CN114666803A - Deployment and control method and system of mobile edge computing system - Google Patents
Deployment and control method and system of mobile edge computing system Download PDFInfo
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Abstract
The application discloses a method and a system for deploying and controlling a mobile edge computing system, wherein the method for deploying and controlling the mobile edge computing system specifically comprises the following steps: initializing state information; acquiring the optimal signal detection result of a user; acquiring an optimal transmitting beam; obtaining an optimal reflection phase; obtaining optimal unmanned aerial vehicle power distribution and calculation resource distribution results; acquiring and outputting the optimal flight path of the unmanned aerial vehicle; judging whether the precision is converged to a preset precision or the iteration frequency reaches the maximum iteration frequency; and if the precision is converged to the preset precision or the iteration frequency reaches the maximum iteration frequency, outputting the optimal result. The unmanned aerial vehicle and intelligent reflecting surface joint design method in the mobile edge computing system can achieve the purpose of joint design of the unmanned aerial vehicle and the intelligent reflecting surface in the mobile edge computing system.
Description
Technical Field
The present application relates to the field of mobile communications, and in particular, to a method and system for deploying and controlling a mobile edge computing system.
Background
At present, with a large-scale internet of things scene oriented to main services such as smart cities, smart traffic, smart agriculture and environmental monitoring, ultra-large-scale sensor node data needs to be collected, which provides a serious challenge to the existing communication technology. In addition, under the drive of a series of artificial intelligence technology applications such as virtual/augmented reality, face recognition, automatic driving, intelligent factories and the like, future terminal equipment of the internet of things generates computation-intensive business requirements, the requirements generally have the characteristics of low time delay and high computation requirement, and the terminal equipment cannot complete computation tasks locally depending on self limited computation power and energy. Therefore, the tasks are guaranteed to be effectively calculated, and the calculation of the moving edge is carried out at the same time. The computing potential of the network can be further excited through the unmanned aerial vehicle-assisted mobile edge computing system, and the current research focus is to provide computing task unloading service for ground terminal equipment by carrying an edge computing server by utilizing the maneuvering performance of the unmanned aerial vehicle. An Intelligent Reflective Surface (IRS) is a passive planar reflective array, in which a plurality of Reconfigurable elements (Reconfigurable elements) are arranged in order on the Surface, and each element can perform individual phase shift and amplitude control on an incident signal, so as to change the transmission characteristic of the incident signal. According to the number of antennas at a transmitting end, the beam forming research of the intelligent reflecting surface is divided into the following two types: 1) for a SISO system, a transmitting end and a receiving end are both equipped with only one antenna. When the transmission signal reaches the IRS, the IRS adjusts the amplitude and the phase of the reflection signal in a software programming mode, so that the reflection signal and signals of other paths are constructively added, and the expected signal power of a receiving end is enhanced, and the process is the passive beam forming of the IRS; 2) passive + active beamforming is applicable to multi-antenna systems, i.e. the transmitting end is equipped with an antenna array consisting of a plurality of antennas. Before signal transmission, signals may be precoded at a transmitting end to form a beam with directivity, which is also called active beamforming. By the active and passive beam forming combined mode, transmission signals can be obviously enhanced, and communication quality is improved.
In the current unmanned aerial vehicle edge computing system, although an unmanned aerial vehicle can establish a line-of-sight transmission path with a ground terminal at a large probability for communication, for urban environments with densely distributed obstacles or field environments with frequent altitude changes, the signal between the unmanned aerial vehicle and the ground is seriously faded, and the signal transmission faces the risk of strong blocking. At this moment, unmanned aerial vehicle's wireless coverage is unstable, can appear covering the blind area even. In contrast, although the traditional large-scale multi-antenna technology can enhance the signal strength to resist the influence of channel fading, the signal processing complexity of the transmitting and receiving end and the communication energy consumption of the unmanned aerial vehicle are additionally increased, which affects the expandability and the application range of the system for the terminal of the internet of things powered by the battery and the unmanned aerial vehicle with limited energy in a specific application scene.
Therefore, how to provide a method for deploying and controlling a mobile edge computing system to improve the performance of the edge computing system is a problem that needs to be solved urgently by those skilled in the art.
Disclosure of Invention
The application provides a deployment and control method of a mobile edge computing system, which specifically comprises the following steps: initializing state information; responding to the initialization state information, and acquiring an optimal signal detection result of a user; responding to the signal detection result which is obtained by the user and is optimal, and obtaining an optimal transmitting beam; acquiring an optimal reflection phase in response to acquiring an optimal transmit beam; responding to the obtained optimal transmitting wave beam, obtaining optimal unmanned aerial vehicle power distribution and calculation resource distribution results; responding to the obtained optimal unmanned aerial vehicle power distribution and calculation resource distribution results, and obtaining and outputting an optimal unmanned aerial vehicle flight track; judging whether the precision is converged to a preset precision or the iteration frequency reaches the maximum iteration frequency; and if the precision is converged to the preset precision or the iteration frequency reaches the maximum iteration frequency, outputting the optimal result.
As above, the initialization state information includes the number of initialization ground user equipments, the number of intelligent reflector reflection units, the number of unmanned aerial vehicle antennas, the total system time slot, the length of each time slot, the trajectory representation of the unmanned aerial vehicle, the maximum user transmission power, the maximum unmanned aerial vehicle transmission power, the maximum calculation frequency of the unmanned aerial vehicle and the ground wireless access point, the system communication bandwidth and the white noise power, and the convergence accuracy and the maximum number of iterations.
The above, wherein the signal detection result is determined
The concrete expression is as follows:
wherein ILA matrix representing dimensions of L x L,
hur[n]respectively represent the channel coefficients between the intelligent reflecting surface and the wireless access point, between the unmanned aerial vehicle and the wireless access point, and between the unmanned aerial vehicle and the intelligent reflecting surface, sigma2Representing white noise power.
As above, wherein the optimal transmit beam wk[n]The concrete expression is as follows:
As above, wherein the optimal reflection phase shift θk，m[n]The concrete expression is as follows:
wherein
To represent
The m-th element is a group of elements,
represents hur[n]M-th row vector, wk[n]Representing the best transmit beam.
As above, obtaining the optimal unmanned aerial vehicle power allocation and calculation resource allocation result specifically includes the following sub-steps: acquiring first input information; acquiring optimal unmanned aerial vehicle power distribution and calculation resource distribution results according to the first input information; wherein the first input information includes initialization state information, an optimal signal detection result, an optimal transmission beam, and an optimal reflection phase.
As above, wherein, obtain and output best unmanned aerial vehicle flight trajectory, specifically include the following substep: acquiring second input information; according to the second input information, solving and outputting the optimal flight path of the unmanned aerial vehicle by using a convex optimization toolbox; wherein the second input information includes initialization state information, optimal signal detection results, optimal transmit beams, optimal reflection phases, and optimal drone power allocation and computational resource allocation results.
As above, among other things, updating the computing capacity of the system and the obtained optimal signal detection result, optimal transmission beam, optimal reflection phase, and optimal drone power allocation and computing resource allocation result.
As above, if the calculation capacity of the system converges to the specified accuracy or if the iteration count reaches the maximum iteration count, the iteration count is increased by 1, and the user-optimized signal detection result is obtained again.
A deployment and control system of a mobile edge computing system specifically comprises an initialization unit, an optimal signal detection result acquisition unit, an optimal transmission beam acquisition unit, an optimal reflection phase acquisition unit, an optimal distribution acquisition unit, an optimal track acquisition unit, a judgment unit and an output unit; an initialization unit for initializing state information; an optimal signal detection result acquisition unit for acquiring an optimal signal detection result of a user; an optimal transmission beam obtaining unit for obtaining an optimal transmission beam; an optimal reflection phase acquisition unit for acquiring an optimal reflection phase; the optimal allocation obtaining unit is used for obtaining optimal unmanned aerial vehicle power allocation and calculation resource allocation results; the optimal track acquisition unit is used for acquiring and outputting an optimal unmanned aerial vehicle flight track; the judging unit is used for judging whether the precision is converged to a preset precision or the iteration frequency reaches the maximum iteration frequency; if the calculated capacity of the system is not converged to the specified precision, or if the iteration times do not reach the maximum iteration times, the optimal signal detection result of the user is obtained again; and the output unit is used for outputting the optimal result if the calculation capacity of the system converges to the specified precision or if the iteration times reach the maximum iteration times.
The application has the following beneficial effects:
the unmanned aerial vehicle and intelligent reflecting surface joint design method in the mobile edge computing system can achieve the purpose of joint design of the unmanned aerial vehicle and the intelligent reflecting surface in the mobile edge computing system.
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In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments described in the present application, and other drawings can be obtained by those skilled in the art according to the drawings.
FIG. 1 is a block diagram of the internal architecture of a deployment, control system for a mobile edge computing system provided in accordance with an embodiment of the present application;
fig. 2 is a flowchart of a method for deploying and controlling a mobile edge computing system according to an embodiment of the present application.
Detailed Description
The technical solutions in the embodiments of the present application are clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are some, but not all, embodiments of the present application. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
The invention provides a deployment and control method and a deployment and control system of a mobile edge computing system.
Scene assumption is as follows: there are K ground users in the target area, and a ground wireless access point and a unmanned aerial vehicle can provide MEC calculation service simultaneously. The ground user needs to transmit the calculation task to the unmanned aerial vehicle, and after the unmanned aerial vehicle receives the calculation task, the unmanned aerial vehicle determines to forward part of the task to the ground wireless receiving point for calculation according to the situation. Suppose the total time slot of the system is N and the length of each time slot is deltat(ii) a The number of the intelligent reflecting surface reflecting units is M; the flight path of the nth time slot of the unmanned plane is denoted as q [ n ]]. The time of transmission of user k to the drone in each time slot is
The time when the unmanned aerial vehicle transmits the k data of the user to the wireless access point is
In addition, use
Indicating the phase theta of the nth slot of the k-th service user to the mth intelligent unit of the intelligent reflectork,m[n]Controlling; the user transmission power being a fixed value pt(ii) a The unmanned plane beam forming vector and the transmitting power of the unmanned plane to a user k in each time slot are wk[n]And pk[n](ii) a The uplink signal detection vector in each time slot of the unmanned aerial vehicle is Tk[n](ii) a The system communication bandwidth and the white noise power are respectively B and sigma2。
Example one
Fig. 1 illustrates a deployment and control system of a mobile edge computing system according to the present application.
Based on the above scenario assumptions, the computational capacity C of the definition system is specifically expressed as:
wherein
The amount of off-loading tasks to the drone by the ground user k at time slot n is indicated. Wherein
The concrete expression is as follows:
wherein h isu,k[n]Represents the channel coefficient to drone for user k at time slot n, (·)HRepresentation matrixOr a conjugate transpose of the vector.
Expressed as the time of transmission of user k to the drone in each time slot, B represents the system communication bandwidth, ptIndicating that the user transmit power is a fixed value,
indicating the determined signal detection result.
In addition, the unmanned aerial vehicle transmits the data volume of the user k to the wireless access point in the time slot n
The concrete expression is as follows:
wherein
hur[n]Respectively representing the channel coefficients between the intelligent reflecting surface and the wireless access point, between the unmanned aerial vehicle and the wireless access point and between the unmanned aerial vehicle and the intelligent reflecting surface,
a phase shift matrix representing the intelligent reflecting surface in the nth slot of the service user k, diag (x) representing that the vector x is changed into a square matrix, wherein the diagonal elements respectively correspond to each element of the vector x, and other elements are all 0.
Representing the time, σ, at which the drone transmits user k data to the wireless access point2Representing white noise power.
The calculation amount of the unmanned plane to the user k in the time slot n is
Wherein f isk[n]For unmanned aerial vehicle toComputing resources allocated by user k, cuRepresenting the number of CPU cycles, δ, required per 1bit of data calculatedtIndicating the length of each slot. In the whole process of system operation, the data volume transmitted by the unmanned aerial vehicle to the wireless access point cannot exceed the data volume received by the unmanned aerial vehicle, that is, the following causal constraint relationship needs to be satisfied:
wherein
Indicating the amount of offloading tasks for ground user k to the drone at time slot n,
indicating that the drone transmits the amount of data for user k to the wireless access point in time slot n +1,
representing the amount of computation of the drone on user k at time slot n + 1.
The system specifically comprises the following units: an initialization unit 110, an optimal signal detection result acquisition unit 120, an optimal transmission beam acquisition unit 130, an optimal reflection phase acquisition unit 140, an optimal allocation acquisition unit 150, an optimal trajectory acquisition unit 160, a determination unit 170, and an output unit 180.
The initialization unit 110 is used to initialize the state information.
The optimal signal detection result obtaining unit 120 is connected to the initialization unit 110, and is configured to obtain a signal detection result optimal for a user.
The optimal transmission beam obtaining unit 130 is connected to the optimal signal detection result obtaining unit 120, and is configured to obtain an optimal transmission beam.
The optimal reflection phase acquiring unit 140 is connected to the optimal transmission beam acquiring unit 130, and is used for acquiring an optimal reflection phase.
The optimal allocation obtaining unit 150 is connected to the optimal reflection phase obtaining unit 140, and is configured to obtain optimal unmanned aerial vehicle power allocation and calculation resource allocation results.
The optimal trajectory acquisition unit 160 is connected to the optimal distribution acquisition unit 150, and is configured to acquire and output an optimal unmanned aerial vehicle flight trajectory.
The determining unit 170 is connected to the optimal trajectory obtaining unit 160 and the optimal signal detection result obtaining unit 120, respectively, and is configured to determine whether to converge to a preset precision or whether the number of iterations reaches a maximum number of iterations. If the calculation capacity of the system does not converge to the specified accuracy, or if the iteration count does not reach the maximum iteration count, the optimal signal detection result obtaining unit 120 re-executes obtaining of the user optimal signal detection result.
The output unit 180 is connected to the determining unit 170, and is configured to output an optimal result if the calculated capacity of the system converges to a specified accuracy, or if the number of iterations reaches the maximum number of iterations.
Example two
As shown in fig. 2, a method for deploying and controlling a mobile edge computing system provided by the present application specifically includes the following steps:
step S210: the state information is initialized.
The initialization state information comprises the number of initialization ground user equipment, the number of intelligent reflecting surface reflecting units, the number of unmanned aerial vehicle antennas, the total system time slot, the length of each time slot, unmanned aerial vehicle track representation, the maximum user transmitting power, the maximum unmanned aerial vehicle transmitting power, the maximum calculating frequency of the unmanned aerial vehicle and a ground wireless access point, system communication bandwidth and white noise power, convergence accuracy and the maximum iteration number.
Step S220: and responding to the initialization state information to acquire the optimal signal detection result of the user.
Specifically, uplink signal detection control is performed, and the best signal detection result of the user is obtained at the unmanned aerial vehicle end, so that the receiving performance is best.
Determined signal detection result
The concrete expression is as follows:
wherein ILA matrix representing dimensions of L x L,
hur[n]respectively represents the channel coefficients between the intelligent reflecting surface and the wireless access point, between the unmanned aerial vehicle and the wireless access point and between the unmanned aerial vehicle and the intelligent reflecting surface, sigma2Representing white noise power.
Step S230: in response to obtaining the user's best signal detection result, the best transmit beam is obtained.
Wherein, the beam forming control of the unmanned aerial vehicle is carried out to obtain the best transmitting beam.
Optimum transmit beam wk[n]The concrete expression is as follows:
Step S240: in response to acquiring the optimal transmit beam, an optimal reflection phase is acquired.
Wherein an optimal reflection phase of the reflection unit of the agent, an optimal reflection phase shift theta, is determinedk，m[n]The concrete expression is as follows:
wherein
To represent
The m-th element is a group of elements,
represents hur[n]M-th row vector, wk[n]Representing the best transmit beam.
Step S250: and responding to the acquisition of the optimal transmitting beam, and acquiring optimal unmanned aerial vehicle power allocation and calculation resource allocation results.
Wherein, the power and the calculation control of the unmanned aerial vehicle are carried out, and the optimal power distribution value and the calculation resource distribution of the unmanned aerial vehicle are obtained by a CCCP (Secondary-Convex procedure) method.
The step S250 specifically includes the following sub-steps:
step S2501: first input information is acquired.
Specifically, the first input information includes initialization state information in step S210, an optimal signal detection result in step S220, an optimal transmission beam in step S230, and an optimal reflection phase in step S240.
Step S2502: and acquiring the optimal unmanned aerial vehicle power distribution and calculation resource distribution results according to the first input information.
Specifically, by using a CCCP method, the unmanned aerial vehicle power and calculation optimization problem is changed into a convex problem, and then a convex optimization tool box is used for solving to obtain the optimal unmanned aerial vehicle power distribution and calculation resource distribution result.
Step S260: and responding to the acquired optimal unmanned aerial vehicle power distribution and calculation resource distribution results, and acquiring and outputting an optimal unmanned aerial vehicle flight track.
Wherein, the optimal flight trajectory of the unmanned aerial vehicle is obtained by an SCA (sequential convex approximation) method, and the step S260 specifically includes the following substeps:
step S2601: and acquiring second input information.
The second input information includes the initialization state information in step S210, the optimal signal detection result in step S220, the optimal transmit beam acquisition in step S230, the optimal reflection phase in step S240, and the optimal drone power allocation and computational resource allocation result in step S250.
Step S2602: and solving by using a convex optimization toolbox according to the second input information to obtain the optimal flight track of the unmanned aerial vehicle, and outputting the optimal flight track.
Step S270: and judging whether the precision is converged to a preset precision or the iteration frequency reaches the maximum iteration frequency.
After each iteration is completed, the calculated capacity of the system obtained last time, the obtained optimal signal detection result, the optimal transmitting beam, the optimal reflection phase, the optimal unmanned aerial vehicle power allocation result and the calculation resource allocation result are updated.
If the calculated capacity of the system converges to the specified accuracy, or if the number of iterations reaches the maximum number of iterations, the iteration is terminated, and step S280 is performed. Step S280: and outputting the best result.
The optimal result represents the user's optimal signal detection result, optimal transmit beam, optimal reflection phase, optimal drone power allocation and computational resource allocation results, and optimal drone flight trajectory.
Wherein the specified precision can be preset according to actual conditions.
And if the calculated capacity of the system converges to the specified precision or if the iteration number reaches the maximum iteration number, adding 1 to the iteration number, and re-executing the steps S220-S260 until the calculated capacity of the system converges to the preset precision or the iteration number reaches the maximum iteration number.
The application has the following beneficial effects:
the unmanned aerial vehicle and intelligent reflecting surface joint design method in the mobile edge computing system can achieve the purpose of joint design of the unmanned aerial vehicle and the intelligent reflecting surface in the mobile edge computing system. Particularly, on one hand, a signal detection vector of the unmanned aerial vehicle can be designed, and the signal receiving strength is improved; the method comprises the steps that a beam forming vector of the unmanned aerial vehicle is designed, and the signal transmission capacity of an unloading task is enhanced; and meanwhile, the flight track of the unmanned aerial vehicle is optimized, and the coverage performance is improved. On the other hand, the intelligent reflecting surface unit is subjected to phase shift design, so that the transmission characteristic of a channel is improved, and the transmission performance of signals is improved. Through the joint design of the unmanned aerial vehicle and the intelligent reflecting surface, the calculation capacity of the system can be improved obviously finally.
Although the present application has been described with reference to examples, which are intended to be illustrative only and not to be limiting of the application, changes, additions and/or deletions may be made to the embodiments without departing from the scope of the application.
The above description is only for the specific embodiments of the present application, but the scope of the present application is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present application, and shall be covered by the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.
Claims (10)
1. A deployment and control method of a mobile edge computing system is characterized by comprising the following steps:
initializing state information;
responding to the initialization state information, and acquiring an optimal signal detection result of a user;
responding to the signal detection result which is obtained by the user and is optimal, and obtaining an optimal transmitting beam;
acquiring an optimal reflection phase in response to acquiring the optimal transmit beam;
responding to the obtained optimal transmitting wave beam, obtaining optimal unmanned aerial vehicle power distribution and calculation resource distribution results;
responding to the obtained optimal unmanned aerial vehicle power distribution and calculation resource distribution results, and obtaining and outputting an optimal unmanned aerial vehicle flight track;
judging whether the precision is converged to a preset precision or the iteration frequency reaches the maximum iteration frequency; and if the precision is converged to the preset precision or the iteration frequency reaches the maximum iteration frequency, outputting the optimal result.
2. The method of deploying and controlling a mobile edge computing system according to claim 1, wherein initializing the state information comprises initializing a number of ground user equipments, a number of intelligent reflector units, a number of drone antennas, a total system time slot, a length of each time slot, a drone trajectory representation, a user maximum transmit power, a drone and ground wireless access point maximum computing frequency, a system communication bandwidth and a white noise power, and a convergence accuracy and a maximum number of iterations.
3. The method for deploying and controlling a mobile edge computing system according to claim 1, wherein the determined signal detection result
The concrete expression is as follows:
wherein ILA matrix representing dimensions of L x L,
hur[n]respectively represents the channel coefficients between the intelligent reflecting surface and the wireless access point, between the unmanned aerial vehicle and the wireless access point and between the unmanned aerial vehicle and the intelligent reflecting surface, sigma2Representing white noiseAnd (4) power.
4. The method for deploying and controlling a mobile edge computing system according to claim 1, wherein the optimal transmit beam wk[n]The concrete expression is as follows:
5. The method for deploying and controlling a mobile edge computing system according to claim 1, wherein the optimal reflection phase shift θk，m[n]The concrete expression is as follows:
wherein
Represent
The m-th element of the first group,
represents hur[n]M-th row vector, wk[n]Representing the best transmit beam.
6. The deployment and control method of the mobile edge computing system according to claim 1, wherein the obtaining of the optimal unmanned aerial vehicle power allocation and computing resource allocation result specifically comprises the following substeps:
acquiring first input information;
acquiring optimal unmanned aerial vehicle power distribution and calculation resource distribution results according to the first input information;
wherein the first input information includes initialization state information, an optimal signal detection result, an optimal transmission beam, and an optimal reflection phase.
7. The deployment and control method of the mobile edge computing system according to claim 1, wherein the obtaining and outputting the optimal unmanned aerial vehicle flight trajectory specifically comprises the following sub-steps:
acquiring second input information;
solving and outputting the optimal flight track of the unmanned aerial vehicle by using a convex optimization toolbox according to the second input information;
wherein the second input information includes initialization state information, optimal signal detection results, optimal transmit beams, optimal reflection phases, and optimal drone power allocation and computational resource allocation results.
8. The method of deployment and control of a mobile edge computing system of claim 1, further comprising updating the computing capacity of the system and the obtained optimal signal detection results, optimal transmit beams, optimal reflection phases, and optimal drone power allocation and computing resource allocation results.
9. The deployment and control method of mobile edge computing system according to claim 8, wherein if the computing capacity of the system converges to a specified accuracy or if the number of iterations reaches the maximum number of iterations, the number of iterations is increased by 1, and the user's best signal detection result is obtained again.
10. A deployment and control system of a mobile edge computing system is characterized by specifically comprising an initialization unit, an optimal signal detection result acquisition unit, an optimal transmission beam acquisition unit, an optimal reflection phase acquisition unit, an optimal distribution acquisition unit, an optimal track acquisition unit, a judgment unit and an output unit;
an initialization unit for initializing state information;
an optimal signal detection result acquisition unit for acquiring an optimal signal detection result of a user;
an optimal transmission beam obtaining unit for obtaining an optimal transmission beam;
an optimal reflection phase acquisition unit for acquiring an optimal reflection phase;
the optimal allocation obtaining unit is used for obtaining optimal unmanned aerial vehicle power allocation and calculation resource allocation results;
the optimal track acquisition unit is used for acquiring and outputting an optimal unmanned aerial vehicle flight track;
the judging unit is used for judging whether the precision is converged to a preset precision or the iteration frequency reaches the maximum iteration frequency; if the calculated capacity of the system is not converged to the specified precision, or if the iteration times do not reach the maximum iteration times, the optimal signal detection result of the user is obtained again;
and the output unit is used for outputting the optimal result if the calculated capacity of the system converges to the specified precision or if the iteration frequency reaches the maximum iteration frequency.
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| CN116684925A (en) * | 2023-07-24 | 2023-09-01 | 南京图策信息科技有限公司 | Unmanned aerial vehicle-mounted intelligent reflecting surface safe movement edge calculation method |
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