JP2006285925A - Method and apparatus for reservation to avoid particle collision - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method and an apparatus which replace all objects, such as arbitrary vehicles, air planes, ships, submarines, humans, robots, machines and structures, with particles or groups of particles to allow the particles to perform virtual collision calculations; and which avoid collisions. <P>SOLUTION: In the method, objects, such as vehicles, are expressed as a group of particles, and the particles are provided with a three-dimensional space so that they can safely brake and rotate proportional to movement states. Virtual collision calculations between the space and target particles are performed in the three-dimensional virtual space to control particle movements, so that the particles add a virtual collision reactive force to only themselves to brake and rotate themselves. The system dynamically avoids collisions at any time with controlling both a machine system and an operator through control of middle inner force senses, in which control signals are provided to a control system and an operation system. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a method for reserving collision avoidance by causing a particle to perform virtual collision calculation.

  Conventional collision avoidance means in vehicles and the like limit the number of objects such as preceding vehicles to a small number, detect and recognize these using radar or sound wave, some communication means, and use the relationship between distance and speed Most of the methods perform the control of the mechanical system, the communication and display of the information system, the deceleration and warning, etc. by judging the possibility of approach and collision (see, for example, Patent Document 1).

  The number of objects is not limited to this, and there are some that try to avoid collisions with many objects by accurately calculating the relative speed with the objects (see, for example, Patent Document 2).

  In addition to the above-described means, there are various object detection means such as infrared rays, GPS, and images. There are various communication means such as inter-vehicle communication, inter-vehicle communication, inter-car center communication (see, for example, Patent Document 3), and in some cases, the vehicle broadcasts its own position, opens a mutual communication link, and information. There is also a proposal for transmitting (see, for example, Patent Document 4). In view of these, it is considered that the detection of collision avoidance objects and communication means will be rapidly improved through infrastructure maintenance and the like.

  As a method for determining the possibility of collision, there is a method for evaluating crossability or the like (for example, refer to Patent Document 5) and a method for performing interference check of a three-dimensional geometric model (for example, refer to Patent Document 6). However, many are ambiguously described (see, for example, Patent Document 1), and in general, it is considered that there are many simple things such as calculating the braking distance from the speed and comparing it with the forward distance. Many of the proposals are mostly limited to the driver's driving support and information provision such as mechanical control, information communication and display.

  One of the advanced vehicle operation methods is platooning and follow-up. As an extension of this, the system detects the obstacles and crosses a certain value, and then disengages the platoon and runs individually, confirms that there are no obstacles, and then returns to the platoon driving to maximize the traffic capacity. Attempts have also been made (see, for example, Patent Document 5).

  Also, a method for avoiding a collision has been proposed for an aircraft (Patent Document 7).

  In order to prevent a large number of moving bodies from colliding with each other and other obstacles, there is also a technique for deriving a collision avoidance signal from an artificial force field model that generates a repulsive force with a mutual proximity (Patent Document 8). In this proposal, a repulsive force necessary to separate an object is obtained, and a control signal corresponding to this is issued.

Some suggest object collision avoidance. However, it is an idea to avoid duplication by occupying cells, and cannot be used for dynamic collision avoidance (Patent Document 9).
Patent Publication 2004-155303 (Solution means) Patent Publication 10-143245 (Solution) Patent Publication 2005-44167 (Solution) Patent Publication 10-188199 (Solution) Patent Publication 2004-276732 (Solution means) Patent Publication 2004-1217 (Solution) Patent Publication 2004-93538 (Solution) Patent Publication 10-97316 (Solution) Patent Publication 8-241437 (Solution)

Issues that the technology is trying to solve

  The problems with the conventional methods described in the background art are that the method of judging and evaluating the possibility of collision is ambiguous, the target of collision avoidance is limited to a small number, and the task processing of collision avoidance is individual. In addition, the main purpose is the control of the mechanical system at the stage when the collision risk becomes clear or the warning to the operator via the information system, and it does not guarantee the collision avoidance in advance. Although the detection function is always and dynamically activated, it does not always calculate the collision avoidance in advance and dynamically, and compares the magnitude of the kinetic energy or inertial force of the subject and the object Therefore, there is no appropriate deceleration or turning distance, the field of view that can be searched or detected is narrow, and the relationship between the field of view and the range of the object to be avoided is uncertain. Catching , Side and rear, behind invisible obstacles, presence and approach of objects from above and below, possibility of collision, etc. are not fully considered, collision avoidance in any scene It can be expressed in a unified way, including not being considered as possible, and collision avoidance of not only vehicles but also vehicles, aircraft, ships, submarines, humans, robots, machines, structures and other objects or fish and birds. There are no collision avoidance calculations and controls, no super-high speed, no super-multiplicity, and so on.

  For example, as one of the advanced vehicle operation methods, platooning and obstacle detection are detected, the platooning is performed individually, traveling is confirmed, there is no obstacle, and the lane driving is resumed. Theoretically, attempts have been made to maximize this, but it is safe when a vehicle appears to interrupt the platoon from the side or when a flying object approaches from above. There is no means to continue or leave the platooning and return to individual driving.

  The cause of this is that the object that may collide is captured in a narrow range, and the possibility of collision is known at the time when the possibility of braking and steering is sufficiently left against the collision. This is because there is a lack of means for performing the collision avoidance preliminary action or this action without relying on the above.

  If a collision is unavoidable due to the possibility of collisions and actions, despite the wide range of objects that may collide, it may be due to infrastructure deficiencies, pilot violations or skills. May be due to lack of collision, lack of collision avoidance, or force majeure.

  For example, earthquakes and tsunamis cannot be prevented, and their occurrence is considered to be due to force majeure. However, for damage caused by earthquakes and tsunamis, it is not appropriate to make this a force majeure. It should be a lack of infrastructure, a lack of skills and regulations such as designers or administration, and a lack of measures to prevent damage. The same applies to the collision of all objects such as vehicles, aircraft, ships, submarines, humans, robots, machines, structures, and so on.

  From the above discussion, in order to avoid collisions of all objects such as vehicles, aircraft, ships, submarines, humans, robots, machines, structures, etc. If there is a method, it will be possible to avoid collision of all objects such as vehicles, airplanes, ships, submarines, humans, robots, machines, structures, etc. by using them effectively.

The requirements necessary for collision avoidance of such vehicles and the like vary greatly depending on the environment in which collision avoidance is considered. Where it gets stuck, it must be a guarantee of collision avoidance. That is, the requirements for collision avoidance can be summarized as follows.
-Avoid collisions regardless of the number, speed, and controllability of objects.
-Address invisible and hidden objects.
• The final means of collision avoidance is machine control. Warning and information display are only transmitted by intermediate force control, and the final judgment of the control is not based on the operator's human skill, but is made a secret function as in ABS (Anti Lock Braking System).
・ It has a unified means of adapting not only to vehicles but also to aircraft, ships, submarines, humans, robots, machines, structures and other objects.

  In this sense, the “collision avoidance signal” from the “artificial force field model that generates repulsive force with the degree of mutual proximity” prevents the “multiple moving objects” from colliding with each other and other obstacles. It is worth noting that Japanese Patent Application Laid-Open No. 2004-151867 that derives “repulsive force necessary to separate an object” and issues a “control signal” corresponding to this. However, since an object moving at a distance or at a high speed is not considered, the greatest weakness is that no repulsive force is generated unless the object to be collided is very close. In addition, even if the repulsive force that can separate the object to be collided can be calculated, it is calculated in a very close state, so the objects that can be braked or stopped by that control signal are limited, and the collision It does not include time allowances or thoughts to circumvent the situation.

  On the other hand, when fish and birds form a flock and fly, fish and birds do not collide with each other. Also, in order to avoid foreign enemies, they change their direction as a group and try to escape from predators, but they still do not collide with each other. This is because each has a wide field of view, knows the actions of neighboring friends, changes direction so as not to contact and collide with each other, and increases or decreases the speed. In addition, when a foreign enemy enters the field of view, the fish and birds at the outer edge of the flock just take a collision avoidance action to change the direction and increase or decrease the speed in order to escape from the foe. The fish and birds inside are only responsive to similar behavior in sight, and both flocks and individuals can avoid collisions with predators. In other words, recognition of external enemies, a wide field of view that makes it possible in the distance, determination of how to escape, action, always knowing that individual is obstructed from view similar to that action, Safety is maintained. Vehicles, aircraft, ships, submarines, humans, robots, machines, structures, and all other objects have sufficient visibility and discrimination capabilities, similar to fish and birds, and enough to escape to avoid collision with each other. It is necessary to keep avoiding collision with an object in close proximity while performing a time margin, a retreating action, and a retreating action such as braking, steering, acceleration / deceleration and the like.

  The present invention assumes that an arbitrary vehicle, aircraft, ship, submarine, human, robot, machine, structure, or any other object is replaced with a particle or a group of particles, and virtually collides with particles as a means of particle collision avoidance. The present invention relates to a method and apparatus for making calculations and reserving collision avoidance.

Means for solving the problem

  In a virtual space, it is a three-dimensional space that can be expanded and reduced around the particle of interest (hereinafter referred to as the particle of interest) and in the direction of motion, and the position, velocity, acceleration, mass, kinetic energy, motion of the particle of interest A space determined by a resistance such as friction (hereinafter referred to as a motion parameter) caused by a path, a virtual space required for the target particle to reach a required deceleration or stop by braking and steering, and an arbitrary occupied space around the target particle To handle particles having a space that envelops both of them (hereinafter referred to as a space reservation area) (Claim 1).

  By examining other particles that may invade the space reservation area over an arbitrary range every unit time by some method, the boundary of the space reservation area between the current position and the unit time elapses. Search for all particles that may collide, examine their attributes, and place them in a monitorable state until they leave the search range (claim 2).

  A virtual barrier is provided at the boundary of the space reservation area so that a virtual collision can be calculated between the boundary of the space reservation area and a particle that attempts to enter the space reservation area.

  A virtual collision point is obtained between one or a plurality of collision-prone particles searched by the above means and the boundary of the space reservation area, and the general characteristics at the collision point are known by knowing attributes such as the motion parameters of the partner particle. To calculate a virtual rebound direction and a collision reaction force (hereinafter referred to as a virtual collision calculation).

  Among the collision reaction forces obtained by the virtual collision calculation, the collision reaction force is applied only to the target particle without applying the collision reaction force to the partner particle that has entered the space reservation area of the target particle. .

  The braking force and steering force are applied to the target particle by the collision reaction force applied only to the target particle, the motion parameter is corrected by solving the motion equation of the target particle, and the space reservation area of the target particle is corrected by the corrected motion parameter. Is reduced and rotated (claim 6).

  The motion parameters and the space reservation region corrected by the virtual collision calculation between the particle having the possibility of collision and the boundary of the space reservation region are used for the purpose of the motion recorded in the kinetic energy and the particle attribute of the particle of interest, Acceleration / deceleration and enlargement / reduction based on conditions (Claim 7).

  When the particles are combined and moving in groups (hereinafter referred to as particle groups), each target particle constituting the particle groups receives a braking force and a steering force by the virtual collision calculation, and the particle groups Change the direction and posture of the particle swarm by adding braking and steering only to itself without affecting other particles or particle swarms, and to the extent possible to collide with other particles or swarms. Trying to avoid (claim 8).

  By referring to particle attributes in the collision avoidance, virtual collision calculation is not performed between particles constituting the same particle group (claim 9).

  In the virtual collision calculation and unilateral collision avoidance described above, if the particles constituting the partner particle group also have an attribute for performing virtual collision calculation and collision avoidance with a space reservation area, The virtual collision calculation is performed, and both try to avoid the collision as much as possible (claim 10).

  The above calculation method and any medium and apparatus on which it is recorded (claim 11).

The invention's effect

  According to the present invention, the virtual collision reaction force is calculated by performing the virtual collision calculation at the boundary of the space reservation area sufficiently before the particle collides, and the collision reaction force is given only to itself and not given to the target particle. Thus, active pre-collision avoidance can be achieved only by own active braking and steering without accompanying collision avoidance of target particles.

  If the target particle has a space reservation area and has an attribute for avoiding collision by performing virtual collision calculation, it is possible to avoid collision by performing virtual collision calculation with each other.

  As long as the target particle is registered in the virtual space together with its attributes by some means, even if the target particle exists in a position where it cannot be searched in the normal field of view of the particle, it can always be searched. It is possible to know the kinetic energy and kinetic parameters required for the virtual collision calculation, and even if the mass of the target particle is large and moving at high speed, collision avoidance is possible if there is sufficient visibility.

  Even when the field of view of the particle of interest is limited to the normal range, the minimum collision avoidance can be achieved in the same manner as the collision avoidance of fish and birds. However, since the field of view is not sufficient, collision avoidance cannot be avoided when braking avoidance and steering are insufficient even if collision avoidance cannot be started with sufficient time margin. In such a case, the collision is inevitable by any other means.

  Since the search for the target particle and the virtual collision calculation are repeated every unit time, collision can be avoided dynamically.

  Even if a large number of particles are subject to virtual collision calculation, collision can be avoided as long as virtual collision calculation and others are performed at high speed, and the only issues are communication speed and calculation speed.

  Even if the target particle is moving at high speed, collision avoidance can be avoided as long as virtual collision calculation and the like are performed at sufficiently high speed, and the only issues are communication speed and calculation speed.

  When the target particle is surrounded by a plurality of target particles, the target particle is surrounded as a result of avoiding collision with the target particle by arbitrarily scaling the three-dimensional space that extends around the target particle in the space reservation area. It is possible to move to the center of the space formed by the target particles. Thus, for example, when the surrounding target particles constitute a plurality of parts and the part of the target particle is located in the space formed by these parts, this part is brought into contact with the space formed by the surrounding parts. It can be moved to the center of the space without collision.

  When the parts made up of particles are gathered together to form a space to form a gap of a specific shape, and the part to which the target particle belongs also has a specific shape, the latter is connected to the surrounding parts in the center of the former It tries to be positioned so that it doesn't touch and collide, and it will rotate its posture. That is, the principle of non-contact is given between the parts, and the movement can be performed while controlling the posture so as to fit the gap of the space formed by the parts.

  If the space between the parts has a shape and area that allows the part to which the particle of interest belongs to pass, it is necessary as long as braking and steering by the virtual collision calculation of the part to which the particle of interest belongs is in time. This gap can be passed through braking, acceleration based on the kinetic energy of the particles, and attitude control.

  That is, according to the present invention, it is physically possible and non-contact when dealing with the movement of particles or any vehicle, aircraft, ship, submarine, human, robot, machine, structure or any other object that the particles constitute. Under these principles, it is possible to exercise them arbitrarily.

  Utilizing the present invention, the result of the virtual collision calculation is communicated and interlocked with a real control system in real time or in advance, and the machine control system is controlled through intermediate force control etc. If the sense of force is transmitted, the collision avoidance control in the real space and the warning to the pilot can be performed at the same time, and the risk of the collision due to the misjudgment of the pilot is fundamentally reduced.

  Even in an object such as an aircraft or a ship that has a large inertial force and cannot be easily braked or steered, for example, there is no fundamental difference in handling between the state of platooning and the state of detachment from platooning. Handling is easy and simple, and even if a crossing of the route is about to occur, the collision is avoided by each braking and steering, and the risk of collision with the target object is not greatly impaired, and the route is monopolized or shared safely. Can be occupied.

  The same is true for all objects such as vehicles, aircraft, ships, submarines, humans, robots, machines, structures and others. For example, by transmitting the result of the virtual collision calculation to an individual through some individual communication means, it becomes a weak person relief / protection / warning / safety guidance system.

  When buildings or roads are subject to collision avoidance, if the shape of the structure is known and fixed, it can be treated in the same way by treating it in a virtual space by particleizing it in advance. Collision avoidance is also possible. In addition, it is possible to avoid collisions with a structure simply by periodically investigating and particleizing in order to know new constructions, changes, etc., and registering and updating the virtual space.

  Similarly, by detecting the state of all objects such as vehicles, aircraft, ships, submarines, humans, robots, machines, structures, etc., it is possible to avoid collision between them by repeatedly registering and updating in the virtual space. It becomes.

  By utilizing the present invention, a collision accident prevention simulator, a simulator for searching for a traffic jam and its solution, a high-speed, multiple disassembly / assembly simulator for parts gripped by a robot hand, and a problem solving in the real world based on these Simulation and control are possible.

  The best mode for carrying out the present invention will be described below with reference to the accompanying drawings.

  FIG. 1 is a schematic diagram of a space reservation area according to the present invention projected onto a plane.

  FIG. 2 is a schematic diagram showing a virtual collision projected on a plane at the boundary of the space reservation area.

  As shown in FIG. 1, the space reservation area includes a space that extends around the particle and a space that has a size and a width related to the motion parameter of the particle. By considering a space reservation area that combines these spaces individually or in combination, only the space that extends around the particle when in a static state, and the size and spread related to the motion parameters when in a dynamic state. It is possible to continuously handle the space reservation areas in the static case and the dynamic case by adding the space having

  Register particles and their attributes in the virtual space. Any means of knowing the particles and their attributes is irrelevant.

  A target particle is selected, and a space reservation area is set in relation to the motion parameter.

  A considerably wide range including a space reservation area is arbitrarily set, and particles registered in the virtual space and their attributes are searched. The search means is not limited.

  From the motion parameters of the searched particles, target particles that may cross the boundary of the space reservation region within the next unit time are selected. There is no limitation on the means of selection.

  As shown in FIG. 2, for target particles that may cross the boundary of the space reservation area of the target particle, the collision point with the boundary of each space reservation area is calculated, and at the collision point, the boundary of the space reservation area The virtual collision calculation is performed with the barrier of the. The collision calculation may be performed using a general method, and the motion direction and the collision reaction force after the collision may be calculated with high accuracy.

  The collision reaction force after the collision is not given to the partner particle, but the collision reaction force is given only to the target particle itself.

  The particle of interest brakes and steers itself using the collision reaction force. The braking and steering by the collision reaction force can be obtained by adding the direction in which the collision reaction force acts and the collision reaction force to the load term of the equation of motion of the particle of interest.

  Since the motion parameter of the particle of interest changes due to braking and steering, the space reservation area is also corrected accordingly.

  Since the target particles continue to move as they are, there is a possibility that the space reservation area between the target particles and the target particle will continue the virtual collision. The virtual collision calculation and the braking and steering by the collision reaction force are repeated until the next unit time passes, so that the target particle with the possibility of collision does not advance until the collision possibility disappears. Possible target particles never pass by. Similar virtual collision calculations are performed with other target particles, and any collision reaction force is incorporated into the equation of motion of the target particle as described above to newly determine a motion parameter. Along with this, the particle of interest repeats braking and steering, and gradually changes the direction of motion and the space reservation area.

  As described above, as long as the space reservation area is maintained, the target particle body does not collide, and can move while avoiding collision with the target particle. When a command is written to perform arbitrary motion in the attribute of the target particle and sufficient kinetic energy corresponding to it is given, the target particle to achieve the objective while avoiding collision with the target particle Tries to exercise.

  As described above, there is a possibility that an obstacle can be bypassed by braking and steering when a collision is inevitable if the movement is continued as it is. When the braking distance is insufficient, the emphasis is placed on the steering, and the collision is avoided by the wraparound of the obstacle due to the detour. The emphasis on braking and steering depends on the attributes of the particles.

  If the particle of interest combines with other particles to form a particle group and has some shape, this particle group has not yet collided with other similar or isolated particles. One after another, small virtual collision avoidance is performed, and the direction and speed of the motion are gradually changed to try to avoid collision avoidance.

  When the particle group changes the direction and speed of movement by the space reservation area and the virtual collision calculation, the posture of the particle group also changes. The direction of the posture change is a direction that avoids collision with the target particle or particle group, and takes an average distance from them, so the particle group is a space formed by surrounding particle groups by controlling the posture. Along the shape.

  As described above, if a gap formed by other parts in the virtual space can physically pass, the parts formed by the particles control the posture and pass along the gap.

  2a in FIG. 2 is a particle of interest. The arrow means the motion vector of the particle of interest. Reference numeral 2b denotes a space reservation area in the movement direction of the target particle. The space extending around the target particle is a part of the space reservation area for the periphery of the particle whose range can be arbitrarily changed according to the attribute of the particle, as described in the explanation of the reference numerals in FIG.

  2c of FIG. 2 is a particle which may collide with the boundary of the space reservation area | region of the focused particle searched for inside the virtual space, and its motion vector.

  Since the particles with the possibility of collision intersect the space reservation area of the target particle, a virtual collision occurs at the boundary of the space reservation area. This collision point is 2e.

  When the virtual collision calculation is performed at the collision point, the movement direction and the collision reaction force after the collision are obtained.

  When the collision reaction force is not applied to the partner particle but only to the target particle, what actually acts on the partner particle is held and rotated as shown in FIG. 2 with respect to the target particle. Acts as follows. Along with this, the speed of the particle of interest decreases, changes its direction, and simultaneously tries to reduce the space reservation area.

  The space-reserved region of the particle of interest tries to increase again by its kinetic energy based on the attribute of the particle of interest, but the particles with the possibility of collision continue to have a collision reaction force against the space-reserved region of the particle of interest. If it continues to be added, it cannot proceed as it is, and by repeating this virtual collision calculation, the time increment is maintained without being advanced until it becomes possible to proceed without virtual collision.

  When the space reservation area is sufficiently reduced and rotated, the particle of interest decelerates and changes the direction of motion. The potential particle and the particle of interest do not collide and can move freely.

  When the particle of interest is about to move in a specific direction or target based on the attributes of the particle of interest, the particle of interest will return to its original motion state until the next exploration of a particle that may collide. It becomes possible to continue the exercise with respect to the direction and the target.

  When applied to particles, vehicles, aircraft, ships, submarines, humans, robots, machines, structures, and all other objects, these perform virtual collision calculations with other similar particles and actually Collision avoidance can be started before the collision.

  It is the schematic diagram which projected and showed the space reservation area | region on the plane.   It is the schematic diagram which showed the virtual collision in the boundary of a space reservation area | region.

Explanation of symbols

FIG.
1a: focused particle 1b: motion vector 1c: surrounding space reservation area 1d: space reservation area 1e in the direction of motion 1e: braking distance 1f: example of steering distance 1g: example of steering distance 1h: steerable range

FIG.
2a: focused particle 2b: space reservation area 2c in the moving direction: particle 2d with possibility of collision: next predicted position 2e: virtual collision point 2f: collision reaction force

Claims (11)

  In a virtual space, it is a three-dimensional space that can be expanded and reduced around the particle of interest (hereinafter referred to as the particle of interest) and in the direction of motion, and the position, velocity, acceleration, mass, kinetic energy, motion of the particle of interest A space determined by a resistance such as friction (hereinafter referred to as a motion parameter) caused by a path, a virtual space required for the target particle to reach a required deceleration or stop by braking and steering, and an arbitrary occupied space around the target particle Dealing with particles that have a space that envelops both (hereinafter referred to as a space reservation area).   By examining other particles that may invade the space reservation area over an arbitrary range every unit time by some method, the boundary of the space reservation area between the current position and the unit time elapses. Search for all particles that may collide, examine their attributes, and leave them in a monitorable state until they leave the search range.   A virtual barrier is given to the boundary of the space reservation area so that a virtual collision can be calculated between the boundary of the space reservation area and a particle trying to enter the space reservation area.   A virtual collision point is obtained between one or a plurality of collision-prone particles searched by the above means and the boundary of the space reservation area, and the general characteristics at the collision point are known by knowing attributes such as the motion parameters of the partner particle. To calculate a virtual repulsion direction and collision reaction force (hereinafter referred to as virtual collision calculation).   Among the collision reaction forces obtained by the virtual collision calculation, the collision reaction force is applied only to the target particle without applying the collision reaction force to the partner particle that has entered the space reservation area of the target particle.   The braking force and steering force are applied to the target particle by the collision reaction force applied only to the target particle, the motion parameter is corrected by solving the motion equation of the target particle, and the space reservation area of the target particle is corrected by the corrected motion parameter. Shrink and rotate.   The motion parameters and the space reservation region corrected by the virtual collision calculation between the particle having the possibility of collision and the boundary of the space reservation region are used for the purpose of the motion recorded in the kinetic energy and the particle attribute of the particle of interest, Accelerate, decelerate, and scale up / down based on conditions.   When the particles are combined and moving in groups (hereinafter referred to as particle groups), each target particle constituting the particle groups receives a braking force and a steering force by the virtual collision calculation, and the particle groups Change the direction and posture of the particle swarm by adding braking and steering only to itself without affecting other particles or particle swarms, and to the extent possible to collide with other particles or swarms. Try to avoid.   The virtual collision calculation is not performed between particles constituting the same particle group by referring to the attribute of the particle in the collision avoidance.   In the virtual collision calculation and unilateral collision avoidance described above, if the particles constituting the partner particle group also have an attribute for performing virtual collision calculation and collision avoidance with a space reservation area, The virtual collision calculation described above is performed, and both parties try to avoid the collision to the extent possible.   The above calculation method and an arbitrary medium and apparatus on which it is recorded.

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