are interpolated by the finite element method using a linear tetrahedral mesh.
- the device makes it possible to simulate different constitutive laws provided that one can extract locally, approximately and for a computation step, a linear relation between the forces exerted and displacements around a local configuration. If U k represents the displacement vector in the local coordinate system of an object at the current time t and if U k -i represents the vector of displacement in the local coordinate system of the object at the previous computation step t-1, we have the following relation:
- A is a matrix allowing to define the deformation of the object at the local level
- F k is a vector representing the external forces applied to the object expressed in the local coordinate system
- b is a vector which has a value in l space of displacements and which depends on the model of deformation of the object
- U k -i is a vector whose instantaneous values are known at the beginning of the step of computation, of the current instant t.
- A is a matrix allowing to define the deformation of the object at the local level
- F k is a vector representing the external forces applied to the object expressed in the local coordinate system
- b is a vector which has a value in l space of displacements and which depends on the model of deformation of the object
- U k -i is a vector whose instantaneous values are known at the beginning of the step of computation, of the current instant t.
- the proposed system then implements a collision detection process which allows geometrically testing the intersections. existing between the objects 223, 230 of the scene and the preferred directions for removing the objects from this collision ( Figures 6 and 7). If we consider an object 221 which, in a position 223, comes into interaction with another object 230, the preferred direction can be calculated only on geometric criteria (case of Figure 6) or can depend on the configuration by which the objects 223, 230 collided taking into account an intermediate movement 222 of at least one of the objects between the preceding calculation step and the current calculation step (case of FIG. 7). In all cases, the collision detection process makes it possible to extract pairs of elements of intersecting objects, a length and a direction of interference between these two elements.
- an element is either a point, or a segment, or the face of a triangle.
- Collision detection can take into account three canonical cases of intersection between two objects: point / triangle intersection, segment / segment intersection, triangle / point intersection.
- the method can also provide a set of nearby object elements which could potentially collide following the integration of contact forces. A distance and a direction separating these elements are then calculated. Thanks to the description of all the interferences and proximities between the objects, the set of collision groups of the scene can be constructed. Each group will then go into the contact module. After detecting a collision, processing in the contact module makes it possible to determine the configuration of the first contact between two calculation time steps.
- a list of triangles is extracted. composing the pair of objects. If we have a rigid object and a deformable object, the coordinates of the triangle representing the deformable object are translated in the frame of reference of the rigid object at separate moments of sampling of simulation T and Tl. For any pair possible triangle / triangle there is a linear interpolation of the displacement of three points Di, D 2 , D 3 of the triangle deformable between the initial and final positions at the discrete sampling instants T and Tl. It is then possible to operate three different types of tests represented in FIGS.
- Test 1 corresponds to the case where a collision plane is formed by the rigid triangle and will establish a constraint on the point concerned of the deformable triangle.
- Test 2 corresponds to the case where a collision plane is formed by a rigid segment and a deformable segment at the instant of collision t, and will establish a constraint on two points of the deformable object.
- Test 3 corresponds to the case where a collision plane is formed by the deformable object at the moment of collision and will establish a constraint on three points of the deformable triangle.
- the invention can be applied as well in the case of collisions between a rigid object and a deformable object as in the case of collisions between two deformable objects.
- the contact module will be described below in more detail with reference to the preferred case of a description of the triangle objects.
- the contact module is called as many times as there are groups of collisions in the scene at the time of the calculation.
- the collision detection module has stored in a memory space for each collision: - the normal, - the pair of objects and the elements affected by the collision, - (possibly) the points of application of the contact force.
- the collision detection algorithm does not give the points of application of the contact force (case illustrated in Figure 6 of a detection without intermediate movement), they must be reconstructed and in all cases, it must be interpolated these points of application compared to the model of deformation chosen.
- the two chosen points 41, 51 are located at the intersection of each of the two segments Qi, Q 2 , resp. Pi, P 2 with the plane formed by the face of the other triangle in intersection.
- the vector connecting the two points found 41, 51 is called ⁇ .
- a Point / Face intersection between a triangle 60 defined by vertices Pi, P 2 , P 3 and a triangle 70 defined by vertices Qi In the case of a Point / Face intersection between a triangle 60 defined by vertices Pi, P 2 , P 3 and a triangle 70 defined by vertices Qi,
- alpha and 1-alpha are the barycentric coordinates on the first segment Qi, Q 2 and Beta, 1-Beta on the second segment Pi, P 2 , ai, bi, q are the coordinates of the normal and the triangle 40, Wi , W 2 are the coordinates of the first segment Qi, Q 2 , Vi, V 2 are the coordinates of the second segment Pi, P 2 .
- ai, bi, q are the coordinates of the normal nor of the triangle 60, the interpenetration distance ⁇ between the triangles 60 and 70 is written:
- Wi, W 2 , W 3 are the coordinates of the first triangle 60, and Vi are the coordinates of the contact point 71 constituted by a vertex Qi of the second triangle 70.
- An identical interpolation is used for the contact force. Once the point of application of the contact forces has been found, the mechanical characteristics of the objects are transferred to the defined space of the contacts. For the rest, we suppose that we treat a group of m contacts with n objects.
- J c is a Jacobian matrix m * 6n which transfers the instantaneous linear and angular motion in the contact space
- M is a diagonal block matrix corresponding to the mass and inertia of the n objects of the contact group
- J c ⁇ is the transposed matrix of J c .
- Ne 1 represents the matrix of passage from the space of displacements of the mesh towards the space of displacements with contacts and A is a matrix as defined above.
- the contact modeling is chosen so as to respect physical laws as well as possible. For the sake of simplification, it may nevertheless preferably be considered that the contacts will not change direction during the resolution of the calculation even if in practice this is not strictly the case.
- the first postulate of Signorini's problem is that there is no interference between objects if they are solid (materials do not mix). Thus, one wishes that after the resolution of the problem displacement in contact is positive or null:
- the second postulate is that one is in the case of a contact without friction, therefore the contact force is directed according to the normal: f> 0 (10)
- X t + 1 X t + ⁇ / 2 dt (X / + X t + 1 ')
- X t + 1 ' X / + ⁇ / 2 dt (X t "+ X 1 + 1 ")
- the coefficient 1/4 can be different if another method of integrating accelerations is used. If the mechanical model chosen does not include global characteristics and if the mass and inertia are integrated at the local level in the model of deformation, one uses only equation (5) which already implicitly includes a numerical integration in time.
- LCP linear complementarity problem
- there are many solving algorithms see for example Murty, KG, Linear Complementarity, Linear and Nonlinear Programming. Internet Edition 1997) which are capable of solving the problem in a time compatible with the performances requested by the haptics.
- a calculation can be made at a frequency of the order of 500 Hz to 1000 Hz for a reasonable number of contacts (for example 30 to 40 contacts) using the main Pivot algorithm on a Pentium IV 2GHz PC type computer.
- Figure 3 illustrates the interaction between a deformable object 80, such as pliers with another object 90.
- the deformable object 80 is virtually attached to the haptic interface (since it is held by the user) in an area of a node O defining an OxoyoZn coordinate system.
- FIGS. 10A to 10C show the example of a deformable object 80 constituted by a clip placed on a tube 91. We see different deformations of the clip 80 in positions 81, 82, 83 different with respect to the tube 91.
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Abstract
Description
Claims
Applications Claiming Priority (2)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
FR0403037A FR2868180B1 (fr) | 2004-03-24 | 2004-03-24 | Procede et dispositif de simulation interactive du contact entre objets |
PCT/FR2005/000699 WO2005093610A2 (fr) | 2004-03-24 | 2005-03-23 | Procede et dispositif de simulation interactive du contact entre objets |
Publications (1)
Publication Number | Publication Date |
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EP1728182A2 true EP1728182A2 (fr) | 2006-12-06 |
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Application Number | Title | Priority Date | Filing Date |
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EP05741914A Withdrawn EP1728182A2 (fr) | 2004-03-24 | 2005-03-23 | Procede et dispositif de simulation interactive du contact entre objets |
Country Status (5)
Country | Link |
---|---|
US (1) | US20070268288A1 (fr) |
EP (1) | EP1728182A2 (fr) |
CA (1) | CA2566276A1 (fr) |
FR (1) | FR2868180B1 (fr) |
WO (1) | WO2005093610A2 (fr) |
Families Citing this family (13)
Publication number | Priority date | Publication date | Assignee | Title |
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KR100888475B1 (ko) * | 2007-02-02 | 2009-03-12 | 삼성전자주식회사 | 모델간 충돌 여부 검사 방법 및 장치 |
US9098944B2 (en) * | 2010-03-04 | 2015-08-04 | Pixar | Scale separation in hair dynamics |
US8731880B2 (en) | 2010-09-14 | 2014-05-20 | University Of Washington Through Its Center For Commercialization | Invertible contact model |
US20140002492A1 (en) * | 2012-06-29 | 2014-01-02 | Mathew J. Lamb | Propagation of real world properties into augmented reality images |
US9934339B2 (en) | 2014-08-15 | 2018-04-03 | Wichita State University | Apparatus and method for simulating machining and other forming operations |
CN105354876B (zh) * | 2015-10-20 | 2018-10-09 | 何家颖 | 一种基于移动终端的实时立体试衣方法 |
CN106202247B (zh) * | 2016-06-30 | 2017-10-13 | 哈尔滨理工大学 | 一种基于经纬度的碰撞检测方法 |
CN106202642B (zh) * | 2016-06-30 | 2017-10-13 | 哈尔滨理工大学 | 一种基于瞬态显示延迟处理的计算机切割模拟方法 |
WO2019088681A1 (fr) * | 2017-10-31 | 2019-05-09 | 경희대학교산학협력단 | Procédé d'amélioration de sécurité et d'évaluation de sécurité pour robot |
US11654550B1 (en) * | 2020-11-13 | 2023-05-23 | X Development Llc | Single iteration, multiple permutation robot simulation |
CN112989449B (zh) * | 2021-03-26 | 2023-08-15 | 温州大学 | 一种运动刚度优化的触觉力反馈仿真交互方法及装置 |
CN113919159B (zh) * | 2021-10-14 | 2022-10-21 | 云南特可科技有限公司 | 一种物流空间优化方法 |
CN114626293A (zh) * | 2022-02-23 | 2022-06-14 | 中国科学院深圳先进技术研究院 | 预测碰撞仿真结果的方法、装置、设备及存储介质 |
-
2004
- 2004-03-24 FR FR0403037A patent/FR2868180B1/fr not_active Expired - Fee Related
-
2005
- 2005-03-23 CA CA002566276A patent/CA2566276A1/fr not_active Abandoned
- 2005-03-23 EP EP05741914A patent/EP1728182A2/fr not_active Withdrawn
- 2005-03-23 WO PCT/FR2005/000699 patent/WO2005093610A2/fr active Application Filing
- 2005-03-23 US US10/593,834 patent/US20070268288A1/en not_active Abandoned
Non-Patent Citations (1)
Title |
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CHRISTAN DURIEZ ET AL: "Interactive haptics for virtual prototyping of deformable objects: snap-in tasks case", PROCEEDINGS OF EUROHAPTICS'03, 9 July 2003 (2003-07-09), pages 159 - 175, XP055254647, Retrieved from the Internet <URL:http://www.eurohaptics.vision.ee.ethz.ch/2003/08.pdf> [retrieved on 20160302] * |
Also Published As
Publication number | Publication date |
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CA2566276A1 (fr) | 2005-10-06 |
WO2005093610A2 (fr) | 2005-10-06 |
WO2005093610A3 (fr) | 2006-09-21 |
FR2868180A1 (fr) | 2005-09-30 |
US20070268288A1 (en) | 2007-11-22 |
FR2868180B1 (fr) | 2006-06-16 |
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