CN114115240B - Unmanned equipment control method and device - Google Patents
Unmanned equipment control method and device Download PDFInfo
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Abstract
The invention discloses a control method and a device for unmanned equipment, which relate to the field of unmanned equipment and are used for determining a basic occupation area of obstacles around the unmanned equipment, wherein the basic occupation area comprises at least one of an area occupied by a detected obstacle at a current position and an area occupied by a predicted position of the obstacle, then, aiming at each basic boundary, the distance from the area center of the basic occupation area to a straight line where the basic boundary is located is smaller than a projection point corresponding to an expansion boundary of the basic boundary on the normal line where the basic boundary is located, the distance between the projection point and the area center is used as a constraint condition, the expansion boundary corresponding to the basic boundary is determined, and the basic occupation area is adjusted according to the expansion boundary corresponding to each basic boundary contained in the basic occupation area, so that the adjusted occupation area corresponding to the obstacle is obtained, and the running safety of the unmanned equipment is ensured according to the adjusted occupation area.
Description
Technical Field
The present disclosure relates to the field of unmanned driving, and in particular, to a method and apparatus for controlling an unmanned device.
Background
In the unmanned technique, the unmanned device needs to observe the positions of surrounding obstacles and predict the positions of the surrounding obstacles in a next period of time, so as to avoid the obstacles.
In practical application, both the observation result of the unmanned device on the obstacle position and the prediction result of the surrounding obstacle position have certain uncertainty, so in the prior art, the occupied area of the obstacle position can be enlarged according to a fixed margin, for example, if the obstacle appears as a rectangular area on the ground plane, each side of the rectangular area can be outwardly enlarged by a fixed width, so that the unmanned device can avoid the obstacle through the enlarged occupied area of the obstacle, and the safety of the unmanned device is ensured as much as possible.
However, the occupied area of the obstacle is enlarged by fixing a margin, which is usually set manually according to experience, and the occupied area of the unmanned device may not be accurately adjusted, and too large or too small an enlargement may cause a problem, such as causing sudden braking of the unmanned device.
Therefore, how to accurately adjust the occupied area of the obstacle is a problem to be solved.
Disclosure of Invention
The present disclosure provides a method and an apparatus for controlling an unmanned device, so as to partially solve the above-mentioned problems in the prior art.
The technical scheme adopted in the specification is as follows:
the specification provides a control method of unmanned equipment, which comprises the following steps:
determining a base occupancy zone of an obstacle surrounding an unmanned device, the base occupancy zone comprising at least one of a zone occupied by the obstacle at a current location and a zone occupied by a predicted location of the obstacle as viewed;
aiming at each basic boundary contained in the basic occupation area, determining an expansion boundary corresponding to the basic boundary by taking the distance between the area center of the basic occupation area and the straight line where the basic boundary is positioned as a constraint condition, wherein the distance is smaller than the projection point corresponding to the expansion boundary of the basic boundary on the straight line where the basic boundary is positioned and on the normal line passing through the area center, and the distance between the projection point and the area center is taken as a constraint condition;
according to the expansion boundary corresponding to each basic boundary contained in the basic occupation area, adjusting the basic occupation area to obtain an adjusted occupation area corresponding to the obstacle;
and controlling the unmanned equipment according to the adjusted occupied area.
Optionally, the constraint condition is used to represent a constraint that an arbitrary safe position in a random coordinate system is located outside a basic boundary of the obstacle, and the extended boundary is used to represent a boundary of the safe position, where the random coordinate system is a coordinate system with a center of an actual position of the obstacle as an origin.
Optionally, determining an extended edge corresponding to the basic boundary by using a distance from a region center of the basic occupied region to a line where the basic boundary is located, where the distance is smaller than a projection point corresponding to an extended boundary of the basic boundary on a normal line of the line where the basic boundary is located, and the distance between the projection point and the region center as a constraint condition specifically includes:
and determining an expansion boundary corresponding to the basic boundary by taking the constraint condition that the probability of the distance between the projection point corresponding to the expansion boundary smaller than the basic boundary on the normal line of the basic boundary and the region center is not smaller than the set probability.
Optionally, the constraint condition includes an uncertainty factor, where the uncertainty factor is used to convert the constraint condition into a deterministic constraint to obtain the expansion boundary, where the uncertainty factor includes a deviation between an actual position of an obstacle and the center of the area, and a difference between an obstacle orientation corresponding to a basic occupied area and an actual orientation of the obstacle, where the obstacle orientation corresponding to the basic occupied area is an observed or predicted obstacle orientation.
Optionally, the uncertainty factor corresponds to a desired matrix and a covariance matrix, and the desired matrix and the covariance matrix are used to convert the constraint condition into a deterministic constraint to obtain the expansion boundary.
Optionally, before the obstacle is avoided according to the adjusted occupied area, the method further includes:
determining each vertex of the adjusted occupied zone;
determining, for each vertex, a connection line from the center of the adjusted occupied area to the vertex;
if the included angle between the two expansion boundaries corresponding to the vertex and the connecting line does not exceed the set angle, determining a truncated edge aiming at the vertex between the two expansion boundaries corresponding to the vertex;
intercepting the adjusted occupied area according to the intercepting edge of at least one vertex to obtain an intercepted occupied area containing the center of the adjusted occupied area;
according to the adjusted occupied area, obstacle avoidance is carried out on the obstacle, and the method specifically comprises the following steps:
and according to the occupied area after interception, obstacle avoidance is carried out on the obstacle.
Optionally, determining a truncated edge for the vertex between two extension boundaries corresponding to the vertex specifically includes:
Determining a vertex corresponding to the vertex in the basic occupation area as a target vertex;
determining a vertical line passing through the target vertex and perpendicular to a line connecting the center of the region and the target vertex;
and determining a truncated edge for the vertex between two expansion boundaries corresponding to the vertex according to the perpendicular line.
Optionally, the base footprint comprises at least one obstacle footprint predicted for the obstacle;
the method for determining the extended boundary corresponding to the basic boundary by taking the constraint condition that the probability of the distance between the extended boundary smaller than the basic boundary and the region center is not smaller than the set probability, wherein the distance from the region center of the basic occupied region to the straight line where the basic boundary is located is smaller than the projection point corresponding to the extended boundary of the basic boundary on the normal line where the basic boundary is located, specifically comprises the following steps:
determining a corresponding certainty probability of each obstacle occupation area predicted for the obstacle;
determining a component probability corresponding to each obstacle occupation area according to the certainty probability corresponding to each obstacle occupation area and the set probability;
based on the component probability corresponding to the obstacle occupying area, determining the expansion boundary corresponding to the basic boundary by taking the constraint condition that the probability of the distance between the projection point corresponding to the expansion boundary smaller than the basic boundary on the normal line of the basic boundary and the component probability corresponding to the area occupied area is not smaller than the component probability corresponding to the obstacle occupying area.
Optionally, for each obstacle occupation area, determining a component probability corresponding to the obstacle occupation area according to the deterministic probability corresponding to each obstacle occupation area and the set probability specifically includes:
taking the deterministic probability corresponding to the obstacle occupation area as the weight corresponding to the obstacle occupation area, weighting the component probability corresponding to the obstacle occupation area to be solved, and obtaining the weighted component probability corresponding to the obstacle occupation area to be solved;
and solving the component probability corresponding to each obstacle occupation area by taking the sum value of the weighted component probabilities to be solved corresponding to each obstacle occupation area as a constraint condition.
The specification provides a control device of unmanned equipment, includes:
a region determination module for determining a base occupation region of an obstacle surrounding an unmanned device, the base occupation region including at least one of a region occupied by the obstacle at a current location and a region occupied by a predicted location of the obstacle;
the boundary determining module is used for determining an expansion boundary corresponding to the basic boundary by taking the distance from the region center of the basic occupation region to the straight line where the basic boundary is located as a constraint condition for each basic boundary contained in the basic occupation region, wherein the distance between the projection point corresponding to the expansion boundary smaller than the basic boundary on the normal line of the straight line where the basic boundary is located and the region center;
The adjustment module is used for adjusting the basic occupation area according to the expansion boundary corresponding to each basic boundary contained in the basic occupation area to obtain an adjusted occupation area corresponding to the obstacle;
and the control module is used for controlling the unmanned equipment according to the adjusted occupied area.
The present description provides a computer-readable storage medium storing a computer program which, when executed by a processor, implements the control method of the unmanned device described above.
The present specification provides an unmanned device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing a control method of the unmanned device when executing the program.
The above-mentioned at least one technical scheme that this specification adopted can reach following beneficial effect:
as can be seen from the above method, a basic occupation area of an obstacle around the unmanned device can be determined, where the basic occupation area includes at least one of an area occupied by the observed obstacle at the current position and an area occupied by the predicted position of the obstacle, then, for each basic boundary included in the basic occupation area, a distance from a center of the area of the basic occupation area to a straight line where the basic boundary is located is smaller than a projection point corresponding to an extended boundary of the basic boundary on a normal line where the basic boundary is located, and a distance between the extended boundary and the center of the area is a constraint condition, an extended boundary corresponding to the basic boundary is determined, and the basic occupation area is adjusted according to the extended boundary corresponding to each basic boundary included in the basic occupation area, so that an adjusted occupation area corresponding to the obstacle is obtained, and then, the unmanned device is controlled according to the adjusted occupation area.
From the above, it can be seen that, according to the method, the distance from the center of the area of the basic occupied area to the straight line where the basic boundary is located is smaller than the projection point corresponding to the extended boundary of the basic boundary on the normal line where the basic boundary is located, and the distance between the extended boundary and the center of the area is taken as a constraint condition, so that the extended boundary meeting the constraint condition is determined, and further, a more accurate extended boundary is determined to a certain extent, and further, a more accurate occupied area after adjustment is determined, and the unmanned equipment is controlled according to the occupied area after adjustment, so that the running safety of the unmanned equipment can be ensured to a certain extent.
Drawings
The accompanying drawings, which are included to provide a further understanding of the specification, illustrate and explain the exemplary embodiments of the present specification and their description, are not intended to limit the specification unduly. In the drawings:
fig. 1 is a schematic flow chart of a control method of an unmanned device in the present specification;
FIG. 2 is a schematic diagram of a constraint for a base boundary provided in the present specification;
FIG. 3 is a schematic illustration of an expansion boundary provided in the present specification;
FIG. 4 is a schematic illustration of an adjusted footprint provided in the present specification;
FIG. 5 is a schematic illustration of a post-interception occupied area provided herein;
FIG. 6 is a schematic illustration of an adjusted occupancy zone corresponding to each predicted occupancy zone of an obstacle provided herein;
fig. 7 is a schematic diagram of a control device of the unmanned device provided in the present specification;
fig. 8 is a schematic view of the unmanned device corresponding to fig. 1 provided in the present specification.
Detailed Description
For the purposes of making the objects, technical solutions and advantages of the present specification more apparent, the technical solutions of the present specification will be clearly and completely described below with reference to specific embodiments of the present specification and corresponding drawings. It will be apparent that the described embodiments are only some, but not all, of the embodiments of the present specification. All other embodiments, which can be made by one of ordinary skill in the art without undue burden from the present disclosure, are intended to be within the scope of the present disclosure.
The following describes in detail the technical solutions provided by the embodiments of the present specification with reference to the accompanying drawings.
Fig. 1 is a schematic flow chart of a control method of an unmanned device in the present specification, specifically including the following steps:
S101: a base occupancy zone of an obstacle surrounding an unmanned device is determined, the base occupancy zone comprising at least one of a zone occupied by the obstacle at a current location and a zone occupied by a predicted location of the obstacle as viewed.
In practical applications, it is often necessary to observe and predict the position of an obstacle during the running of the unmanned device, and not only the observation of the predicted position of the obstacle, but also the actual existence of certain deviation, that is, not only the observation of the predicted position of the obstacle, and possibly certain uncertainty, and the control method of the unmanned device provided in the present specification is to eliminate such uncertainty.
Based on this, a base occupancy zone of the obstacle surrounding the unmanned device may be determined, the base occupancy zone comprising at least one of a zone occupied by the observed obstacle at the current location and a zone occupied by the predicted location of the obstacle. The basic occupation area may refer to an occupation area of a current position of an obstacle with a certain uncertainty and a predicted position of the obstacle, which are preliminarily determined by the unmanned device. Correspondingly, the actual position of the obstacle corresponds to the actual occupied area.
S102: and aiming at each basic boundary contained in the basic occupation area, determining an expansion boundary corresponding to the basic boundary by taking the distance between the area center of the basic occupation area and the straight line where the basic boundary is positioned as a constraint condition, wherein the distance is smaller than the projection point corresponding to the expansion boundary of the basic boundary on the straight line where the basic boundary is positioned and the normal line passing through the area center, and the distance between the projection point and the current position of the barrier.
After the basic occupation area is determined, for each basic boundary included in the basic occupation area, determining an expansion boundary corresponding to the basic boundary by taking a distance from the area center of the basic occupation area to a straight line where the basic boundary is located as a constraint condition, wherein the distance is smaller than a projection point corresponding to the expansion boundary of the basic boundary on a normal line where the basic boundary is located, and the distance between the projection point and the current position of the obstacle.
This constraint is mentioned above for determining the extended boundary satisfying a condition that the above-mentioned constraint can be understood as a constraint for finding a boundary capable of dividing the actual occupied area of the obstacle and the safe area located outside the actual occupied area of the obstacle, i.e., as long as the area outside the extended boundary is safe, wherein the above-mentioned constraint can be expressed by the formula:
Wherein (x ', y') is a coordinate in a random coordinate system,for the distance from the area center of the basic occupation area to the line where the basic border is located, +.>The random coordinate system is a coordinate system with the center of the actually occupied area of the obstacle as the origin, and can be understood as a hypothetical coordinate system, the constraint condition can be expressed as a constraint that any safety position under the random coordinate system is located outside the base boundary of the obstacle, and the expanded boundary is used to represent the boundary of the safety position, so that the constraint condition in the present specification can be expressed as the above formula by introducing the random coordinate system, as shown in fig. 2.
FIG. 2 is a schematic diagram of a constraint for a base boundary provided in the present specification.
One example of a polygon-based footprint in fig. 2, (x 0, y 0) is the center of the area,for a basic border of the basic occupation area, < > for>For the above mentioned distance from the area center of the basic occupied area to the line where the basic border is located,/->For the above-mentioned angle between the region center of the basic occupied region and the normal line of the straight line of the basic boundary (from the region center to the normal line of the straight line of the basic boundary), (x ', y') is a coordinate in a random coordinate system, the above formula is intended to find out that the position of ++ - >The outer (x ', y') distribution.
Since (x ', y') in the above formula is a coordinate in the random coordinate system and is uncertain, a coordinate system with (x 0, y 0), that is, the center of the region as the origin, can be constructed as a fixed coordinate system, the x-axis direction of the fixed coordinate system is taken as the basis to occupy the direction of the obstacle corresponding to the region, the direction of the obstacle may also have a certain uncertainty, the x-axis direction of the random coordinate system is the actual direction of the obstacle, that is, the random coordinate system is a coordinate system constructed by taking the assumed actual pose of the obstacle as the standard, the conversion relationship between the fixed coordinate system and the random coordinate system can be determined, and the finally obtained expansion boundary needs to be represented by the fixed coordinate system, that is:
wherein Deltax is Φ Δy Φ For the deviation between the area center of the basic occupied area and the actual position of the obstacle (i.e., the area center of the actual occupied area of the obstacle), Δψ Φ Deviation between the orientation of the obstacle corresponding to the base occupation area and the actual orientation of the obstacle. It can be seen that Deltax Φ 、Δx Φ Δψ Φ Is uncertain, and therefore, the certainty factor in this specification is Δx Φ 、Δx Φ Δψ Φ Namely, a deviation between the actual position and the current position of the obstacle and a deviation between the orientation of the obstacle corresponding to the basic occupied area, which is an observed or predicted orientation, and the actual orientation of the obstacle.
The above conversion relation can determine the expression of the coordinates in the random coordinate system represented by the coordinates in the fixed coordinate system, namely:
the above formula is brought into a formula corresponding to the constraint condition, and the following can be obtained:
because of the generally small uncertainty in the obstacle orientation, Δψ is Φ In most cases smaller, so a first order taylor approximation can be made to the left to obtain:
the above composition still contains Deltax Φ 、Δx Φ Δψ Φ These three uncertainty factors, and thus the above equation remains an opportunity constraint that needs to be translated into a deterministic constraint. This requires extracting the uncertainty factor and thus obtaining the final representation of the constraintConditional formula 1:
it can be seen that the uncertainty factors are all contained in the three-dimensional vector d of the first term on the left of the above equation, and therefore the desired matrix and covariance matrix of the three-dimensional vector d can be determined, so that the opportunity constraint is converted into a deterministic constraint by the desired matrix and covariance matrix, assuming Δx Φ 、Δy Φ Δψ Φ The expected matrix and covariance matrix of d, which all satisfy the normal distribution, are as follows:
wherein E (d) is a desired matrix, var (d) is a covariance matrix, and the covariance matrix isAndThe standard deviation of the position and the orientation of the obstacle, respectively, can be determined by an error coefficient given by a prediction module or an observation module of the unmanned device, and the error coefficient is used for representing the average error of the prediction module or the observation module for performing position prediction or position observation.
Converting equation (1) into deterministic constraints, a condition may also be introduced, i.e., the constraint may be changed to: the distance from the region center of the basic occupied region to the straight line where the basic boundary is located is smaller than the probability of the distance between the projection point corresponding to the extended boundary of the basic boundary on the normal line of the straight line where the basic boundary is located and the region center is not smaller than the set probability. Here, a set probability is introduced, which may refer to a confidence level that is preset, and this set probability is expressed as 1-epsilon, and epsilon may be referred to as a tolerance, which may be a smaller probability that is set, for example, epsilon is 5%, and then the set probability is 95%.
By introducing a set probability, the covariance matrix and the expectation matrix, the above equation 1 can be converted into the following equation 2:
wherein F is -1 The above formula 2 is arranged in a standard normal distribution to obtain formula 3:
it can be seen that the above Deltax is not included in formula (3) Φ 、Δy Φ Δψ Φ These three uncertainty factors (include Deltax Φ 、Δy Φ Δψ Φ Standard deviation corresponding to each otherAnd +.>For a determined statistical parameter), equation 3 is a deterministic constraint, and it can be understood that equation 3 satisfies a condition that lies outside the base boundary, and that equation 3 appears as a hyperbolic right branch (right part of one hyperbola) as shown in fig. 3.
Fig. 3 is a schematic diagram of an expanded boundary provided in the present specification.
The straight line where the hyperbolic virtual axis is located is taken as the basic boundaryThe line of the real axis is from (x 0, y 0) to +.>Is a perpendicular to the axis of the half-solid length +.>The included angle between the asymptote and the imaginary axis is
The following conclusions can also be drawn from the above reasoning:
1. when (when)When decreasing, a becomes smaller and +.>(expansion boundaries) will gradually get closer to the asymptote; when->When decreasing to 0, a decreases to 0, < >>(expansion boundary) degenerates to a break point +.>A broken line on the upper part.
2. When (when)When the beta is reduced, the beta is gradually reduced, and the hyperbola edge is gradually straightened; up to- >When decreasing to 0, β decreases to 0, < >>Degenerate to be parallel to->Is a straight line of (a).
3. When epsilon increases, a and beta become smaller gradually, and the hyperbola is gradually close toUntil epsilon increases to 0.5, a, beta decrease to 0,/and so on>Let go of->If epsilon is increased to more than 0.5, a and beta become negative, and ++>Can enter the barrier to become +.>The inner hyperbola is branched.
S203: and adjusting the basic occupation area according to the expansion boundary corresponding to each basic boundary contained in the basic occupation area to obtain an adjusted occupation area corresponding to the obstacle.
S204: and controlling the unmanned equipment according to the adjusted occupied area.
After determining the expansion boundary corresponding to each basic boundary included in the basic occupation area according to the constraint condition, the basic occupation area can be adjusted, so that an adjusted occupation area corresponding to the obstacle is obtained, and as shown in fig. 4, unmanned equipment can be controlled according to the adjusted occupation area.
Figure 4 is a schematic view of an adjusted footprint provided in this specification,
as can be seen from fig. 4, the adjusted occupied area may be obtained by intersecting the extension boundaries, and an area outside the adjusted occupied area may be regarded as a safe area, i.e. an area that can be reached by the unmanned device.
Wherein,
and, in addition, the processing unit,
thus, the first and second substrates are bonded together,
in the above series of equations, pr () is a probability, p is a secure position,the half space outside the expansion boundary corresponding to the determined i-th base boundary (i.e., the space to the right of the expansion boundary of the right branch of the hyperbola as drawn in fig. 3 can be regarded as the half space).
Since equation 4 can be derived to equation 6, equation 5 is a more conservative safety constraint than equation 6, and therefore, the safety constraint of equation 6 can be replaced by the safety constraint of equation 5, where equation 5 represents a safety constraint in which the probability of the half space outside each expanded boundary being a safety region is not less than 1-epsilon, and equation 4 represents a probability of the region outside the adjusted occupied region being a safety region is not less than the probability of the half space outside one expanded boundary being a safety region, and thus equation 6 can be derived: the probability that the area outside the adjusted occupied area obtained by intersecting each expansion boundary is a safe area is not less than 1-epsilon, so that the adjusted occupied area obtained by intersecting each expansion boundary can be regarded as the actual occupied area of the obstacle, and the unmanned equipment can avoid the obstacle according to the adjusted occupied area.
It should be noted that, as can be seen from the derivation of the above equations 4 to 6, the probability of the safety region outside the adjusted occupied region may be larger than 1- ε (the preset set probability), and thus, the adjusted occupied region may have a problem that the original basic occupied region is more expanded by some expansion boundary, for example, the positions of the point A and the point B in FIG. 3 are more protruded than the basic occupied region, and thus, such a position may be a more expanded position, and the adjusted occupied region may be further adjusted.
Specifically, each vertex of the adjusted occupied area can be determined, a connecting line from the center of the area of the adjusted occupied area to the vertex is determined for each vertex, if the included angle between two expansion boundaries corresponding to the vertex and the connecting line does not exceed a set angle, a intercepting edge for the vertex is determined between the two expansion boundaries corresponding to the vertex, and according to the intercepting edge of at least one vertex, the adjusted occupied area is intercepted, so that the intercepted occupied area containing the center of the adjusted occupied area is obtained, and the unmanned equipment is controlled through the intercepted occupied area.
The occupation area after interception can be as shown in fig. 4.
Fig. 5 is a schematic view of a post-interception occupied area provided in the present specification.
As can be seen from fig. 5, the truncated occupied area has a number of shorter sides than the adjusted occupied area, and these sides may be referred to as truncated sides, where the area of the adjusted occupied area is reduced by the truncated sides, so that the truncated sides are used to reduce the area of the vertex corresponding to the offset side that is extended by the adjusted occupied area compared to the base occupied area. When the extended area corresponding to one vertex in the adjusted occupied area is more prominent, a truncated edge can be constructed to truncate the area which is more prominent at the vertex, the truncated edge is specifically determined to be constructed at which vertices, a connecting line between the vertex and the center of the area of the adjusted occupied area can be determined through the above, then the included angle between the connecting line and two extended boundaries corresponding to the vertex is determined, if the included angles are acute angles, it is indicated that the extended area corresponding to the vertex is more prominent, and the truncated edge can be constructed at the vertex.
There may be various ways of constructing the truncated edge, for example, a vertex corresponding to the vertex may be determined in the basic occupation area as a target vertex, a vertical line passing through the target vertex and perpendicular to a line between the center of the area and the target vertex may be determined, and then, according to the vertical line, a truncated edge for the vertex may be determined between two extended boundaries corresponding to the vertex, that is, a hyperbola with a real axis located on a line between the target vertex and the center of the area and with an imaginary axis located on a line perpendicular to the line passing through the target vertex may be determined as a truncated edge (that is, the target vertex may be set as a basic boundary, and an extended boundary with respect to the target vertex may be determined as a truncated edge). For another example, the compensation degree may be preset, and the truncated edge may be constructed according to the compensation degree.
It should be noted that, in a scenario of predicting the position of an obstacle, the prediction model may give prediction results with a plurality of different weights for the obstacle, where each prediction result is a predicted occupied area of the obstacle for the obstacle, where the weight corresponding to each prediction result referred to herein is a deterministic probability that the prediction model outputs for the prediction result, in this scenario, the adjusted occupied area corresponding to each prediction result may be further determined for each prediction result, and when the unmanned device performs obstacle avoidance, obstacle avoidance is performed through the adjusted occupied area corresponding to each prediction result.
Specifically, a deterministic probability corresponding to each obstacle occupying area in at least one obstacle occupying area may be determined, and for each obstacle occupying area, a component probability corresponding to the obstacle occupying area may be determined according to the deterministic probability corresponding to each obstacle occupying area and the set probability.
And then, based on the component probability corresponding to the obstacle occupying area, determining the expansion boundary corresponding to the basic boundary by taking the constraint condition that the probability of the distance between the projection point corresponding to the expansion boundary smaller than the basic boundary on the normal line of the basic boundary and the area center is not smaller than the component probability corresponding to the obstacle occupying area, wherein the distance between the projection point and the area center is smaller than the distance between the projection point corresponding to the expansion boundary and the basic boundary.
The component probability corresponding to each obstacle occupation area needs to be determined through a preset condition, wherein the preset condition is that for each obstacle occupation area, the deterministic probability corresponding to the obstacle occupation area is used as the weight of the component probability corresponding to the obstacle occupation area, and the component probabilities corresponding to the obstacle occupation areas are weighted and summed to obtain the set probability.
That is, for an obstacle occupation area, the deterministic probability corresponding to the obstacle occupation area may be used as the weight corresponding to the obstacle occupation area, the component probability corresponding to the obstacle occupation area to be solved may be weighted to obtain the weighted component probability corresponding to the obstacle occupation area to be solved, and the sum of the weighted component probabilities corresponding to each obstacle occupation area is used as the constraint condition to solve the component probability corresponding to each obstacle occupation area.
In this way, when determining that an occupied area of an obstacle corresponds to the adjusted occupied area, for each basic boundary corresponding to the occupied area of the obstacle, the extended boundary corresponding to the basic boundary may be determined by using, as a constraint condition, a distance from the center of the area to a straight line where the basic boundary is located, which is smaller than a projection point corresponding to the extended boundary corresponding to the basic boundary on a normal line where the basic boundary is located, and a probability of a distance between the projection point and the center of the area is not smaller than a component probability corresponding to the occupied area of the obstacle.
The above-described respective obstacle occupation regions and the component probabilities corresponding to each obstacle occupation region are explained below in the form of an example, as shown in fig. 6.
Fig. 6 is a schematic diagram of an adjusted occupied area corresponding to each predicted occupied area of the obstacle provided in the present specification.
Fig. 6 shows a case where the base occupied area includes predicted two obstacle occupied areas for the same obstacle, one of the two obstacle occupied areas is an obstacle occupied area (referred to as z 1) where the obstacle is predicted to go straight, the other is an obstacle occupied area (referred to as z 2) where the obstacle is predicted to turn right, the predicted probabilities corresponding to the two obstacle occupied areas are 0.92 and 0.08, respectively, the case shown in fig. 5 is a case where the component probabilities of three different obstacle occupied areas are determined, and the component probabilities of the three obstacle occupied areas are combined to determine the final area where obstacle avoidance is required (therefore, when the component probabilities of the obstacle occupied areas are determined, the component probabilities of at least one of the obstacle occupied areas can be determined, and the adjusted occupied areas corresponding to the various obstacle occupied areas are determined by combining the component probabilities of each of the obstacle occupied areas, so as to avoid the obstacle).
As can be seen from the figure, the set probability is 1-epsilon (95%), epsilon is 5%, and the component probability of each obstacle occupation area determined by the set probability can be three:
0.92×1％+0.08×51％＝5％
The component probability of z1 is 1-1% (i.e. 99%), and the component probability of z2 is 1-51% (i.e. 49%), and the calculation mode is that the target probabilities (i.e. 1% and 51% in the above formula) corresponding to the two obstacle occupation regions are determined in the above formula, and are multiplied and summed with the corresponding deterministic probabilities respectively, so that epsilon can be finally obtained, and the component probability corresponding to the obstacle occupation region can be determined through the target probability of each obstacle occupation region.
0.92×5％+0.08×5％＝5％
0.92×5.35％+0.08×1％＝5％
Similarly, the two formulas are respectively: the component probability of z1 is 1-5% (i.e., 95%), the component probability of z2 is 1-5% (i.e., 95%), the component probability of z1 is 1-5.35% (i.e., 94.65%), and the decomposition probability of z2 is 1-1% (i.e., 99%).
In the above example, the theoretical support for determining the various component probabilities and determining the adjusted region by each component probability is as follows: the following formulas 7 and 8 are equivalent to each other.
Wherein the filling condition of formula 7 is formula 8, z j For the j-th predicted obstacle occupation area, there are m kinds of obstacle occupation areas in total, and each kind of obstacle occupation area can be regarded as a normal distribution, so that the predicted plural kinds of obstacle occupation areas are mixed normal distribution.
The following is a demonstration of the filling condition of formula 7 as formula 8:
sufficiency demonstrates that:
bringing equation 8 into equation 7 yields:
the necessity proves that: can not get
Obviously:
in addition, in the case of the optical fiber,
the above-mentioned unmanned apparatus may refer to an apparatus capable of realizing automatic driving such as an unmanned vehicle, an unmanned plane, an automatic distribution apparatus, or the like. Based on the above, the control method of the unmanned equipment provided by the specification can be used for adjusting the basic occupation area of the obstacle with uncertainty, so that the more accurate occupation area is obtained, and the unmanned equipment can be particularly applied to the field of distribution through the unmanned equipment, such as business scenes of distribution such as express, logistics, take-out and the like by using the unmanned equipment.
According to the method, the unmanned equipment can determine the expansion boundary meeting the constraint condition according to the constraint condition that the distance from the area center of the basic occupation area to the straight line where the basic boundary is located is smaller than the projection point corresponding to the expansion boundary of the basic boundary on the normal line where the basic boundary is located and the distance from the area center, so that the more accurate expansion boundary is determined to a certain extent, the more accurate occupation area after adjustment is determined, and the unmanned equipment control is performed according to the occupation area after adjustment, so that the running safety of the unmanned equipment can be ensured to a certain extent.
The control method of the unmanned equipment provided for one or more embodiments of the present disclosure further provides a corresponding control device of the unmanned equipment based on the same thought, as shown in fig. 7.
Fig. 7 is a schematic diagram of a control device of an unmanned device provided in the present specification, specifically including:
a region determination module 701, configured to determine a base occupation region of an obstacle surrounding the unmanned device, where the base occupation region includes at least one of a region occupied by the observed obstacle at a current position and a region occupied by a predicted position of the obstacle;
the boundary determining module 702 is configured to determine, for each base boundary included in the base occupation area, an extended boundary corresponding to the base boundary by using, as a constraint condition, a distance between a distance from a center of the area of the base occupation area to a line where the base boundary is located, a projection point corresponding to an extended boundary smaller than the base boundary on a line where the base boundary is located and a normal line passing through the center of the area, and the distance between the projection point and the center of the area;
an adjustment module 703, configured to adjust the basic occupation area according to the expansion boundary corresponding to each basic boundary included in the basic occupation area, so as to obtain an adjusted occupation area corresponding to the obstacle;
And the control module 704 is used for controlling the unmanned equipment according to the adjusted occupied area.
Optionally, the constraint condition is used to represent a constraint that an arbitrary safe position in a random coordinate system is located outside a basic boundary of the obstacle, and the extended boundary is used to represent a boundary of the safe position, where the random coordinate system is a coordinate system with a center of an actual position of the obstacle as an origin.
Optionally, the boundary determining module 702 is specifically configured to determine the expansion boundary corresponding to the basic boundary by using, as a constraint condition, that a distance from the region center of the basic occupied region to the line where the basic boundary is located is smaller than a probability of a projection point corresponding to the expansion boundary of the basic boundary on a normal line of the line where the basic boundary is located being not smaller than a set probability.
Optionally, the constraint condition includes an uncertainty factor, where the uncertainty factor is used to convert the constraint condition into a deterministic constraint to obtain the expansion boundary, where the uncertainty factor includes a deviation between an actual position of an obstacle and the center of the area, and a difference between an obstacle orientation corresponding to a basic occupied area and an actual orientation of the obstacle, where the obstacle orientation corresponding to the basic occupied area is an observed or predicted obstacle orientation.
Optionally, the uncertainty factor corresponds to a desired matrix and a covariance matrix, and the desired matrix and the covariance matrix are used to convert the constraint condition into a deterministic constraint to obtain the expansion boundary.
Optionally, before obstacle avoidance of the obstacle according to the adjusted occupied area, the control module 704 is further configured to determine each vertex of the adjusted occupied area; determining, for each vertex, a connection line from the center of the adjusted occupied area to the vertex; if the included angle between the two expansion boundaries corresponding to the vertex and the connecting line does not exceed the set angle, determining a truncated edge aiming at the vertex between the two expansion boundaries corresponding to the vertex; intercepting the adjusted occupied area according to the intercepting edge of at least one vertex to obtain an intercepted occupied area containing the center of the adjusted occupied area;
the control module 704 is specifically configured to avoid the obstacle according to the intercepted occupied area.
Optionally, the control module 704 is specifically configured to determine, in the base occupation area, a vertex corresponding to the vertex as a target vertex; determining a vertical line passing through the target vertex and perpendicular to a line connecting the center of the region and the target vertex; and determining a truncated edge for the vertex between two expansion boundaries corresponding to the vertex according to the perpendicular line.
Optionally, the base footprint comprises at least one obstacle footprint predicted for the obstacle;
the boundary determining module 702 is specifically configured to determine a deterministic probability corresponding to each obstacle occupation area predicted for the obstacle; determining a component probability corresponding to each obstacle occupation area according to the certainty probability corresponding to each obstacle occupation area and the set probability; based on the component probability corresponding to the obstacle occupying area, determining the expansion boundary corresponding to the basic boundary by taking the constraint condition that the probability of the distance between the projection point corresponding to the expansion boundary smaller than the basic boundary on the normal line of the basic boundary and the component probability corresponding to the area occupied area is not smaller than the component probability corresponding to the obstacle occupying area.
Optionally, the boundary determining module 702 is specifically configured to take the deterministic probability corresponding to the obstacle occupation area as the weight corresponding to the obstacle occupation area, weight the component probability corresponding to the obstacle occupation area to be solved, and obtain the weighted component probability corresponding to the obstacle occupation area to be solved; and solving the component probability corresponding to each obstacle occupation area by taking the sum value of the weighted component probabilities to be solved corresponding to each obstacle occupation area as a constraint condition.
The present specification also provides a computer-readable storage medium storing a computer program operable to perform the above-described control method of the unmanned device provided in fig. 1.
The present specification also provides a schematic block diagram of the unmanned device shown in fig. 8. As shown in fig. 8, at the hardware level, the unmanned device includes a processor, an internal bus, a network interface, a memory, and a nonvolatile memory, and may of course include hardware required by other services. The processor reads the corresponding computer program from the nonvolatile memory into the memory and then runs the computer program to realize the control method of the unmanned equipment described in the above figure 1. Of course, other implementations, such as logic devices or combinations of hardware and software, are not excluded from the present description, that is, the execution subject of the following processing flows is not limited to each logic unit, but may be hardware or logic devices.
In the 90 s of the 20 th century, improvements to one technology could clearly be distinguished as improvements in hardware (e.g., improvements to circuit structures such as diodes, transistors, switches, etc.) or software (improvements to the process flow). However, with the development of technology, many improvements of the current method flows can be regarded as direct improvements of hardware circuit structures. Designers almost always obtain corresponding hardware circuit structures by programming improved method flows into hardware circuits. Therefore, an improvement of a method flow cannot be said to be realized by a hardware entity module. For example, a programmable logic device (Programmable Logic Device, PLD) (e.g., field programmable gate array (Field Programmable Gate Array, FPGA)) is an integrated circuit whose logic function is determined by the programming of the device by a user. A designer programs to "integrate" a digital system onto a PLD without requiring the chip manufacturer to design and fabricate application-specific integrated circuit chips. Moreover, nowadays, instead of manually manufacturing integrated circuit chips, such programming is mostly implemented by using "logic compiler" software, which is similar to the software compiler used in program development and writing, and the original code before the compiling is also written in a specific programming language, which is called hardware description language (Hardware Description Language, HDL), but not just one of the hdds, but a plurality of kinds, such as ABEL (Advanced Boolean Expression Language), AHDL (Altera Hardware Description Language), confluence, CUPL (Cornell University Programming Language), HDCal, JHDL (Java Hardware Description Language), lava, lola, myHDL, PALASM, RHDL (Ruby Hardware Description Language), etc., VHDL (Very-High-Speed Integrated Circuit Hardware Description Language) and Verilog are currently most commonly used. It will also be apparent to those skilled in the art that a hardware circuit implementing the logic method flow can be readily obtained by merely slightly programming the method flow into an integrated circuit using several of the hardware description languages described above.
The controller may be implemented in any suitable manner, for example, the controller may take the form of, for example, a microprocessor or processor and a computer readable medium storing computer readable program code (e.g., software or firmware) executable by the (micro) processor, logic gates, switches, application specific integrated circuits (Application Specific Integrated Circuit, ASIC), programmable logic controllers, and embedded microcontrollers, examples of which include, but are not limited to, the following microcontrollers: ARC 625D, atmel AT91SAM, microchip PIC18F26K20, and Silicone Labs C8051F320, the memory controller may also be implemented as part of the control logic of the memory. Those skilled in the art will also appreciate that, in addition to implementing the controller in a pure computer readable program code, it is well possible to implement the same functionality by logically programming the method steps such that the controller is in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers, etc. Such a controller may thus be regarded as a kind of hardware component, and means for performing various functions included therein may also be regarded as structures within the hardware component. Or even means for achieving the various functions may be regarded as either software modules implementing the methods or structures within hardware components.
The system, apparatus, module or unit set forth in the above embodiments may be implemented in particular by a computer chip or entity, or by a product having a certain function. One typical implementation is a computer. In particular, the computer may be, for example, a personal computer, a laptop computer, a cellular telephone, a camera phone, a smart phone, a personal digital assistant, a media player, a navigation device, an email device, a game console, a tablet computer, a wearable device, or a combination of any of these devices.
For convenience of description, the above devices are described as being functionally divided into various units, respectively. Of course, the functions of each element may be implemented in one or more software and/or hardware elements when implemented in the present specification.
It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
In one typical configuration, a computing device includes one or more processors (CPUs), input/output interfaces, network interfaces, and memory.
The memory may include volatile memory in a computer-readable medium, random Access Memory (RAM) and/or nonvolatile memory, such as Read Only Memory (ROM) or flash memory (flash RAM). Memory is an example of computer-readable media.
Computer readable media, including both non-transitory and non-transitory, removable and non-removable media, may implement information storage by any method or technology. The information may be computer readable instructions, data structures, modules of a program, or other data. Examples of storage media for a computer include, but are not limited to, phase change memory (PRAM), static Random Access Memory (SRAM), dynamic Random Access Memory (DRAM), other types of Random Access Memory (RAM), read Only Memory (ROM), electrically Erasable Programmable Read Only Memory (EEPROM), flash memory or other memory technology, compact disc read only memory (CD-ROM), digital Versatile Discs (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices, or any other non-transmission medium, which can be used to store information that can be accessed by a computing device. Computer-readable media, as defined herein, does not include transitory computer-readable media (transmission media), such as modulated data signals and carrier waves.
It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article or apparatus that comprises the element.
It will be appreciated by those skilled in the art that embodiments of the present description may be provided as a method, system, or computer program product. Accordingly, the present specification may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present description can take the form of a computer program product on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) having computer-usable program code embodied therein.
The description may be described in the general context of computer-executable instructions, such as program modules, being executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types. The specification may also be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules may be located in both local and remote computer storage media including memory storage devices.
In this specification, each embodiment is described in a progressive manner, and identical and similar parts of each embodiment are all referred to each other, and each embodiment mainly describes differences from other embodiments. In particular, for system embodiments, since they are substantially similar to method embodiments, the description is relatively simple, as relevant to see a section of the description of method embodiments.
The foregoing is merely exemplary of the present disclosure and is not intended to limit the disclosure. Various modifications and alterations to this specification will become apparent to those skilled in the art. Any modifications, equivalent substitutions, improvements, or the like, which are within the spirit and principles of the present description, are intended to be included within the scope of the claims of the present description.
Claims (11)
1. A control method of an unmanned apparatus, comprising:
determining a base occupancy zone of an obstacle surrounding an unmanned device, the base occupancy zone comprising at least one of a zone occupied by the obstacle at a current location and a zone occupied by a predicted location of the obstacle as viewed;
aiming at each basic boundary contained in the basic occupation area, determining an expansion boundary corresponding to the basic boundary by taking the probability that the distance from the area center of the basic occupation area to the straight line where the basic boundary is positioned is not less than the probability that the probability of the distance between the projection point corresponding to the expansion boundary of the basic boundary on the normal line where the basic boundary is positioned and the area center is not less than the set probability as a constraint condition;
According to the expansion boundary corresponding to each basic boundary contained in the basic occupation area, adjusting the basic occupation area to obtain an adjusted occupation area corresponding to the obstacle;
and controlling the unmanned equipment according to the adjusted occupied area.
2. The method of claim 1, wherein the constraint is used to represent a constraint that is outside a base boundary of the obstacle for any safe location in a random coordinate system, the extended boundary being used to represent a boundary of the safe location, the random coordinate system being a coordinate system having a center of an actual location of the obstacle as an origin.
3. The method of claim 1, wherein the constraint condition includes an uncertainty factor, the uncertainty factor being used to convert the constraint condition into a deterministic constraint to obtain the expansion boundary, the uncertainty factor including a deviation between an actual position of an obstacle and a center of the area and a difference between an actual orientation of an obstacle corresponding to a basic occupied area and an actual orientation of the obstacle, the obstacle orientation corresponding to the basic occupied area being an observed or predicted obstacle orientation.
4. The method of claim 3, wherein the uncertainty factor corresponds to a desired matrix and a covariance matrix, the desired matrix and the covariance matrix to be used to convert the constraint condition to a deterministic constraint to obtain the expanded boundary.
5. The method of claim 1, wherein prior to obstacle avoidance of the obstacle based on the adjusted occupancy zone, the method further comprises:
determining each vertex of the adjusted occupied zone;
determining, for each vertex, a connection line from the center of the adjusted occupied area to the vertex;
if the included angle between the two expansion boundaries corresponding to the vertex and the connecting line does not exceed the set angle, determining a truncated edge aiming at the vertex between the two expansion boundaries corresponding to the vertex;
intercepting the adjusted occupied area according to the intercepting edge of at least one vertex to obtain an intercepted occupied area containing the center of the adjusted occupied area;
according to the adjusted occupied area, obstacle avoidance is carried out on the obstacle, and the method specifically comprises the following steps:
and according to the occupied area after interception, obstacle avoidance is carried out on the obstacle.
6. The method of claim 5, wherein determining a truncated edge for the vertex between two expansion boundaries corresponding to the vertex, specifically comprises:
determining a vertex corresponding to the vertex in the basic occupation area as a target vertex;
determining a vertical line passing through the target vertex and perpendicular to a line connecting the center of the region and the target vertex;
and determining a truncated edge for the vertex between two expansion boundaries corresponding to the vertex according to the perpendicular line.
7. The method of claim 1, wherein the base footprint comprises at least one obstacle footprint predicted for the obstacle;
the method for determining the extended boundary corresponding to the basic boundary by taking the constraint condition that the probability of the distance between the extended boundary smaller than the basic boundary and the region center is not smaller than the set probability, wherein the distance from the region center of the basic occupied region to the straight line where the basic boundary is located is smaller than the projection point corresponding to the extended boundary of the basic boundary on the normal line where the basic boundary is located, specifically comprises the following steps:
determining a corresponding certainty probability of each obstacle occupation area predicted for the obstacle;
Determining a component probability corresponding to each obstacle occupation area according to the certainty probability corresponding to each obstacle occupation area and the set probability;
based on the component probability corresponding to the obstacle occupying area, determining the expansion boundary corresponding to the basic boundary by taking the constraint condition that the probability of the distance between the projection point corresponding to the expansion boundary smaller than the basic boundary on the normal line of the basic boundary and the component probability corresponding to the area occupied area is not smaller than the component probability corresponding to the obstacle occupying area.
8. The method of claim 7, wherein for each obstacle occupation area, determining the component probability corresponding to the obstacle occupation area according to the deterministic probability corresponding to the obstacle occupation area and the set probability, specifically comprises:
taking the deterministic probability corresponding to the obstacle occupation area as the weight corresponding to the obstacle occupation area, weighting the component probability corresponding to the obstacle occupation area to be solved, and obtaining the weighted component probability corresponding to the obstacle occupation area to be solved;
And solving the component probability corresponding to each obstacle occupation area by taking the sum value of the weighted component probabilities to be solved corresponding to each obstacle occupation area as a constraint condition.
9. A control device for an unmanned apparatus, comprising:
a region determination module for determining a base occupation region of an obstacle surrounding an unmanned device, the base occupation region including at least one of a region occupied by the obstacle at a current location and a region occupied by a predicted location of the obstacle;
the boundary determining module is used for determining an extended boundary corresponding to the basic boundary by taking a constraint condition that the probability of the distance between each basic boundary contained in the basic occupation area and the region center is not less than the set probability by taking the distance from the region center of the basic occupation area to the straight line where the basic boundary is located as a projection point corresponding to the extended boundary smaller than the basic boundary on the normal line where the basic boundary is located;
the adjustment module is used for adjusting the basic occupation area according to the expansion boundary corresponding to each basic boundary contained in the basic occupation area to obtain an adjusted occupation area corresponding to the obstacle;
And the control module is used for controlling the unmanned equipment according to the adjusted occupied area.
10. A computer readable storage medium, characterized in that the storage medium stores a computer program which, when executed by a processor, implements the method of any of the preceding claims 1-8.
11. An unmanned device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the method of any of the preceding claims 1-8 when executing the program.
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| CN112230634A (en) * | 2019-06-26 | 2021-01-15 | 北京海益同展信息科技有限公司 | Robot obstacle avoidance method and device |
| CN110887484A (en) * | 2019-10-14 | 2020-03-17 | 重庆邮电大学 | Mobile robot path planning method based on improved genetic algorithm and storage medium |
| CN111026131A (en) * | 2019-12-30 | 2020-04-17 | 深圳前海达闼云端智能科技有限公司 | Method and device for determining expansion area, robot and storage medium |
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| CN112950707A (en) * | 2020-12-29 | 2021-06-11 | 广州极飞科技股份有限公司 | Method for determining obstacle region |
| CN112987762A (en) * | 2021-05-10 | 2021-06-18 | 北京三快在线科技有限公司 | Trajectory planning method and device, storage medium and electronic equipment |
| CN112987760A (en) * | 2021-05-10 | 2021-06-18 | 北京三快在线科技有限公司 | Trajectory planning method and device, storage medium and electronic equipment |
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