CN101286188A - Dummy emulation system force feedback computation method - Google Patents

Dummy emulation system force feedback computation method Download PDF

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CN101286188A
CN101286188A CNA2008100664806A CN200810066480A CN101286188A CN 101286188 A CN101286188 A CN 101286188A CN A2008100664806 A CNA2008100664806 A CN A2008100664806A CN 200810066480 A CN200810066480 A CN 200810066480A CN 101286188 A CN101286188 A CN 101286188A
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collision
tool
particle
virtual tool
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CN101286188B (en
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陈辉
王琼
王平安
马炘
吴剑煌
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Shenzhen Institute of Advanced Technology of CAS
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Shenzhen Institute of Advanced Technology of CAS
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Abstract

The invention discloses a calculation method for force feedback in a virtual system, which comprises the following steps: step 1: a virtual environment comprising a virtual space, a virtual object and a virtual tool is established, attributes of the virtual tool are set, and a point set model which includes a plurality of mass points and surrounds the virtual tool is constructed; step 2: the virtual tool and a force feedback device are bound, the motion states of the virtual tool and the virtual object in the virtual space are tracked, whether the virtual tool and the virtual object collide or not is judged, if yes, step 3 is implemented; the step 3: the line speeds and the motion speeds before and after the collision of all the collision mass points of the virtual tool during the collision are respectively calculated, and the received impact during the collision process is also calculated; step 4: the resultant forces and the resultant moments of forces of all the collision mass points of the virtual tool are calculated and sent to the force feedback device. The calculation method takes full account of the self-rotation features of a virtual surgical instrument and can be applied in a surface model or a body model adopted in the virtual surgery.

Description

The computing method of power feel feedback in a kind of dummy emulation system
Technical field
The present invention relates to the virtual emulation technical field, in particular, in a kind of dummy emulation system, for virtual tool with rotation characteristic, power is felt the computing method of feeding back can be widely used in medical technology, for example calculating of realizable force feel feedback in virtual operation artificial system.
Background technology
The virtual emulation technology has obtained widely using, especially in the application of medical domain.For example, virtual operation is the virtual reality emulation application system that is used for simulating the various phenomenons that may run into specially in surgical procedure.By virtual operation the operator is immersed in the virtual surgical scene, virtual operation instrument is experienced and how study carries out various operations by handling.On the one hand it can help the intern to learn, grasp the anatomical structure of human body, the training that undergos surgery, and the ability of various emergency case is dealt with in cultivation; Can also allow the surgeon carry out simulation and postoperative effect prediction in art preplanning, the art on the other hand, make operation safer, reliable and accurate at a real sufferer.
The technology of virtual operation realizes mainly comprising the reconstruction of surgical environments and two parts of simulation of surgical procedure.Wherein the reconstruction of surgical environments mainly comprises the reconstruction of medical data and visual; The simulation of surgical procedure mainly comprises for the simulation of the various variations of virtual human body organ under the virtual operation instrument effect and the simulation that provides visual feedback and power to feel various sensory feedback such as feedback to medical personnel.
Outstanding virtual operation artificial system should be able to provide many perceived effects as the aspects such as vision, sense of touch and the sense of hearing as true for the operator.The hardware configuration of existing virtual operation artificial system based on force feedback comprises that mainly visual display device and power feels feedback device, and software systems mainly comprise modules such as Visual Display, sense of touch drafting and deformation simulative.The operator handles the virtual operation instrument of being seen on the screen by the mechanical arm on the power feel feedback device, in reality environment, take place mutual and carry out corresponding operation technique with operative site, calculate the power that produces when mutual and moment and feel that by power feedback device passes to the operator, mutual operative region also can produce corresponding distortion simultaneously.The sense of touch drafting module is mainly used in the power feel feedback between virtual operation instrument and the virtual human body histoorgan.Various virtual operation instruments are carried out in the method for power feel feedback at great majority at present, contact between virtual operation instrument and the virtual human body organ need be reduced to the contact of being undertaken by between point or line and the virtual human body organ, utilize Hooke's law to simulate each contact force by the spring shock absorption model then, the most a plurality of power combine and feed back to the operator.But, at self having the particularly sham operated apparatus of rotation of kinetic characteristic, for example bone drill, mill bone object, swing saw etc. feel that the method for feedback is complicated relatively more owing to also need to consider the kinetic characteristic of himself so such virtual operation instrument is carried out power.
In the world, some scholars had once carried out deep research to virtual bone emulation surgical technic.The skeleton model that most of virtual bone-operating uses all is based on volume drawing.From 2002, Marco Agus has delivered a series of papers and has set forth a kind of virtual operation training system (Agus M that is applicable to any bone, Giachetti A, Gobbetti E, Zanetti G, Zorcolo A.A multiprocessordecoupled system for the simulation of temporal bone surgery[J] .ComputerVisualization in Science, 2002,5 (A1:35-4A3 has used Hertz ' s contact theory to estimate the contact force that bone is produced when distortion in this system.But in this system, only used the collision detection of single-point, this is easy to cause the concussion of power and discontinuous, is unfavorable for the real contact force effect of analog feedback.
Pertersik is on the basis of Marco, proposed a kind of again based on the collision detection algorithm calculating virtual operation instrument of multiple spot and reciprocal force (the Petersik A between the skeleton model, Pflesser B, Tiede U, Hohne K H, Leuwer R.Haptic Volume Interaction with Anatomic Models atSub-Voxel Resolution[C] .Proc IEEE VR, Orlando, FL, Mar 2002:66-72), and continue again single voxel is segmented at power feel feedback fraction and display part, therefore compared originally and came Calculation Method according to single voxel, this method can obtain more accurate power feel impression and finer and smoother screen picture is drawn, thereby makes model fineness and use not be subjected to the restriction of voxel size.But, in the reciprocal process of power, because system do not consider the virtual operation instrument that it is special---the rotation of bone drill is to the influence of power Model Calculation, and this rotation is very crucial to the feedback force that authentic and valid simulation bone drill or mill bone object are produced when removing bone.
2006, the people such as Morris of biorobot testing laboratory of Stanford Univ USA, developed one and be applicable to that the training beginner can grasp (the Morris D of operative training system of grinding bone technical ability in bone surgery, Sewell C, Barbagli F, Blevins NH, Girod S, Salisbury K.Visuohaptic simulation of bone surgery for training and evaluation[J] .IEEETransactions on Computer Graphics and Applications, 2006,26 (6): 48-57), its data that proposed the use mixed type are used surface model that smooth surface is shown on the one hand and are played up, and use volume data to carry out the power feel on the other hand and play up.Play up the stage in the power feel, when Morris comes in contact by virtual operation instrument and bone, calculate the voxel that all are immersed to virtual operation instrument inside, and the method by ray trace, according to the distance of each voxel to the circular tool central point, try to achieve each voxel to the stressed contribution of virtual operation instrument, but still there are some problems in this method, because the calculating of all contact forces all be based on virtual operation instrument inside voxel vector and be not based on the geological information on skeleton model surface, so feel the concussion that causes power when playing up easily and discontinuous carrying out power.
People (Eric A such as Eric in 2006, Alan L.Real-time Volumetric Haptic and VisualBurrhole Simulation[C], 2007IEEE Virtual Reality Conference, 2007:247-250) proposed to use the method for voxmap point-shell to simulate mutual between virtual operation instrument and the bone, minimizing power discontinuous, but because this method is the normal vector that is based on tool surfaces equally when the direction of computing power, the direction of the real power that virtual operation instrument is experienced takes place when mutual so be unfavorable for definite expression virtual operation instrument and bone.
But there is following shortcoming in prior art:
(1), lack consideration at virtual operation instrument displacement characteristic, the feedback force that the characteristic of virtual operation instrument high speed rotation is produced when authentic and valid simulation bone drill or mill bone object are removed bone is very crucial.
(2), adopt based on power in the method simulation bone-operating of volume drawing or iso-surface patch and feel the generation of feedback, need carry out the calculating of force feedback to a large amount of discrete voxel datas respectively, cause the concussion of power and discontinuous easily.
Therefore, also not have at present systematically to carry out dynamic sensing interexchanging at the virtual tool that self has the rotation characteristic, power is felt the computing method of feeding back.Especially for virtual operation instrument, for example bone drill and mill bone object etc., physical characteristicss such as the shape of instrument commonly used, rotation the most in bone surgery and bone plastic operation do not have specialized designs and set up a kind of model of dynamic sensing interexchanging.
Therefore, there is defective in prior art, needs to improve.
Summary of the invention
Technical matters to be solved by this invention is volume drawing or the iso-surface patch model that does not rely on virtual objects, how to provide in a kind of dummy emulation system, and especially in the virtual operation artificial system, power is felt the computing method of feedback.
Technical scheme of the present invention is as follows:
A kind of computing method that the power feel is fed back in virtual system, it may further comprise the steps: A1, set up virtual environment, comprising Virtual Space, virtual objects and virtual tool, the attribute of described virtual tool is set, make up the point set model of forming by a plurality of particles, surround described virtual tool; Wherein, described attribute comprises quality, angular velocity and moving radius; A2, described virtual tool and force feedback equipment being bound, followed the tracks of described virtual tool and the motion state of described virtual objects in described Virtual Space, judge whether described virtual tool and described virtual objects bump, is then to carry out A3; A3, respectively collide particle, calculate it respectively before collision and linear velocity and movement velocity after the collision for what described virtual tool bumped, and the impulsive force that in collision process, is subjected to; Making a concerted effort and resultant moment of whole collision particles of A4, the described virtual tool of calculating, send to described force feedback equipment.
Described computing method, wherein, described virtual environment is the virtual operation environment, and described virtual objects is a virtual organ, and described virtual tool is a virtual operation instrument.
Described computing method, wherein, described virtual operation instrument is virtual bone drill; And in the steps A 1, each particle of described point set model is the central point of each tri patch of described virtual bone drill.
Described computing method, wherein, in the steps A 1, described virtual tool has rotation character; And described attribute also comprises kind, model, spin velocity and rotation radius.
Described computing method, wherein, in the steps A 1, described structure surrounds the point set model of described virtual tool, and execution following steps: A11, the basis condition of pre-seting are determined the quantity of the particle of described point set model; A12, distribute according to the profile of described virtual tool and to choose each particle; A13, according to the position of each particle, and the quality of described virtual tool is provided with the quality of each particle; Wherein, the quality sum that constitutes whole particles of described point set model is the quality of described virtual tool.
Described computing method, wherein, each point mass of described point set model is identical.
Described computing method, wherein, in the steps A 2, described judgement judges whether described virtual tool and described virtual objects bump, and adopts collision detection algorithm to realize; Wherein, described collision detection algorithm comprises the level collision bounding box collision detection algorithm of binary tree mode.
Described computing method, wherein, in the steps A 3, adopt linear velocity and movement velocity after following steps are calculated described collision respectively: the linear velocity after A31, the described collision, adopt linear velocity before the described collision to multiply by one and pre-set the linear velocity coefficient and obtain; Movement velocity after A32, the described collision adopts movement velocity before the described collision to multiply by one and pre-sets coefficient of restitution and obtain.
Described computing method, wherein, in the steps A 3, adopt following steps to calculate the described impulsive force of a certain collision particle: A33, will collide linear velocity and movement velocity and linear velocity collision after and the movement velocity of particle before collision, synthesize this collision particle on the section speed and perpendicular to the speed in section, calculate particle suffered impulsive force in collision process according to theorem of momentum and Coulomb law.
Described computing method, wherein, in the steps A 4, adopt following steps to calculate described making a concerted effort: to the impulsive force of respectively colliding particle of described virtual tool, after synthesize, the environmental forces that is subjected to described virtual tool synthesizes again, obtain described with joint efforts.
Adopt such scheme, the present invention has taken into full account the rotation characteristic of virtual tool itself, virtual operation instrument etc. for example, set up a kind of model of new dynamic sensing interexchanging, do not rely on the volume drawing or the iso-surface patch model of virtual human body organ, on surface model that the computing method of this force feedback can be applied to adopt in the virtual operation or the phantom type.Thereby can in virtual operation or other are used, reproduce truly contain the rotation characteristic virtual tool with virtual objects the power when mutual feel and feed back; This force feedback model directly can also be used on the surface model and phantom type of various data; Therefore, can unite with display model fast and effectively, be applied to the simulation of force feedback in the virtual reality system, improve the sense of reality and the feeling of immersion of dynamic sensing interexchanging.
Description of drawings
Fig. 1 is a method overview flow chart of the present invention;
Fig. 2 is the process flow diagram of one embodiment of the present invention;
Fig. 3 is a power model synoptic diagram in the virtual operation of the present invention;
Fig. 4 is a calculating virtual tool time rotational of the present invention, the linear velocity synoptic diagram of putting on the sphere;
Fig. 5 is the vertical relation synoptic diagram that horizontal momentum of the present invention and vertical impulse satisfy;
Fig. 6 for the degree of depth of the vertical surface direction of one embodiment of the present invention and virtual tool be subjected to make a concerted effort between concern synoptic diagram;
Fig. 7 is the synoptic diagram that concerns between the degree of depth of vertical surface direction of one embodiment of the present invention and the normal pressure;
Fig. 8 is the synoptic diagram that concerns between the virtual tool rotation linear velocity of one embodiment of the present invention and the friction force.
Embodiment
Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.Need to prove, below with in the virtual operation, the interaction between virtual surgical operating instrument and the virtual human body organ, when real-time dynamic sensing interexchanging, the power that is produced is felt the example that is calculated as of feedback; But the present invention is equally applicable to itself have the various virtual tools of a fixed angular speed rotation, in the Virtual Space, virtual objects is done the time spent, the computing method of power feel feedback.More particularly, the contact computing method of the power that produced of virtual haptic technical research and virtual human body organ, be widely used in fields such as medical science, industrial design, recreation, robot, in description of the invention, with the virtual operation is that the basis is described, but the computing method of not repelling power feel feedback described in the invention, and the computation model of power feel feedback are used for the application system that other can provide virtual haptic.
For example, the three-dimensional model of medical data comprises voxel model and 3-D geometric model, and voxel model is directly to utilize the medical image gathered (model of display process is carried out in gray scale of z) locating or brightness for x, y at voxel.3-D geometric model is by medical image being carried out segmented extraction, utilizing iso-surface extracting to rebuild the polygonal grid model of the various human tissue organs that generate, for example tri patch model and tetrahedron model etc.In the present invention, be that the 3-D geometric model with medical data is that the basis is described, be not applied to voxel model but do not repel the present invention, that is to say that the application from the 3-D geometric model is equally applicable to voxel model.
In general, the operating theater instruments that contains spinning motion is an operating theater instruments commonly used in the operation, for example bone drill, mill bone object etc., in the present invention, with operating theater instruments commonly used in this Orthopeadic Surgery of bone drill is that the basis is described, but the present invention is equally applicable to simulate the operating theater instruments that other contain the rotation characteristic.
Aim of the present invention be simulation itself contain the virtual tool of rotation characteristic and object when mutual power feel the emulated computation method of feedback, the friction force and the normal pressure that produce when instrument by utilizing the movement velocity simulation high-speed rotation of instrument when boring pairing linear velocity of angular velocity and operation tool and dummy object collision, and the impulsive force of utilizing theorem of impulse and Coulomb law simulation tool to be subjected at collision process; What the impulsive force at last comprehensive many points of impingement place and environmental forces simulation tool were suffered makes a concerted effort and resultant moment.In view of the above, overall technological scheme of the present invention the invention provides a kind of computing method that the power feel is fed back in virtual system as shown in Figure 1, and it may further comprise the steps:
A1, set up virtual environment,, the attribute of described virtual tool is set, make up point set model that forms by a plurality of particles, the described virtual tool of encirclement comprising Virtual Space, virtual objects and virtual tool; Wherein, described attribute comprises quality, angular velocity and moving radius.
For example, described virtual tool has rotation character; And described attribute also comprises kind, model, spin velocity and rotation radius.
And for example, described structure surrounds the point set model of described virtual tool, and execution following steps: A11, the basis condition of pre-seting are determined the quantity of the particle of described point set model; A12, distribute according to the profile of described virtual tool and to choose each particle; A13, according to the position of each particle, and the quality of described virtual tool is provided with the quality of each particle; Wherein, the quality sum that constitutes whole particles of described point set model is the quality of described virtual tool.Be more preferably, each point mass of described point set model is identical.
A2, described virtual tool and force feedback equipment being bound, followed the tracks of described virtual tool and the motion state of described virtual objects in described Virtual Space, judge whether described virtual tool and described virtual objects bump, is then to carry out A3.
For example, described judgement judges whether described virtual tool and described virtual objects bump, and can adopt collision detection algorithm to realize; Wherein, described collision detection algorithm comprises the level collision bounding box collision detection algorithm of binary tree mode.
A3, respectively collide particle, calculate it respectively before collision and linear velocity and movement velocity after the collision for what described virtual tool bumped, and the impulsive force that in collision process, is subjected to.
For example, can adopt linear velocity and movement velocity after following steps are calculated described collision respectively: the linear velocity after A31, the described collision, adopt linear velocity before the described collision to multiply by one and pre-set the linear velocity coefficient and obtain; Movement velocity after A32, the described collision adopts movement velocity before the described collision to multiply by one and pre-sets coefficient of restitution and obtain.
Can also adopt following steps to calculate the described impulsive force of a certain collision particle: A33, will collide linear velocity and movement velocity and linear velocity collision after and the movement velocity of particle before collision, synthesize this collision particle on the section speed and perpendicular to the speed in section, calculate particle suffered impulsive force in collision process according to theorem of momentum and Coulomb law.
Making a concerted effort and resultant moment of whole collision particles of A4, the described virtual tool of calculating, send to described force feedback equipment.For example, can adopt following steps to calculate described making a concerted effort: to the impulsive force of respectively colliding particle of described virtual tool, after synthesize, the environmental forces that is subjected to described virtual tool synthesizes again, obtain described with joint efforts.
That is to say, adopt the inventive method, at first be provided with virtual operation instrument and with the attribute of virtual human body organ, and the point set model of constructing virtual operating theater instruments; Real-time follow-up virtual operation instrument and the motion state of virtual human body organ in the Virtual Space then, and judge between virtual operation instrument and the virtual human body organ whether bump; If collision has taken place, then calculate respectively and respectively collide particle before collision and linear velocity and movement velocity after the collision, otherwise continue to follow the tracks of; Calculate collision particle suffered impulsive force in collision process, and calculate and make a concerted effort, comprise the impulsive force and the environmental forces at all collision particle places; Calculate resultant moment at last, will make a concerted effort and the resultant moment power that passes to is felt feedback device, feel that by power feedback device passes to the operator.
For example, described virtual environment is the virtual operation environment, and described virtual objects is a virtual organ, and described virtual tool is a virtual operation instrument, and as shown in Figure 2, the particular flow sheet for this embodiment is described in detail as follows.
Step 1: follow the tracks of the conversion of object in the Virtual Space.The reconstruction of surgical environments comprises the model of the three-dimensional model of importing medical data and operating theater instruments and shows in the virtual operation.The user can pass through input equipment, for example mouse, keyboard, force feedback equipment etc., to dummy object move, operation such as rotation and scaling.Need to follow the tracks of this evolution of object in the Virtual Space, so that carry out the collision detection between the object of virtual tool.
Step 2: the attribute that operating theater instruments is set.Operating theater instruments of the same race often comprises multiple different model.The model of a virtual operation instrument can be simulated the operating theater instruments of multiple model.For example virtual bone drill model is made up of a series of tri patchs that are evenly distributed on the ball surface, at the true attribute of the operating theater instruments of being simulated the attribute of virtual operation instrument is set, and comprises mass M, spin velocity ω, the radius R of instrument rotation.
Step 3: structure surrounds the point set model of operating theater instruments.In order to increase the authenticity in the force feedback process, the present invention can use the collision detection of multiple spot, replace virtual operation instrument by many points that are distributed on the tool surfaces, abbreviate the point set model as, in the process of carrying out collision detection, detect these points, or the tri patch at some place, judge whether it bumps with model.
In general, choosing of point preferably followed following two principles:
Point set wants probably to depict the profile of operating theater instruments, and point is many more intensive more, and the profile that can depict is accurate more, so the result of collision detection is also just approximate more.Can be as the case may be, for example organ model, calculating strength, power sense refreshing frequency etc. pre-set condition, determine the quantity of the particle of described point set model.
The point that point is concentrated all is the close particle of quality, is more preferably particle identical in quality, and the quality sum of being had a few equals the gross mass of operating theater instruments, and the quality of supposing operating theater instruments is M, and the quality of each point is mi, then has: M = Σ i = 1 N m i .
Consider above two factors, in specific operation process, the central point that the present invention can choose virtual bone drill model intermediate cam dough sheet is the point of this tri patch instead, what therefore employed point set model just was made up of the central point of all model surface tri patchs in the force feedback process.
Step 4: follow the tracks of operating theater instruments moving in the Virtual Space.With virtual operation instrument model and force feedback equipment binding, the i.e. position and the direction at the mechanical arm place of in the Virtual Space, having represented force feedback equipment by the position and the direction of virtual operation instrument.Follow the tracks of virtual operation instrument moving in the Virtual Space, comprise position, the anglec of rotation and movement velocity.
Step 5: collision detection.Follow the tracks of virtual operation instrument and object moving in the Virtual Space, whether detect in real time has collision to take place between the two, if bump, detect on the virtual operation instrument point that all and object model bump successively, and call and feel computing module to exert oneself.
Collision detection algorithm has been subjected to the many scholars' of field of Computer Graphics extensive concern and research, and there have been a lot of very ripe algorithms at present, because haptic interaction is simulated exigent refreshing frequency, 500-1000Hz for example also need choose or merges different collision detection algorithm in the application kind of reality at the mechanism of different contact situations.
The present invention can adopt the multiple spot collision detection model based on system of virtual operation, utilized the detection method of the level collision bounding box of AABBTree, at first create the binary tree of the bounding volume hierarchy (BVH) of object and virtual bone drill model, then their binary trees are successively intersected test, until detecting the tri patch that all bump.
Step 6: calculate linear velocity and the movement velocity of each point of impingement before collision.In the force feedback process, detect on the operating theater instruments point that all and object bump according to above-mentioned collision detection steps in sequence, analytical calculation is stressed respectively at each point, it is synthetic to participate in the suffered power of the point of collision at last again, just obtained being subjected to joint efforts.Only analyze the stressing conditions of one of them point in the numerous points that participate in collision here, suppose that this point of impingement is P iAs can be seen, the bone drill instrument is with movement velocity V from Fig. 3 iHit static bone surface, when therefore colliding, contact point P iMovement velocity be V iThe angular velocity of supposing the instrument rotation is
Figure A20081006648000151
The radius of instrument is R, then can obtain the linear velocity of any one point on the instrument, as shown in Figure 4, and P then iThe linear velocity at some place is: V → iw = ω → × r →
Wherein, | r → | = R sin θ , Direction be along
Figure A20081006648000154
θ is P iAnd the angle between the radius; The speed rotation that can change with per minute 50,000 when the bone drill that uses in operation starts, so the angular velocity of instrument rotation size is for changeing 10,000 radians p.s., direction be along
Figure A20081006648000155
P iThe linear velocity of point Equal the multiplication cross of angular velocity and radius vectors, direction and sphere are tangent.In order to reduce the calculated amount in the real-time, interactive process, this method is when the tri patch model of Core Generator, the coordinate position of the relative world coordinate system of the central point of each tri patch of meeting storage, and the rotation linear velocity vector of each dough sheet central point so that after reciprocal process in can read at any time and be used for to calculate.
Variation by the virtual operation instrument displacement can obtain P iThe movement velocity at place
Figure A20081006648000157
Next this movement velocity is decomposed.At P iThe point at place is created a section, can select P in the model iTri patch on the bone surface at place is as section A, then P iThe linear velocity of point is parallel with A.Will
Figure A20081006648000158
On section A and direction, decompose, obtain perpendicular to A: V i → = V i n → + V i τ → ; Wherein Be perpendicular to the component of A, It is the component on A.
Step 7: calculate linear velocity and the movement velocity of each point of impingement after collision.Generally speaking, the bone generation sharp impacts when instrument and static state is to impact the rotational velocity of the instrument that can influence: speed reduces, and direction can change, and therefore, need reset the angular velocity of instrument.For the simplification of problem, can suppose that collision finishes, the angular velocity of instrument recovers initial value.By revising the mode of single-point linear velocity, avoid revising angular velocity brings again the linear velocity of being had a few on the instrument is recomputated on one side workload.According to following mode, calculate the moment change of linear velocity when collision finishes, suppose collision back point P iThe linear velocity direction constant, size reduces, and satisfies with rotation linear velocity before the collision: | U iω → | = C | V iω → | , 0<C<1 is a constant; That is to say that the linear velocity after the described collision adopts linear velocity before the described collision to multiply by one and pre-sets linear velocity coefficient C and obtain, linear velocity coefficient C can measure by experiment, also can rule of thumb select, and the present invention does not impose any restrictions this.
Suppose
Figure A200810066480001513
Be the return movement speed of instrument after colliding with bone, the movement velocity preceding with collision has following relation, | U i → | = e | V i → | ; Wherein e is a coefficient of restitution, just relative separation speed after the collision and the ratio that collides relative velocity of approach before.That is to say that the movement velocity after the described collision adopts movement velocity before the described collision to multiply by one and pre-sets coefficient of restitution and obtain; Coefficient of restitution e can measure by experiment, also can rule of thumb select, and the present invention does not impose any restrictions this.
Mode according to step 6 is decomposed the movement velocity of returning after colliding, U i → = U i n → + U i τ → ; U wherein i nBe perpendicular to the component of A, U i τIt is the component on A.
Step 8: calculate particle suffered impulsive force in collision process.Linear velocity and movement velocity before and after the particle collision of calculating based on step 6 and step 7 are with particle P iLinear velocity after linear velocity before collision and movement velocity and the collision and movement velocity are through a series of decomposable processes, again synthesize the speed on the speed on the section and vertical and section again, utilization theorem of momentum and Coulomb law calculating particle suffered impulsive force in collision process.Therefore, can obtain following relational expression: V ic τ → = V i τ → + V iω → , U ic τ → = U i τ → + U iω → .
Wherein,
Figure A20081006648000164
Be P iRotation linear velocity before collision, Be V iSpeed component on the section,
Figure A20081006648000166
Be the previous moment P of collision iSpeed component on the A of section, then P iSpeed perpendicular to section A before collision is
Figure A20081006648000167
In like manner,
Figure A20081006648000168
Be P iRotation linear velocity after collision,
Figure A20081006648000169
Be
Figure A200810066480001610
Speed component on the section,
Figure A200810066480001611
Be a back moment P of collision iMovement velocity on the A of section, then P iSpeed perpendicular to section A after collision is
Figure A200810066480001612
Postulated point P iMomentum on the section and satisfy Coulomb law perpendicular to the momentum in section.Can derive point of impingement P according to this relation iSpeed after bumping with object, be included on the section speed and perpendicular to the speed on the section.
According to theorem of impulse, P as can be known iMomentum change on the A of plane equals P iThe momentum that is subjected on A can obtain following relational expression: m i U ic τ → - m i V ic τ → = ∫ t i 0 t i 1 f τ → ( t ) dt = S i τ → (equation 1).
Wherein
Figure A200810066480001614
Be particle P iThe friction force that on the section, is subjected to,
Figure A200810066480001615
Be P iThe momentum that on the section, is subjected to, Δ t=t I1-t I0It is collision time; Then according to Coulomb law, the ratio of the size of friction force and normal pressure equals friction factor, then: | f τ → ( t ) | = μ | f n → ( t ) | (equation 2).
Wherein
Figure A20081006648000171
Be perpendicular to the power on the direction of section, connect cube journey 1 and equation 2, as can be known: | S i τ → | = μ ∫ t 0 t 1 | f n → ( t ) | dt = μ | S i n → | , Wherein, S i nBe P iBe subjected to perpendicular to the momentum on the direction of section.
As can be seen from Figure 4, horizontal momentum
Figure A20081006648000173
And vertical impulse
Figure A20081006648000174
Be vertical, therefore will obtain relation between the two, must seek one and vector can be revolved the matrix R that turn 90 degrees, therefore suppose that the two satisfies such relational expression: μ S i n → = S i τ → R .
Here, the vector of unit length of the Jin Si selected instrument rotation linear velocity of ordering at Pi is
Figure A20081006648000176
Arrive
Figure A20081006648000177
The turning axle of rotation, suppose the coordinate that Pi orders be (xa, ya, za), the direction number of turning axle be (a, b, c), promptly
Figure A20081006648000178
Vector of unit length, therefore can obtain rotation matrix R and be:
R = a 2 c + ab - ac v 0 - c + ab b 2 a v 2 ( b 2 + c 2 ) + bc 0 b + ac - a v 2 ( b 2 + c 2 ) + bc c 2 0 K 1 K 2 K 3 1
Wherein,
K 1=y ac-z ab-a 2x a-a(y ab+z ac)+x a
K 2 = - ab v 2 ( y a c - z a b ) + c v [ - x a v + a v ( y b b + z a c ) ] + b ( - a x a - y a b - z a c ) + y a ;
K 3 = - ac v 2 ( y a c - z a b ) - b v [ - x a v + a v ( y a b + z a c ) ] - c ( ax a + y a b + z a c ) + z a ;
v = a 2 + b 2 ;
Again according to the definition of coefficient of restitution e:
U → i = e V → i ⇒ U i n → + U i τ → = e ( V i n → + V i τ → )
,, can think that coefficient of restitution e is a constant value here for the purpose of simplifying, therefore can be in the hope of P iSpeed after collision:
U i n → = ( E + M ) - 1 [ ( e - 1 ) V i n → + e V i τ → - ( V i τ → + V iω → ) M - C V iω → ] ;
U i τ → = e ( V i n → + V i τ → ) + ( e - C ) V iω → - U i n → ;
Wherein M = R μ , E is a unit matrix, (E+M) -1It is the inverse matrix of (E+M).Known particle P iSpeed after collision just can be obtained particle P according to the definition of momentum iThe momentum that in whole collision process, is subjected to, thus just can obtain particle P iThe average impact that in whole collision process, is subjected to: f ‾ i = f ‾ i τ + f ‾ i n = S i τ → + S i n → t i 1 - t i 0 ; Wherein
Figure A20081006648000183
With Be respectively Component on the A of section and perpendicular to the component on the section.
Step 9: calculate and make a concerted effort, comprise the impulsive force and the environmental forces at all point of impingement places.According to the method described above, analyze all successively on instrument, participate in the point of collision when coming in contact with bone, and the impulsive force that all points of impingement are subjected to
Figure A20081006648000186
Synthetic, wherein: i=1,2 ... N, N are total numbers of participating in the point of collision, the impulsive force that the instrument that therefore can obtain is subjected to make a concerted effort be: f ‾ → = Σ n f ‾ → i .
The environmental forces that the instrument of adding is suffered, here environmental forces generally is the gravity that instrument is subjected to, and also can be buoyancy etc., the instrument that just can obtain is suffered making a concerted effort in reciprocal process: f r → = f g → + f ‾ → ; Wherein,
Figure A20081006648000189
Be the gravity that instrument is subjected to.
In the actual computation, also can calculate respectively on the virtual tool respectively collide impulsive force that particle is subjected to and the particle of environmental forces is made a concerted effort, and then each particle is made a concerted effort to synthesize, calculates total with joint efforts.
Step 10: calculate resultant moment.For the force feedback equipment of three degree of freedom (3DOF), the vector of the power that once mutual result only need come out the power Model Calculation passes to equipment, makes the user can experience operating handle and is applied to user's power sense on hand.And for the force feedback equipment more than the Three Degree Of Freedom, except strong sense, the user can also experience the effect of a turning moment, can carry out Calculating Torque during Rotary in such a way: M → = f r → × L i → ; L wherein iBe from point of impingement P iTo the vector between the o ', the i.e. arm of force.
So far the reciprocal force that has calculated in the virtual operation to be produced will be made a concerted effort and resultant moment is passed to force feedback equipment, pass to the user by force feedback equipment, promptly finish the analog computation of virtual dynamic sensing interexchanging.
Provide below in the concrete plastic and aesthetic surgery, angle of mandible attrition example is further described technical solution of the present invention and the effect that can reach again.
Adopt step as described in Figure 2, utilize from the Clinical CT data and cut apart the three-dimensional model of the skull of rebuilding generation and the three-dimensional model of bone drill instrument; Follow the tracks of size and the evolution of skull in the virtual operation space, the quality and the angular velocity of virtual bone drill is set; Structure is evenly distributed on the point set model of whole bit face; With virtual bone drill and force feedback equipment binding, operate virtual bone drill moving in the virtual operation space, obtain movement velocity and displacement that bone drill moves; If drill bit and skull bump, try to achieve all particle that bumps set; Each point of impingement is tried to achieve collision preceding linear velocity and movement velocity one by one; Try to achieve linear velocity and movement velocity after the point of impingement collides; Try to achieve each particle suffered friction force, normal pressure and impulsive force in collision process; The impulsive force that try to achieve at comprehensive all point of impingement places, and will make a concerted effort in conjunction with trying to achieve with the gravity of virtual bone drill; Try to achieve resultant moment, and will make a concerted effort and resultant moment feed back to the user by force feedback equipment.
By controlling virtual bone drill, repeatedly touch the result of record fictitious force feedback with the carrying out of skull model with the mechanical arm of force feedback.As shown in Figure 6, for making a concerted effort and the relation of the degree of depth of instrument on the vertical surface direction; As shown in Figure 7, the influence of the degree of depth on the vertical surface direction for normal pressure and instrument; As shown in Figure 8, be the relation between the rotation linear velocity of the instrument of the point of impingement on friction force and the bone drill.The result shows that the distribution of the force that the power Model Calculation according to the technical program design spendes mainly is subjected to tool and bores the influence of going deep into the degree of depth and high speed spin velocity, and especially the friction force that the linear velocity of the point of impingement on the bone drill is subjected to when the grinding bone has obtained good linear fit.In the operation of reality, the high speed rotation of instrument is the main factor that enormous function power produces, thereby just can cause sclerotin to be removed.Therefore the rotational velocity of instrument is one of the factor that has influence on a most critical of the suffered friction force of instrument, adopts the present invention, can reproduce force feedback in the bone attrition truly.
Should be understood that, for those of ordinary skills, can be improved according to the above description or conversion, and all these improvement and conversion all should belong to the protection domain of claims of the present invention.

Claims (10)

1, a kind of computing method that the power feel is fed back in virtual system, it may further comprise the steps:
A1, set up virtual environment,, the attribute of described virtual tool is set, make up point set model that forms by a plurality of particles, the described virtual tool of encirclement comprising Virtual Space, virtual objects and virtual tool; Wherein, described attribute comprises quality, angular velocity and moving radius;
A2, described virtual tool and force feedback equipment being bound, followed the tracks of described virtual tool and the motion state of described virtual objects in described Virtual Space, judge whether described virtual tool and described virtual objects bump, is then to carry out A3;
A3, respectively collide particle, calculate it respectively before collision and linear velocity and movement velocity after the collision for what described virtual tool bumped, and the impulsive force that in collision process, is subjected to;
Making a concerted effort and resultant moment of whole collision particles of A4, the described virtual tool of calculating, send to described force feedback equipment.
2, computing method according to claim 1 is characterized in that, described virtual environment is the virtual operation environment, and described virtual objects is a virtual organ, and described virtual tool is a virtual operation instrument.
3, computing method according to claim 2 is characterized in that, described virtual operation instrument is virtual bone drill; And in the steps A 1, each particle of described point set model is the central point of each tri patch of described virtual bone drill.
4, computing method according to claim 1 is characterized in that, in the steps A 1, described virtual tool has rotation character; And described attribute also comprises kind, model, spin velocity and rotation radius.
5, computing method according to claim 1 is characterized in that, in the steps A 1, described structure surrounds the point set model of described virtual tool, carry out following steps:
A11, the basis condition of pre-seting are determined the quantity of the particle of described point set model;
A12, distribute according to the profile of described virtual tool and to choose each particle;
A13, according to the position of each particle, and the quality of described virtual tool is provided with the quality of each particle; Wherein, the quality sum that constitutes whole particles of described point set model is the quality of described virtual tool.
6, computing method according to claim 5 is characterized in that, each point mass of described point set model is identical.
7, computing method according to claim 1 is characterized in that, in the steps A 2, described judgement judges whether described virtual tool and described virtual objects bump, and adopt collision detection algorithm to realize; Wherein, described collision detection algorithm comprises the level collision bounding box collision detection algorithm of binary tree mode.
8, computing method according to claim 1 is characterized in that, in the steps A 3, adopt linear velocity and movement velocity after following steps are calculated described collision respectively:
Linear velocity after A31, the described collision adopts linear velocity before the described collision to multiply by one and pre-sets the linear velocity coefficient and obtain;
Movement velocity after A32, the described collision adopts movement velocity before the described collision to multiply by one and pre-sets coefficient of restitution and obtain.
9, computing method according to claim 1, it is characterized in that, in the steps A 3, adopt following steps to calculate the described impulsive force of a certain collision particle: A33, will collide linear velocity and movement velocity and linear velocity collision after and the movement velocity of particle before collision, synthesize this collision particle on the section speed and perpendicular to the speed in section, calculate particle suffered impulsive force in collision process according to theorem of momentum and Coulomb law.
10, computing method according to claim 1 is characterized in that, in the steps A 4, adopt following steps to calculate described making a concerted effort: to the impulsive force of respectively colliding particle of described virtual tool, after synthesizing, the environmental forces that is subjected to described virtual tool synthesizes again, obtains described making a concerted effort.
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