CN115933701B - Safety corridor optimization generation method and system based on quadratic programming - Google Patents
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Abstract
The invention relates to a safety corridor optimization generation method and system based on quadratic programming, which relate to the unmanned field and comprise the following steps: the method comprises the steps that a rough track of the center of an unmanned vehicle and polygonal information of the unmanned vehicle are utilized to represent a discretized unmanned vehicle movement track; constructing a safe corridor model to be solved and determining an objective function; representing a discretized obstacle movement track by using the obstacle geometric center movement track and the obstacle convex polygon information; determining a vertex vector of the obstacle nearest to the unmanned vehicle and a vertex vector of the unmanned vehicle nearest to the obstacle according to the movement tracks of the unmanned vehicle and the obstacle; establishing obstacle avoidance constraint conditions based on a safety corridor model to be solved; and establishing a quadratic programming model according to the obstacle avoidance constraint conditions and the objective function, and solving to obtain the optimized safety corridor. The invention describes the safety corridor constraint problem as a quadratic programming problem, considers the appearance of the unmanned vehicle and the appearance of the obstacle when generating obstacle avoidance constraint, and improves the efficiency and accuracy of safety corridor generation.
Description
Technical Field
The invention relates to the technical field of path planning of unmanned vehicles, in particular to a safety corridor optimization generation method and system based on quadratic programming.
Background
Unmanned vehicles (simply unmanned vehicles) have become a research hotspot in recent years. The local path planning of the unmanned vehicle is taken as one of the key technologies, and the performance of the unmanned vehicle directly determines whether the unmanned vehicle runs successfully or not.
The unmanned vehicle running track needs to meet three requirements of smoothness, optimality and real-time performance. Therefore, in recent years, many students perform unmanned vehicle track planning by using an optimization-based method, however, the track planning problem with non-convex obstacle avoidance constraint is often described as a non-convex optimization problem, so that the problem is difficult to solve. The non-convex optimization problem can be effectively converted into a convex optimization problem by utilizing the safety corridor. The generation efficiency of the safety corridor becomes an important factor affecting the real-time performance of the track optimization.
In conventional security corridor generation methods, security corridor generation is often described as an integer programming problem. The more obstacles, the lower the safety corridor generation efficiency. In addition, the method directly processes the shape constraint of the unmanned vehicle into the constraint in the planning problem, and the problem solving difficulty is improved in intangible way.
Disclosure of Invention
The invention aims to provide a safety corridor optimization generation method and system based on quadratic programming, which greatly improve the efficiency and accuracy of safety corridor generation.
In order to achieve the above object, the present invention provides the following solutions:
the invention provides a safety corridor optimization generation method based on quadratic programming, which comprises the following steps:
acquiring a rough track to be optimized in a planning time domain of the unmanned aerial vehicle, performing discretization, and representing a discretized unmanned aerial vehicle movement track by utilizing the discretized unmanned aerial vehicle rough track and polygonal information of the unmanned aerial vehicle; the polygon information of the unmanned vehicle comprises a plurality of unmanned vehicle roof point vectors; the unmanned vehicle roof point vector is a vector from the center of the unmanned vehicle to each vertex of the polygonal unmanned vehicle;
constructing a safety corridor model to be solved based on all discretized unmanned vehicle rough track points in a planning time domain, and determining an objective function generated by the safety corridor;
acquiring an obstacle movement track in an unmanned vehicle running environment in a planning time domain, and representing a discretized obstacle movement track by utilizing the geometrical center movement track of each obstacle and the convex polygon information of the obstacle; the obstacle convex polygon information includes a plurality of obstacle vertex vectors; the obstacle vertex vector is a vector from the geometric center of the obstacle to each vertex of the convex obstacle;
determining an obstacle vertex vector, in the obstacle vertex vector, of which the obstacle is nearest to the unmanned vehicle and an unmanned vehicle roof point vector, in the unmanned vehicle roof point vectors according to the discretized unmanned vehicle movement track and the discretized obstacle movement track;
establishing obstacle avoidance constraint conditions based on the safety corridor model to be solved, an obstacle vertex vector of the obstacle nearest to the unmanned vehicle and an unmanned vehicle roof point vector of the unmanned vehicle nearest to the obstacle;
establishing a quadratic programming model generated by a safety corridor according to the obstacle avoidance constraint conditions and the objective function;
and solving the quadratic programming model and bringing the solution value into the safety corridor model to be solved to obtain an optimized safety corridor.
Optionally, the acquiring the rough track to be optimized in the unmanned vehicle planning time domain and performing discretization processing, and using the discretized rough track of the unmanned vehicle and polygon information of the unmanned vehicle to represent the discretized movement track of the unmanned vehicle specifically includes:
dividing the rough track to be optimized in the planning time domain intonA step of phase separation; each stage is a unit time period;
discretizing the rough track to be optimized in each unit time period;
calculating a rough course angle of each unit time period according to the discretized rough track of the unmanned vehicle of each adjacent two unit time periods;
calculating each unmanned vehicle roof point vector according to the rough course angle and the unmanned vehicle length and width information;
and representing the discretized unmanned vehicle movement track by using the discretized unmanned vehicle rough track and each unmanned vehicle vertex vector.
Optionally, the discretized unmanned vehicle motion track is expressed as:
wherein ,kis a time stage sequence number;
respectively represent the firstkThe abscissa and the ordinate of the rough track of the unmanned vehicle in a unit time period; />
Representing a discretized coarse track; />
Is the firstkRough heading angle per unit time period;L car ，W car respectively representing the length and width information of the unmanned vehicle; />
Representing polygon information of the unmanned vehicle;
respectively represent the firstkVector from the center of the unmanned vehicle to each vertex of the polygonal unmanned vehicle in unit time period; />
Representing a collection of drone vertex vectors. />
Optionally, the expression of the safety corridor model to be solved is:
wherein ,H k representing the safety corridorkCorridor steps per unit time period; the corridor step iskThe drivable range of the unmanned vehicle in a unit time period;x l,k is an unmanned vehiclekThe distance from the rough track point in the corridor step to the left boundary of the corridor step in the unit time period;x u,k is an unmanned vehiclekThe distance from the rough track point in the corridor step to the right boundary of the corridor step in the unit time period;y l,k is an unmanned vehiclekThe distance from the rough track point in the corridor step to the lower boundary of the corridor step in the unit time period;y u,k is an unmanned vehiclekThe distance of the rough track point in the corridor step to the upper boundary of the corridor step per unit time period.
Optionally, the determining, according to the discretized motion track of the unmanned vehicle and the discretized motion track of the obstacle, an obstacle vertex vector of the obstacle vertex vector, where the obstacle is closest to the unmanned vehicle, and an unmanned vehicle roof point vector of the unmanned vehicle, where the unmanned vehicle is closest to the obstacle, specifically includes:
in the first placekIn the unit time period, taking a connecting line from a rough track point in the center of the unmanned vehicle to a geometric center motion track point of the obstacle as a projection reference vector;
projecting each obstacle vertex vector in the obstacle polygon information to the projection reference vector to obtain each first projection value;
comparing the magnitudes of the first projection values to obtain an obstacle vertex vector with the minimum first projection value, namely an obstacle vertex vector, of which the obstacle is nearest to the unmanned vehicle, in the obstacle vertex vector;
and determining an unmanned vehicle roof point vector closest to the obstacle based on the discretized unmanned vehicle motion trail and the discretized obstacle motion trail and an obstacle vertex vector closest to the unmanned vehicle by the obstacle.
Optionally, the determining, based on the discretized unmanned vehicle motion trajectory, the discretized obstacle motion trajectory, and an obstacle vertex vector of the obstacle nearest to the unmanned vehicle, an unmanned vehicle roof point vector of the unmanned vehicle nearest to the obstacle specifically includes:
subtracting the vertex vectors of the unmanned vehicles from the vertex vectors of the first type to obtain vertex vectors of a second type; the first type vertex vector is the nearest obstacle vertex vector of the obstacle to the unmanned vehicle;
projecting each second type of vertex vector onto the reference vector to obtain each second projection value;
comparing the magnitude of each second projection value to obtain a second type vertex vector with the minimum second projection value; and the second type of vertex vector with the smallest second projection value is the nearest unmanned roof point vector of the unmanned vehicle from the obstacle.
Optionally, the expression of the obstacle avoidance constraint condition is:
wherein ,A c is a reference vector;
representing an obstacleiAt the position ofkA motion trajectory per unit time period; />
Represent the firstkObstacle per unit time periodiThe obstacle vertex vector nearest to the drone; />
Represent the firstkUnmanned vehicle obstacle in unit time periodiNearest unmanned vehicle vertexVector.
Optionally, the objective function expression is:
wherein ,J area is the range breadth of the safety corridor;J ref the deviation degree is the deviation degree of the safety corridor;
and />
The range breadth weight and the bias weight are represented respectively.
The invention also provides a safety corridor optimization generation system based on quadratic programming, which comprises the following steps:
the unmanned vehicle movement track acquisition module is used for acquiring a rough track to be optimized in the unmanned vehicle planning time domain and performing discretization treatment, and the discretized unmanned vehicle movement track is represented by utilizing the discretized unmanned vehicle rough track and polygonal information of the unmanned vehicle; the polygon information of the unmanned vehicle comprises a plurality of unmanned vehicle roof point vectors; the unmanned vehicle roof point vector is a vector from the center of the unmanned vehicle to each vertex of the polygonal unmanned vehicle;
the safety corridor model building module is used for building a safety corridor model to be solved based on all discretized unmanned vehicle rough track points in a planning time domain and determining an objective function generated by the safety corridor;
the obstacle movement track acquisition module is used for acquiring an obstacle movement track in the unmanned vehicle running environment in the planning time domain, and representing a discretized obstacle movement track by utilizing the geometric center movement track of each obstacle and the convex polygon information of the obstacle; the obstacle convex polygon information includes a plurality of obstacle vertex vectors; the obstacle vertex vector is a vector from the geometric center of the obstacle to each vertex of the convex obstacle;
the target vertex vector determining module is used for determining an obstacle vertex vector, which is closest to the unmanned vehicle, in the obstacle vertex vectors and an unmanned vehicle roof point vector, which is closest to the obstacle, in the unmanned vehicle roof point vectors according to the discretized unmanned vehicle motion track and the discretized obstacle motion track;
the obstacle avoidance constraint condition construction module is used for establishing an obstacle avoidance constraint condition based on the safety corridor model to be solved, an obstacle vertex vector of the obstacle nearest to the unmanned vehicle and an unmanned vehicle roof point vector of the unmanned vehicle nearest to the obstacle;
the secondary planning model construction module is used for constructing a secondary planning model generated by the safety corridor according to the obstacle avoidance constraint conditions and the objective function;
and the safety corridor optimization module is used for solving the quadratic programming model and bringing the solved value into the safety corridor model to be solved to obtain an optimized safety corridor.
Optionally, the expression of the obstacle avoidance constraint condition is:
wherein ,
respectively represent the firstkThe abscissa and the ordinate of the rough track point of the unmanned vehicle in a unit time period;x l,k is an unmanned vehiclekThe distance from the rough track point in the corridor step to the left boundary of the corridor step in the unit time period;x u,k is an unmanned vehiclekThe distance from the rough track point in the corridor step to the right boundary of the corridor step in the unit time period;y l,k is an unmanned vehiclekThe distance from the rough track point in the corridor step to the lower boundary of the corridor step in the unit time period;y u,k is an unmanned vehiclekThe distance from the rough track point in the corridor step to the upper boundary of the corridor step in the unit time period; />
Representing a discretized coarse track; />
To represent an obstacleiIn the first placekA motion trajectory per unit time period; />
Represent the firstkObstacle per unit time periodiThe obstacle vertex vector nearest to the drone; />
Represent the firstkUnmanned vehicle obstacle in unit time periodiThe nearest unmanned roof point vector.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention provides a safety corridor optimization generation method and system based on quadratic programming, comprising the following steps: representing a discretized unmanned vehicle movement track by utilizing a rough track of the center of the discretized unmanned vehicle and polygonal information of the unmanned vehicle; constructing a safety corridor model to be solved based on rough track points of all discretized unmanned vehicle centers, and determining an objective function generated by the safety corridor; representing a discretized obstacle movement track by utilizing the geometric center movement track of each obstacle and the convex polygon information of the obstacle; the barrier convex polygon information comprises vectors from the geometric center of the barrier to the vertexes of each convex edge of the barrier; determining a convex polygon vertex vector of the obstacle nearest to the unmanned vehicle and a polygon vertex vector of the unmanned vehicle nearest to the obstacle according to the discretized unmanned vehicle movement track and the discretized obstacle movement track; establishing obstacle avoidance constraint conditions based on a to-be-solved safety corridor model, wherein the convex polygon vertex vector of the obstacle closest to the unmanned vehicle and the polygon vertex vector of the unmanned vehicle closest to the obstacle; and establishing a quadratic programming model generated by the safety corridor according to the obstacle avoidance constraint conditions and the objective function, and solving to obtain the optimized safety corridor. The invention describes the safety corridor constraint problem as a quadratic programming problem, removes the constraint related to the appearance of the unmanned vehicle in the quadratic programming problem, considers the appearance of the unmanned vehicle and the appearance of the obstacle when generating the obstacle avoidance constraint, further improves the solving efficiency of the quadratic programming problem, and greatly improves the generating efficiency and accuracy of the safety corridor.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a flowchart of a safety corridor optimization generation method based on quadratic programming provided in embodiment 1 of the present invention;
fig. 2 is a schematic diagram of construction of a safety corridor to be solved according to embodiment 1 of the present invention;
fig. 3 is a schematic projection diagram of each obstacle vertex vector to a reference vector according to embodiment 1 of the present invention;
FIG. 4 is a schematic view illustrating the projection of the second type of vertex vector onto the reference vector according to embodiment 1 of the present invention;
fig. 5 is a schematic diagram illustrating a situation that the safety corridor and the obstacle do not overlap and constraint in embodiment 1 of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention aims to provide a safety corridor optimization generation method and system based on quadratic programming, which describe the safety corridor constraint problem as a quadratic programming problem, remove the constraint related to the appearance of an unmanned vehicle in the quadratic programming problem, consider the appearance of the unmanned vehicle and the appearance of an obstacle when generating obstacle avoidance constraint, further improve the solving efficiency, greatly improve the efficiency and accuracy of the generation of the safety corridor and further improve the efficiency and accuracy of the path rule of an unmanned vehicle based on the safety corridor.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
Example 1
As shown in fig. 1, the embodiment provides a quadratic programming-based safety corridor optimization generation method, which includes:
s1: acquiring a rough track to be optimized in a planning time domain of the unmanned aerial vehicle, performing discretization, and representing a discretized unmanned aerial vehicle movement track by utilizing the discretized unmanned aerial vehicle rough track and polygonal information of the unmanned aerial vehicle; the polygon information of the unmanned vehicle comprises a plurality of unmanned vehicle roof point vectors; the unmanned vehicle roof point vector is a vector from the center of the unmanned vehicle to each vertex of the polygonal unmanned vehicle. The rough track of the unmanned vehicle refers to the rough track of the center of the unmanned vehicle. The polygonal unmanned aerial vehicle refers to an unmanned aerial vehicle with a polygonal shape.
Obtaining a rough track to be optimized, which only needs to meet two-point requirements: 1. continuity; 2. the vehicle is collision free at all points of the track. Dividing the rough track into two parts by taking time as a dividing basisnEach stage has a time interval (unit time period) oft in The definition is as follows:
in the formula (1): [t 0 ，t f ]The planning time domain in the whole planning problem is provided.t in Different sizes can be set according to the requirements of users, and the size of the unit time period is arbitrary according to the requirementsSetting. Coarse track discretization is expressed as:
in the formula (2):kas the sequence number of the time phase,k=1，2，3，...，n；
respectively represent the firstkAnd the abscissa and the ordinate of the rough track of the unmanned vehicle in a unit time period. The first step can be obtained by the method (2)kRough heading angle per unit time period +.>
：
wherein ,
respectively represent the firstkThe abscissa and ordinate of the rough trajectory for +1 unit time period; unmanned vehicle using polygon representation with four sides, is provided with +.>
，j=1, 2,3,4; known as (i)kCourse angle of course per unit time period
Can obtain the (th)kUnmanned vehicle polygon information per unit time:
wherein ：
respectively represent the firstkEach unmanned vehicle roof point vector (vector from the unmanned vehicle center to each vertex of the unmanned vehicle polygon) per unit time period; />
Representing a set of vertex vectors. />
In the formula (4):L car ，W car the length and width information of the unmanned vehicle are respectively represented and can be obtained from the parameters of the unmanned vehicle. Combining (2), (3) and (4) to obtain the firstkThe unmanned vehicle trajectory discretization per unit time period is expressed as:
specifically, step S1 includes:
s11: dividing the rough track to be optimized in the planning time domain intonAnd (3) a stage. Each stage is a unit time period.
S12: and discretizing the rough track to be optimized in each unit time period.
S13: and calculating the rough course angle of each unit time period according to the discretized rough track of each adjacent two unit time periods.
S14: and calculating the vertex vectors of the unmanned vehicles according to the course angle and the length and width information of the unmanned vehicles.
S15: and representing the discretized unmanned vehicle movement track by using the discretized unmanned vehicle rough track and each unmanned vehicle vertex vector.
S2: and constructing a safety corridor model to be solved based on all discretized unmanned vehicle rough track points in the planning time domain, and determining an objective function generated by the safety corridor.
Roughness in step S1The track points are key points, a safety corridor to be solved is constructed, as shown in fig. 2 (a), each step represents the vehicle running range in the current time stage, and in fig. 2 (a), the time O is shown in timetThe axis shows the change of the occupied time period of the corridor steps from bottom to top, and the change is sequentially as followst 0 、t 1 、...、t k 、t k+1 、t n A time period. According to the arrow direction in FIG. 2 (a)t k The time zone corridor is observed in magnification as shown in fig. 2 (b). The viewing angle of fig. 2 (b) is converted to fig. 2 (c). The solution variables relating to the formation of the corridor step for the corridor step center section shape are shown in fig. 2 (c). First, thekCritical point of corridor step of unit time period
Left boundary valuex l,k Right boundary valuex u,k Lower boundary valuey l,k Upper boundary valuey u,k Description is made. The boundary values are distances from the four direction boundaries to the key points, respectively, and all the distances are positive values, wherein the key points are represented by black solid dots in fig. 2 (c), and are not necessarily rectangular geometric center points.
In summary, with all rough track points as key points, a series of safety corridors to be solved are constructed as follows:
safety corridor generation mainly considers performance indexes in two aspects, namely safety corridor range breadthJ area And degree of deviation of geometric center of safety corridor from decision trajectoryJ ref The former satisfies the optimality requirement of the track in order to expand the solution space, and the latter solves the guiding acceleration problem by fully utilizing the rough track in the step S1.
The space-time safety corridor final objective function is expressed as:
safety corridor range breadthJ area The concrete steps are as follows:
deviation degree of safety corridorJ ref The concrete steps are as follows:
wherein ,
and />
The range breadth weight and the bias weight are represented respectively.J area As a linear function of the power supply,J ref is a quadratic convex function, and an objective function of linear combination of the quadratic convex function and the quadratic convex functionJ corridor Is a quadratic convex function.
S3: acquiring an obstacle movement track in an unmanned vehicle running environment in a planning time domain, and representing a discretized obstacle movement track by utilizing the geometrical center movement track of each obstacle and the convex polygon information of the obstacle; the obstacle convex polygon information includes a plurality of obstacle vertex vectors; the obstacle vertex vector is the vector from the geometric center of the obstacle to each vertex of the convex obstacle. The convex unmanned vehicle refers to an obstacle in a convex shape.
The method comprises the steps of obtaining a dynamic and static obstacle track sequence, obtaining a motion track of a dynamic and static obstacle (simply referred to as an obstacle) in the environment from a perception module of an unmanned vehicle, taking time as a division basis, and discretizing the motion track of the geometric center of the obstacle to be represented as:
in the formula (10):
respectively represent the firstkPer unit time period, obstacleiIs defined by the geometric center abscissa and ordinate of the lens. The shape of the obstacle is not negligible in describing the collision constraints, and the method uses convex polygons to describe the obstacle. Is provided with
，g=1，2，3，...，g max ，g max The number of the polygon vertices of the obstacle is represented, and the number of the vertices corresponding to different obstacles is different. For the firstkPer unit time period, obstacleiThe convex polygon is
In the formula (11), the amino acid sequence of the compound,i k is shown in the firstkIn the phase time, the total number of obstacles in the scene. The obstacle movement locus is expressed as discretized by combining the formula (10) and the formula (11):
s4: and determining an obstacle vertex vector, in the obstacle vertex vector, of which the obstacle is nearest to the unmanned vehicle and an unmanned vehicle roof point vector, in the unmanned vehicle roof point vectors, of which the unmanned vehicle is nearest to the obstacle according to the discretized unmanned vehicle movement track and the discretized obstacle movement track.
Solving the first step based on the unmanned vehicle information and the obstacle information in the steps S1 and S3kAt a unit time stage, an obstacleiThe nearest polygon vertex to the drone.
Solving the obstacle as shown in FIG. 3iWhen the polygon vertex closest to the unmanned vehicle is a projection reference vector, a line from the center of the unmanned vehicle to the geometric center of the obstacle is taken as a projection reference vectorA c Respectively, the steps S3
Vector representing polygon vertices of an obstacle is projected onto a reference vectorA c And obtaining the vertex vector with the minimum projection value by comparing the projection values, wherein the solving formula is as follows:
in the formula (13), the amino acid sequence of the compound,
the solution is schematically shown in FIG. 5, in FIG. 5 +.>
At the reference vectorA c The projection onto is minimal.
Specifically, step S4 includes:
s41: in the first placekAnd in the unit time period, taking a connecting line from a rough track point in the center of the unmanned vehicle to a geometric center motion track point of the obstacle as a projection reference vector.
S42: and projecting each obstacle vertex vector in the obstacle polygon information onto the projection reference vector to obtain each first projection value.
S43: and comparing the magnitudes of the first projection values to obtain an obstacle vertex vector with the minimum first projection value, namely an obstacle vertex vector of the obstacle vertex vector, wherein the obstacle is nearest to the unmanned vehicle.
The first projection values are calculated by a vector product method, each obstacle vertex vector is respectively subjected to dot multiplication with a projection reference vector to calculate each first projection value, and the obstacle vertex vector with the minimum first projection value is determined by comparing the sizes of the first projection values.
S44: and determining an unmanned vehicle roof point vector closest to the obstacle based on the discretized unmanned vehicle motion trail and the discretized obstacle motion trail and an obstacle vertex vector closest to the unmanned vehicle by the obstacle.
Solving the first image on the basis of the unmanned vehicle information in step S1, the obstacle information in step S3, and the optimal vertex (the obstacle vertex vector having the smallest first projection value) in step S43kStage time (unit time period), unmanned vehicle is away from obstacleiThe nearest polygon vertex.
Solving obstacle of unmanned vehicleiWhen the nearest polygon is at the vertex, the line from the center of the vehicle of the unmanned vehicle to the geometric center of the obstacle is taken as a projection reference vectorA c The results of step S1 and step S43 are respectively obtained
Vector representing polygon vertices of the drone is projected onto a reference vectorA c And obtaining the vertex vector with the minimum projection value by comparing the projection values, wherein the solving formula is as follows:
in the formula (14), the amino acid sequence of the compound,
，/>
obtained by solving in step S43. The solution is schematically shown in FIG. 4, in FIG. 4
In projecting reference vectorsA c The projection onto is minimal.
Specifically, step S44 includes:
s441: subtracting the vertex vectors of the unmanned vehicles from the vertex vectors of the first type to obtain vertex vectors of a second type; the first type of vertex vector is an obstacle vertex vector of the obstacle nearest to the drone.
S442: and respectively projecting each second type of vertex vector onto the reference vector to obtain each second projection value.
S443: comparing the sizes of the second projection values easily obtains a second type vertex vector with the smallest second projection value, wherein the second type vertex vector with the smallest second projection value is an unmanned roof point vector of the unmanned vehicle closest to the obstacle.
Using the obstacle vertices where the obstacle is closest to the vehicle
Subtracting the unmanned vehicle roof point vector is equivalent to translating the unmanned vehicle roof point vector to the upper surface of the barrier vertex, carrying out projection comparison, and finally finding out two nearest vertexes of the unmanned vehicle and the barrier.
In the steps S3 and S4, the shapes of the unmanned vehicles and the shapes of the obstacles are considered, the shapes of the obstacles are uniformly described by using convex polygons, the number of polygonal sides is not limited, and different types of obstacles can be more accurately described.
S5: and establishing obstacle avoidance constraint conditions based on the safety corridor model to be solved, an obstacle vertex vector of the obstacle nearest to the unmanned vehicle and an unmanned vehicle roof point vector of the unmanned vehicle nearest to the obstacle.
Step S2, obtaining that distances from four direction boundaries of the safety corridor to be solved to key points are respectively left boundary valuesx l,k Right boundary valuex u,k Lower boundary valuey l,k Upper boundary valuey u,k Four vertexes of the safety corridor can be obtained, and the vertex coordinates are expressed as follows:
ensuring safety corridor and obstacleThe unmanned vehicles in the safety corridor can be ensured not to collide with the obstacle without overlapping, thus giving out the firstkConstraint conditions that the phase time safety corridor and the obstacle do not overlap are as follows:
in the formula (16), the amino acid sequence of the compound,
the first step obtained in step S44kUnmanned vehicle obstacle in unit time periodiNearest unmanned roof point vector, +.>
The first step obtained in step S43kObstacle per unit time periodiThe obstacle vertex vector nearest to the drone. The effect of the above is as shown in FIG. 5, using the +.>
And step S43 to obtain->
And constructing a separation plane, wherein the separation plane is a dotted line in fig. 5, and according to the separation theorem, if all the vertexes of the safety corridor are on the left side of the separation plane, the constraint of the formula (16) is satisfied, so that the points inside the safety corridor can be ensured not to collide with the obstacle.
In step S5, the obtained obstacle avoidance constraint is a linear inequality constraint, and the inequality constraint related to the plurality of obstacles makes the solution space be a convex polygon, which is beneficial to model solution.
S6: and establishing a quadratic programming model generated by the safety corridor according to the obstacle avoidance constraint conditions and the objective function.
And (3) establishing a quadratic programming model generated by the safety corridor based on the obstacle avoidance constraint in the step S5 and the objective function of the step S2.
Order thek=1，2，3，...，nRepeating steps S4 andstep S5, obtaining the whole planning time domaint 0 ，t f ]An obstacle vertex vector in which an obstacle is closest to an unmanned vehicle and an unmanned roof point vector in which an unmanned vehicle is closest to an obstacle per unit time period. Order thek=1，2，3，...，nRepeating step S5 to obtain the whole planning time domaint 0 ，t f ]A safety corridor size constraint within. And (3) combining the objective function obtained in the step (S2) to establish a quadratic programming model generated by the safety corridor, wherein the quadratic programming model is shown in the following formula (17):
in formula (17): the objective function is a quadratic function, and the constraints are linear inequality constraints, so that the constructed optimization model is a quadratic programming model.
In step S6, the obtained optimization model is a quadratic programming model, and the quadratic programming optimization model is one of the models with the simplest form and the easiest solution in the optimization model. The advantage of the optimized generation of the safety corridor is that the area of the safety corridor is reasonably maximized, and the solution space of the trajectory planning based on the safety corridor is improved.
S7: and solving the quadratic programming model and bringing the solution value into the safety corridor model to be solved to obtain an optimized safety corridor.
Solving the quadratic programming model in the step S7 to obtain an optimal solution:
substituting the optimal solution into the step S2 to construct a safety corridor to be solved, so that the optimal safety corridor can be obtained:
the optimal safety corridor provides obstacle avoidance constraint for unmanned vehicle track planning, and the safety corridor can be utilized to effectively convert a non-convex track planning problem into a convex track planning problem. The safety corridor optimization generation model obtained based on the step S7 maximizes the area of the safety corridor, and can improve the solution space of the track planning based on the safety corridor during solving.
In this embodiment, (1) the obstacle geometry and the vehicle geometry are taken into account during the safety corridor generation. (2) In the generation process of the safety corridor, the obstacle avoidance constraint of the safety corridor is skillfully constructed by utilizing the separation plane theorem, and the constraint is a linear inequality constraint, so that the problem solving is facilitated. (3) When the obstacle avoidance constraint is formulated, the shape of the obstacle and the shape of the unmanned vehicle are considered, and the size constraint is not required to be added in the optimization problem of the formula (17), so that the complexity of the problem is reduced.
Example 2
The embodiment provides a safety corridor optimization generating system based on quadratic programming, which comprises the following components:
the unmanned vehicle movement track acquisition module M1 is used for acquiring a rough track to be optimized in the unmanned vehicle planning time domain and performing discretization treatment, and the discretization unmanned vehicle movement track is represented by utilizing the discretized unmanned vehicle rough track and polygonal information of the unmanned vehicle; the polygon information of the unmanned vehicle comprises a plurality of unmanned vehicle roof point vectors; the unmanned vehicle roof point vector is a vector from the center of the unmanned vehicle to each vertex of the polygonal unmanned vehicle.
The safety corridor model building module M2 is used for building a safety corridor model to be solved based on all discretized unmanned vehicle rough track points in a planning time domain and determining an objective function generated by the safety corridor.
The obstacle movement track acquisition module M3 is used for acquiring an obstacle movement track in an unmanned vehicle running environment in a planning time domain, and representing a discretized obstacle movement track by utilizing the geometric center movement track of each obstacle and the convex polygon information of the obstacle; the obstacle convex polygon information includes a plurality of obstacle vertex vectors; the obstacle vertex vector is the vector from the geometric center of the obstacle to each vertex of the convex obstacle.
The target vertex vector determining module M4 is configured to determine, according to the discretized unmanned vehicle motion trajectory and the discretized obstacle motion trajectory, an obstacle vertex vector closest to the unmanned vehicle among the obstacle vertex vectors and an unmanned vehicle roof point vector closest to the obstacle among the unmanned vehicle roof point vectors.
The obstacle avoidance constraint condition construction module M5 is used for establishing an obstacle avoidance constraint condition based on the safety corridor model to be solved, an obstacle vertex vector of the obstacle nearest to the unmanned vehicle and an unmanned vehicle roof point vector of the unmanned vehicle nearest to the obstacle.
The expression of the obstacle avoidance constraint condition is as follows:
wherein ,
respectively represent the firstkThe abscissa and the ordinate of the rough track point of the unmanned vehicle in a unit time period;x l,k is an unmanned vehiclekThe distance from the rough track point in the corridor step to the left boundary of the corridor step in the unit time period;x u,k is an unmanned vehiclekThe distance from the rough track point in the corridor step to the right boundary of the corridor step in the unit time period;y l,k is an unmanned vehiclekThe distance from the rough track point in the corridor step to the lower boundary of the corridor step in the unit time period;y u,k is an unmanned vehiclekThe distance from the rough track point in the corridor step to the upper boundary of the corridor step in the unit time period; />
Representing a discretized coarse track; />
To represent an obstacleiAt the position ofkOf unit time periodA motion trail; />
Represent the firstkObstacle per unit time periodiThe obstacle vertex vector nearest to the drone; />
Represent the firstkUnmanned vehicle obstacle in unit time periodiThe nearest unmanned roof point vector.
And the secondary planning model construction module M6 is used for building a secondary planning model generated by the safety corridor according to the obstacle avoidance constraint conditions and the objective function.
And the safety corridor optimization module M7 is used for solving the quadratic programming model and obtaining an optimized safety corridor from the safety corridor model to be solved by the solved value.
In this specification, each embodiment is mainly described in the specification as a difference from other embodiments, and the same similar parts between the embodiments are referred to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
The principles and embodiments of the present invention have been described herein with reference to specific examples, the description of which is intended only to assist in understanding the methods of the present invention and the core ideas thereof; also, it is within the scope of the present invention to be modified by those of ordinary skill in the art in light of the present teachings. In view of the foregoing, this description should not be construed as limiting the invention.
Claims (8)
1. The utility model provides a safe corridor optimization generating method based on quadratic programming, which is characterized by comprising the following steps:
acquiring a rough track to be optimized in a planning time domain of the unmanned aerial vehicle, performing discretization, and representing a discretized unmanned aerial vehicle movement track by utilizing the discretized unmanned aerial vehicle rough track and polygonal information of the unmanned aerial vehicle; the polygon information of the unmanned vehicle comprises a plurality of unmanned vehicle roof point vectors; the unmanned vehicle roof point vector is a vector from the center of the unmanned vehicle to each vertex of the polygonal unmanned vehicle;
constructing a safety corridor model to be solved based on all discretized unmanned vehicle rough track points in the planning time domain, and determining an objective function generated by the safety corridor;
acquiring an obstacle movement track in an unmanned vehicle running environment in the planning time domain, and representing a discretized obstacle movement track by utilizing the geometric center movement track of each obstacle and the convex polygon information of the obstacle; the obstacle convex polygon information includes a plurality of obstacle vertex vectors; the obstacle vertex vector is a vector from the geometric center of the obstacle to each vertex of the convex obstacle;
determining an obstacle vertex vector, in the obstacle vertex vector, of which the obstacle is nearest to the unmanned vehicle and an unmanned vehicle roof point vector, in the unmanned vehicle roof point vectors according to the discretized unmanned vehicle movement track and the discretized obstacle movement track;
establishing obstacle avoidance constraint conditions based on the safety corridor model to be solved, an obstacle vertex vector of the obstacle nearest to the unmanned vehicle and an unmanned vehicle roof point vector of the unmanned vehicle nearest to the obstacle;
establishing a quadratic programming model generated by a safety corridor according to the obstacle avoidance constraint conditions and the objective function;
solving the quadratic programming model and bringing the solution value into the safety corridor model to be solved to obtain an optimized safety corridor;
the determining, according to the discretized unmanned vehicle motion track and the discretized obstacle motion track, an obstacle vertex vector of the obstacle vertex vector, of which the obstacle is closest to the unmanned vehicle, and an unmanned vehicle roof point vector of the unmanned vehicle, of which the unmanned vehicle is closest to the obstacle, specifically includes:
in the first placekIn the unit time period, taking a connecting line from a rough track point in the center of the unmanned vehicle to a geometric center motion track point of the obstacle as a projection reference vector;
projecting each obstacle vertex vector in the obstacle polygon information to the projection reference vector to obtain each first projection value;
comparing the magnitudes of the first projection values to obtain an obstacle vertex vector with the minimum first projection value, namely an obstacle vertex vector, of which the obstacle is nearest to the unmanned vehicle, in the obstacle vertex vector;
determining an unmanned vehicle roof point vector closest to an obstacle based on the discretized unmanned vehicle motion trajectory and the discretized obstacle motion trajectory and an obstacle vertex vector closest to the unmanned vehicle by the obstacle;
the determining the unmanned vehicle roof point vector closest to the obstacle based on the discretized unmanned vehicle motion trail, the discretized obstacle motion trail and the obstacle vertex vector closest to the unmanned vehicle specifically comprises the following steps:
subtracting the vertex vectors of the unmanned vehicles from the vertex vectors of the first type to obtain vertex vectors of a second type; the first type vertex vector is the nearest obstacle vertex vector of the obstacle to the unmanned vehicle;
projecting each second type of vertex vector onto the reference vector to obtain each second projection value;
comparing the magnitude of each second projection value to obtain a second type vertex vector with the minimum second projection value; and the second type of vertex vector with the smallest second projection value is the nearest unmanned roof point vector of the unmanned vehicle from the obstacle.
2. The method according to claim 1, wherein the acquiring the rough trajectory to be optimized in the unmanned vehicle planning time domain and performing discretization processing, and using the discretized unmanned vehicle rough trajectory and polygon information of the unmanned vehicle to represent the discretized unmanned vehicle movement trajectory specifically includes:
dividing the rough track to be optimized in the planning time domain intonA step of phase separation; each stage is a unit time period;
discretizing the rough track to be optimized in each unit time period;
calculating a rough course angle of each unit time period according to the discretized rough track of the unmanned vehicle of each adjacent two unit time periods;
calculating each unmanned vehicle roof point vector according to the rough course angle and the unmanned vehicle length and width information;
and representing the discretized unmanned vehicle movement track by using the discretized unmanned vehicle rough track and each unmanned vehicle vertex vector.
3. The method of claim 2, wherein the discretized unmanned vehicle motion profile is represented as:
wherein ,kis a time stage sequence number;
respectively represent the firstkThe abscissa and the ordinate of the rough track of the unmanned vehicle in a unit time period; />
Representing a discretized coarse track; />
Is the firstkRough heading angle per unit time period;L car ，W car respectively representing the length and width information of the unmanned vehicle; />
Representing polygon information of the unmanned vehicle; />
Respectively represent the firstkVector from the center of the unmanned vehicle to each vertex of the polygonal unmanned vehicle in unit time period; />
Representing a collection of drone vertex vectors.
4. A method according to claim 3, characterized in that the expression of the safety corridor model to be solved is:
wherein ,H k representing the safety corridorkCorridor steps per unit time period; the corridor step iskThe drivable range of the unmanned vehicle in a unit time period;x l,k is an unmanned vehiclekThe distance from the rough track point in the corridor step to the left boundary of the corridor step in the unit time period;x u,k is an unmanned vehiclekThe distance from the rough track point in the corridor step to the right boundary of the corridor step in the unit time period;y l,k is an unmanned vehiclekThe distance from the rough track point in the corridor step to the lower boundary of the corridor step in the unit time period;y u,k is an unmanned vehiclekThe distance of the rough track point in the corridor step to the upper boundary of the corridor step per unit time period.
5. The method of claim 1, wherein the obstacle avoidance constraint is expressed as:
wherein ,A c is a reference vector;
representing an obstacleiIn the first placekA motion trajectory per unit time period; />
Represent the firstkObstacle per unit time periodiThe obstacle vertex vector nearest to the drone; />
Represent the firstkUnmanned vehicle obstacle in unit time periodiThe nearest unmanned roof point vector.
6. The method of claim 5, wherein the objective function expression is:
wherein ,
in the formula ,J area is the range breadth of the safety corridor;J ref the deviation degree is the deviation degree of the safety corridor;
and />
The range breadth weight and the bias weight are represented respectively.
7. A quadratic programming-based safety corridor optimization generation system implementing the method of any one of claims 1 to 6, comprising:
the unmanned vehicle movement track acquisition module is used for acquiring a rough track to be optimized in the unmanned vehicle planning time domain and performing discretization treatment, and the discretized unmanned vehicle movement track is represented by utilizing the discretized unmanned vehicle rough track and polygonal information of the unmanned vehicle; the polygon information of the unmanned vehicle comprises a plurality of unmanned vehicle roof point vectors; the unmanned vehicle roof point vector is a vector from the center of the unmanned vehicle to each vertex of the polygonal unmanned vehicle;
the safety corridor model building module is used for building a safety corridor model to be solved based on all discretized unmanned vehicle rough track points in the planning time domain and determining an objective function generated by the safety corridor;
the obstacle movement track acquisition module is used for acquiring an obstacle movement track in the unmanned vehicle running environment in the planning time domain, and representing a discretized obstacle movement track by utilizing the geometric center movement track of each obstacle and the convex polygon information of the obstacle; the obstacle convex polygon information includes a plurality of obstacle vertex vectors; the obstacle vertex vector is a vector from the geometric center of the obstacle to each vertex of the convex obstacle;
the target vertex vector determining module is used for determining an obstacle vertex vector, which is closest to the unmanned vehicle, in the obstacle vertex vectors and an unmanned vehicle roof point vector, which is closest to the obstacle, in the unmanned vehicle roof point vectors according to the discretized unmanned vehicle motion track and the discretized obstacle motion track;
the obstacle avoidance constraint condition construction module is used for establishing an obstacle avoidance constraint condition based on the safety corridor model to be solved, an obstacle vertex vector of the obstacle nearest to the unmanned vehicle and an unmanned vehicle roof point vector of the unmanned vehicle nearest to the obstacle;
the secondary planning model construction module is used for constructing a secondary planning model generated by the safety corridor according to the obstacle avoidance constraint conditions and the objective function;
and the safety corridor optimization module is used for solving the quadratic programming model and bringing the solved value into the safety corridor model to be solved to obtain an optimized safety corridor.
8. The system of claim 7, wherein the obstacle avoidance constraint is expressed as:
wherein ,
respectively represent the firstkThe abscissa and the ordinate of the rough track point of the unmanned vehicle in a unit time period;x l,k is an unmanned vehiclekThe distance from the rough track point in the corridor step to the left boundary of the corridor step in the unit time period;x u,k is an unmanned vehiclekThe distance from the rough track point in the corridor step to the right boundary of the corridor step in the unit time period;y l,k is an unmanned vehiclekThe distance from the rough track point in the corridor step to the lower boundary of the corridor step in the unit time period;y u,k is an unmanned vehiclekThe distance from the rough track point in the corridor step to the upper boundary of the corridor step in the unit time period; />
Representing a discretized coarse track; />
To represent an obstacleiIn the first placekA motion trajectory per unit time period; />
Represent the firstkObstacle per unit time periodiThe obstacle vertex vector nearest to the drone; />
Represent the firstkUnmanned vehicle obstacle in unit time periodiA nearest unmanned roof point vector;A c is a reference vector. />
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