A spatial assembly obstacle avoidance method combining natural forces and artificial potential fields
By combining natural forces and artificial potential fields, the problem of obstacle avoidance in the prior art is solved, and the robot successfully reaches the target position under the action of natural dynamics model.
Patent Information
- Application Number
- CN202211167262.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-09-23
- Publication Date
- 2025-04-29
- Estimated Expiration
- 2042-09-23
AI Technical Summary
In the case where the handling obstacles are large in size or complex in structure, it is difficult to effectively avoid obstacles, resulting in the robot being unable to successfully reach the target position.
Using a spatial combination obstacle avoidance method combining natural forces and artificial potential fields, a repulsive potential function and target position occlusion detection algorithm are constructed, and a motion control law is designed to achieve obstacle avoidance by obtaining the dynamic model of the robot and the basic geometric units of the obstacle.
When the obstacles are large in size or complex in structure, the robot can effectively get rid of obstacle constraints, successfully reach the target position, and have a small amount of control, which is suitable for actual three-dimensional environments.
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Figure CN115357030B_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the field of intelligent body obstacle avoidance motion control, and relates to a spatial assembly obstacle avoidance method combining natural forces and artificial potential fields. Background Art
[0002] In the motion control of real individuals or groups such as wheeled robots, drones, and spacecraft, in order to ensure the safety of individual operations, it is inevitable to consider the avoidance of obstacles in the environment. Among them, the artificial potential field method is widely used in the case of simple obstacle structure and distribution due to its simple construction and simple calculation. On the other hand, in order to successfully use the artificial potential field method for actual complex obstacle avoidance, people have given different solutions to its common local extreme value problem, which can be roughly divided into two types: local extreme value point elimination, such as harmonic function, navigation function, etc., and local extreme value point avoidance, such as adding random perturbations, constructing virtual obstacles, introducing artificial electromagnetic forces, etc. However, most of them have the disadvantages of complex control laws and limited obstacle structure requirements. Summary of the invention
[0003] The purpose of the present invention is to solve the problems in the prior art and to provide a spatial combination obstacle avoidance method combining natural forces and artificial potential fields, which can effectively get rid of obstacle constraints and successfully reach the target position when the obstacle is large in size or complex in structure.
[0004] In order to achieve the above object, the present invention adopts the following technical solutions:
[0005] A spatial assembly obstacle avoidance method combining natural forces and artificial potential fields comprises the following steps:
[0006] Obtain the robot's dynamic model, initial position, target position, structure of obstacle B and various parameter values, and decompose obstacle B into several basic geometric units B i The union of;
[0007] Basic geometric unit B based on obstacle B i , the classical artificial potential function form and point to basic geometric unit B i The distance between obstacle B and obstacle B is constructed, and the gradient of the repulsive potential function of obstacle B is calculated to obtain the obstacle repulsive potential field.
[0008] Design a target position occlusion detection algorithm for the robot based on the geometric structure of obstacle B and the current and target positions of the robot;
[0009] The motion control law is designed for the robot by combining the repulsive potential field of obstacle B and the target position occlusion detection algorithm.
[0010] Furthermore, the dynamic model of the robot is:
[0011]
[0012] Among them, ξ(t) is the robot position vector at time t, ζ(t) is the robot velocity vector at time t, f(ξ(t),ζ(t)) is the robot open-loop dynamics function, and U(t) is the robot control variable at time t.
[0013] Furthermore, the obstacle B is decomposed into n b The union of basic geometric units:
[0014]
[0015] Among them, each basic geometric unit B i All are convex geometric bodies, n b is the number of basic geometric units, i=1,2,...,n b , its jth face F i j It is expressed in the following general form, The basic geometric unit B i Number of faces:
[0016]
[0017] The first equation is F i j The surface equation where the kth inequality is F i j The constraints generated by the kth edge of For face F i j The number of edges.
[0018] Furthermore, the repulsive potential function of the obstacle B can be expressed as follows:
[0019]
[0020] Among them, V i is the basic geometric unit B of the obstacle i The repulsive potential function, n b is the number of basic geometric units, i=1,2,...,n b .
[0021] Furthermore, the obstacle basic geometric unit B i The repulsive potential function is:
[0022]
[0023] Among them, d i (x,y,z) is the distance from point P(x,y,z) to the basic geometric unit B i The distance, D o For the collision avoidance detection distance threshold, at a known point P (x, y, z) in the basic geometric unit B i The nearest neighbor point P on Nearesti Coordinate (x i ,y i ,z i ) is calculated according to the following formula:
[0024]
[0025] Furthermore, the obstacle repelling potential field is:
[0026]
[0027] Among them, F i (x, y, z) is the basic geometric unit B of the obstacle i The repulsive potential field, n b is the number of basic geometric units, i=1,2,...,n b .
[0028] Furthermore, the F i (x, y, z) is given by the corresponding potential function V i The negative gradient of the coordinates of point P is obtained in the form of:
[0029]
[0030] Among them, d i (x,y,z) is the distance from point P(x,y,z) to the basic geometric unit B i distance, α is the obstacle repulsion coefficient, D o For the collision avoidance detection distance threshold, point P to the basic geometric unit B i The distance d i The gradient at point P is:
[0031]
[0032] The known point P is in the basic geometric unit B i The nearest neighbor point P on Nearesti Coordinate (x i ,y i ,z i )hour, Calculated as follows:
[0033]
[0034] Furthermore, the target position occlusion detection algorithm is:
[0035]
[0036] Among them, δ i (x, y, z) is the basic geometric unit B of the obstacle i Occlusion detection function for the target position, n b is the number of basic geometric units, i=1,2,...,n b .
[0037] Furthermore, the δ i (x,y,z) can be expressed as:
[0038]
[0039] in, is the basic geometric unit B of the obstacle i The jth face F i j Occlusion detection function for the target position, The basic geometric unit B i The number of faces, The target position is F i j Take when blocked Otherwise take
[0040] Furthermore, the motion control law is:
[0041] U(t)=δ(ξ(t))(-f(ξ(t),ζ(t))-k p (ξ(t)-ξ r )-k v ζ(t))+U o (t)
[0042] Among them, k p is the position feedback coefficient, k v is the speed feedback coefficient, ξ r is the desired position of the robot, δ(ξ(t)) is the target position occlusion determination function, U o (t) = F(ξ(t)) is the value of the obstacle repulsion potential field at the current position ξ(t) of the robot, that is, x, y, and z are replaced by the three components of ξ(t) respectively.
[0043] Compared with the prior art, the present invention has the following beneficial effects:
[0044] The present invention provides a spatial assembly obstacle avoidance method combining natural forces and artificial potential fields. Based on the specific structural characteristics of the obstacles and the basic geometric unit composition of the spatial assembly obstacles, an obstacle occlusion detection algorithm for the robot's target position is designed, and then a switching control law related to the target position occlusion is constructed, so that when the obstacle size is large or the structure is complex, the robot can still effectively get rid of the obstacle constraint under the action of an almost natural dynamic model (only obstacle avoidance control) and successfully reach the target position. The present invention makes full use of the natural dynamic model to design the obstacle avoidance control law. When the target position is visible to the robot, the robot approaches its target position under the ordinary artificial potential field control law; when the robot's target position is blocked by an obstacle, only the obstacle avoidance term in the robot control law is retained. Since the local extreme value area is distributed in the obstacle occlusion area, the robot can jump out of the local extreme value point with a smaller control amount under the action of the nearly natural dynamic model in the obstacle occlusion area. At the same time, by selecting a suitable coefficient, the control amount amplitude when the target position is not blocked can still be small. This method is applicable to actual three-dimensional environments such as near-Earth space orbits, and can achieve effective avoidance motion for obstacles with larger sizes or more complex structures with a smaller control amount. BRIEF DESCRIPTION OF THE DRAWINGS
[0045] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.
[0046] Figure 1 It is a flowchart of the execution of the obstacle avoidance method of the space combination body combining natural force and artificial potential field of the present invention;
[0047] Figure 2 The geometric structure diagram of the combined obstacle constructed in Example 1 of the present invention;
[0048] Figure 3 A basic geometric unit diagram of the combined obstacle constructed in Example 1 of the present invention;
[0049] Figure 4 The cloud diagram of the potential function distribution of the combined obstacle constructed in Example 1 of the present invention;
[0050] Figure 5 This is a schematic diagram of the meanings of the control law before and after the target position is blocked in Example 1 of the present invention;
[0051] Figure 6The spacecraft obstacle avoidance motion trajectory diagram in Embodiment 1 of the present invention;
[0052] Figure 7 is a graph showing the change of the spacecraft control quantity over time in Example 1 of the present invention;
[0053] Figure 8 is a graph showing the change of the spacecraft position error component over time in Embodiment 1 of the present invention;
[0054] Fig. 9 is a graph showing the change of the minimum distance between the spacecraft and the obstacle surface over time in Example 1 of the present invention;
[0055] Fig.10 The spacecraft motion trajectory diagram of the present invention when the target position obstruction is not considered;
[0056] Fig.11 This is a graph showing how the spacecraft position error modulus changes over time when the target position obstruction is not considered according to the present invention. DETAILED DESCRIPTION
[0057] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.
[0058] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0059] The present invention is further described in detail below in conjunction with the accompanying drawings:
[0060] See also Figure 1 The present invention provides a spatial assembly obstacle avoidance method combining natural forces and artificial potential fields, comprising the following steps:
[0061] Obtain the robot's dynamic model, initial position, target position, geometric structure of obstacle B, and collision avoidance detection distance threshold D o , obstacle repulsion potential coefficient α and other information. The dynamic model of the robot is given in the following form:
[0062]
[0063] Among them, ξ(t) is the robot position vector at time t, ζ(t) is the robot velocity vector at time t, f(ξ(t),ζ(t)) is the robot open-loop dynamics function, and U(t) is the robot control variable at time t.
[0064] Decompose obstacle B into n b The union of the basic geometric units
[0065]
[0066] Among them, each basic geometric unit B i (i=1,2,...,n b ) are all convex geometric bodies, and their jth face F i j ( For B i The number of faces) can be expressed in the following general form (the first equation is F i j The surface equation where k( F i j The number of sides of F) is the number of inequalities i j Constraints generated by the k-th edge of ):
[0067]
[0068] And the distances from points to these basic geometric units can be calculated analytically or numerically.
[0069] Based on the basic geometric unit composition of the obstacle, the form of the classical artificial potential function, and the analytical formula / numerical calculation of the distance from a point to the basic geometric unit, the following form of repulsive potential function is constructed for the obstacle:
[0070]
[0071] Among them, V i is the basic geometric unit B of the obstacle i The repulsive potential function is in the form of
[0072]
[0073] Among them, d i From point P(x,y,z) to basic geometric unit B i distance.
[0074] Calculate the gradient of the obstacle repulsion potential function and obtain the following form of obstacle repulsion potential field, which is used as the obstacle repulsion term in the robot control law:
[0075]
[0076] Among them, F i (x, y, z) is the basic geometric unit B of the obstacle i The repulsive potential field is in the form of
[0077]
[0078] in, From point P to basic geometric unit B i The distance d i The gradient at point P, at a known point P in the basic geometric unit B i The nearest neighbor point P on Nearesti Coordinate (x i ,y i ,z i ) can be calculated according to the following formula:
[0079]
[0080] Based on the basic geometric unit composition of the obstacle, the robot's current position coordinates, and the robot's target position coordinates, the following target position occlusion detection algorithm is designed:
[0081]
[0082] Among them, δ i (x, y, z) is the basic geometric unit B of the obstacle i (i=1,2,...,n b ) The occlusion detection function of the target position (actually represents the target visibility) can be further expressed as:
[0083]
[0084] in, is the basic geometric unit B of the obstacle i The jth face F i j ( The occlusion detection function of the target position is calculated according to the following rules:
[0085] If the robot's current position P(x,y,z) is equal to the target position P r (x r ,y r ,z r ) Connect the line with F i j The intersection point (available vector Fi j The boundary constraints, that is, the system of equations
[0086]
[0087] If there is a solution, the robot's target position is blocked by the basic geometric unit B of the obstacle. i Occlusion, correspondingly
[0088] If f in the above equation system (11) i j (x+λ(x r -x),y+λ(y r -y),z+λ(z r -z))=0, there is no solution, or the solution does not satisfy the boundary constraints shown by the inequality in equation group (11), then the robot target position is not blocked by the basic geometric unit B of the obstacle. i Occlusion, accordingly,
[0089] If and only if the robot's target position P r (x r ,y r ,z r ) is not blocked by any basic geometric unit B i Any face of F i j Only when it is blocked, δ(x,y,z)=1, that is, the target position is visible.
[0090] In order to facilitate the calculation of the occlusion of the target position, it can be an obstacle or its basic geometric unit B i Construct an enveloping ellipsoid (The obstacle or basic geometric unit B i is completely contained), if the system of equations for λ If there is a solution, then the obstacle occlusion detection function δ(x, y, z) or the basic geometric unit B i The occlusion detection function δ i (x,y,z) is taken as 0, otherwise it is taken as 1.
[0091] By taking (x, y, z) in the obstacle repulsion potential field formula (6) as the robot's current position coordinate ξ(t), the robot's obstacle repulsion term U is obtained: o (t) = F(ξ(t)), thus designing the following motion control law for the robot:
[0092] U(t)=δ(ξ(t))(-f(ξ(t),ζ(t))-k p (ξ(t)-ξ r )-kv ζ(t))+U o (t) (12)
[0093] Among them, k p is the position feedback coefficient, k v is the speed feedback coefficient, ξ r is the desired position of the robot, and δ(ξ(t)) is the target position occlusion determination function shown in formula (9). The goal is to enable the robot to successfully reach the target position ξ while effectively avoiding collisions with obstacles and crossing the barrier of obstacles. r .
[0094] The meanings of the various items in the above control law formula (12) are as follows: Figure 6 As shown, the dynamic compensation term is -f(ξ(t),ζ(t)) and the target attraction term is -k p (ξ(t)-ξ r ), the damping term is -k v ζ(t), the obstacle rejection term is U o (t).
[0095] Using the designed control law formula (12) and various parameter settings, the robot motion simulation is performed under the dynamic model shown in formula (1). If the simulation results meet the user's requirements, the simulation ends; otherwise, the collision avoidance detection distance threshold D is adjusted. o , obstacle repulsion potential coefficient α and other parameters, and then re-simulate until the requirements are met.
[0096] Embodiment 1:
[0097] The geometric structure of the spacecraft is relatively regular and can be approximated as a combination of basic geometric bodies such as a sphere and a cuboid, and the structure of the space station has a certain complexity. Therefore, this embodiment takes the obstacle avoidance motion of the companion spacecraft (robot) near the space station (reference spacecraft) as the research object to illustrate the specific implementation method of the present invention.
[0098] S1: Obtain the robot's dynamic model, initial position, target position, geometric structure of obstacle B and other parameter values. Here, referring to the simplified geometric structure of the Chinese space station, the basic geometric unit parameters of the combined obstacle are given as shown in Table 1 (where the capsule is a cylinder with both end faces replaced by hemispheres of the same radius):
[0099] Table 1 Basic geometrical components and parameters of the simplified geometric structure of the Chinese space station
[0100]
[0101]
[0102] Collision avoidance detection distance threshold D o =10m, obstacle repulsion coefficient α = 1m 4 / s 2 , position feedback coefficient k p =10 -5 s -2 , speed feedback coefficient k v =10 -2 s -1 The robot's initial position ξ(0) = (-12.1m, 0, 5.1m) T , target position ξ r =(12.1m,0,5.1m) T , the dynamic model is as follows:
[0103]
[0104] in ω is the angular velocity of the reference spacecraft orbiting the Earth (taken as 1.131×10 -3 rad / s), U(t) is the control quantity required for design.
[0105] S2: Decompose the obstacle into a union of basic geometric units. Since the obstacle geometry has been given in the form of basic geometric units, the basic geometric units are as follows: Figure 3 As shown, Figure 3 (a) is a sphere, Figure 3 (b) is a capsule body, Figure 3 (c) is a cuboid, and each basic geometric unit is a convex body, so no geometric structure decomposition is performed. Only the distance formula from the point to each basic geometric unit is given, as shown in Table 2:
[0106] Table 2 Distance formulas from point P (x, y, z) to several simple geometric bodies
[0107]
[0108]
[0109] The surface constraint formulas of each basic geometric unit are shown in Table 3:
[0110] Table 3 Panel equations of several simple geometric bodies
[0111]
[0112]
[0113] Taking into account the actual position of each basic geometric unit, the distance formula from point P (x, y, z) to each basic geometric unit can be expressed as follows (the subscript number corresponds to the basic geometric unit number):
[0114] Capsule 1:
[0115]
[0116] Capsule 2:
[0117]
[0118] Cuboid 3, 4, 7:
[0119]
[0120] Cuboid 5, 6:
[0121]
[0122] The surface constraint formula of each basic geometric unit is expressed as follows (the subscript number corresponds to the basic geometric unit number):
[0123] Capsule 1:
[0124] Side F1 1 :
[0125] Bottom F1 2 、F1 3 (Use a complete sphere instead): Capsule 2:
[0126] side
[0127] Bottom (Use a complete sphere instead): Cuboid 3, 4, 7 (* replaces the basic geometric unit number):
[0128] Front and back Left and right side
[0129] Up and down
[0130] Cuboid 5, 6 (* replaces the basic geometric unit number):
[0131] Front and back Left and right side
[0132] Up and down
[0133] S3: Based on the basic geometric unit composition of the obstacle, the form of the classical artificial potential function, and the analytical formula / numerical calculation of the distance from a point to the basic geometric unit, a repulsive potential function of the following form is constructed for the obstacle:
[0134]
[0135] Where V i is the basic geometric unit B of the obstacle i The repulsive potential function is in the form of:
[0136]
[0137] where d i From point P(x,y,z) to basic geometric unit B i The distance can be calculated based on the basic geometric unit parameters of the obstacle shown in Table 1 and the distance formula from the point to the basic geometric unit given in Table 2. i The specific formula is (the subscripts correspond to the basic geometric unit numbers):
[0138]
[0139]
[0140]
[0141]
[0142] In order to intuitively display the obstacle repulsion potential function, Figure 4 The distribution cloud diagram of the potential function value in the space near the obstacle is given.
[0143] S4: Calculate the gradient of the obstacle repulsion potential function and obtain the following form of obstacle repulsion potential field as the obstacle repulsion term in the robot control law:
[0144]
[0145] where F i (x, y, z) is the basic geometric unit B of the obstacle i The repulsive potential field is in the form of:
[0146]
[0147] in From point P(x,y,z) to basic geometric unit B iThe distance d i The gradient at point P can be calculated for each basic geometric unit according to the following formula (the subscript corresponds to the basic geometric unit number):
[0148]
[0149]
[0150]
[0151]
[0152] S5: Based on the basic geometric unit composition of the obstacle, the current position coordinates of the companion spacecraft, and the target position coordinates of the companion spacecraft, the following target position occlusion detection algorithm is designed:
[0153]
[0154] where δ i (x, y, z) is the basic geometric unit B of the obstacle i (i=1,2,...,7) The occlusion detection function (actually the target visibility) of the target position can be further expressed as:
[0155]
[0156] is the basic geometric unit B of the obstacle i The jth face F i j ( The occlusion detection function of the target position (actually the target visibility) is calculated according to the following rules:
[0157] Capsule 1:
[0158] when When there is a solution, otherwise
[0159] when When there is a solution, otherwise
[0160] when When there is a solution, otherwise
[0161] Capsule 2:
[0162] when When there is a solution, otherwise
[0163] when When there is a solution, otherwise
[0164] when When there is a solution, otherwise
[0165] Cuboid 3, 4, 7 (* replaces the basic geometric unit number):
[0166] when When there is a solution, otherwise
[0167] when When there is a solution, otherwise
[0168] when When there is a solution, otherwise
[0169] when When there is a solution, otherwise
[0170] when When there is a solution, otherwise
[0171] when When there is a solution, otherwise
[0172] Cuboid 5, 6 (* replaces the basic geometric unit number):
[0173] when When there is a solution, otherwise
[0174] when When there is a solution, otherwise
[0175] when When there is a solution, otherwise
[0176] when When there is a solution, otherwise
[0177] when When there is a solution, otherwise
[0178] when When there is a solution, otherwise
[0179] If and only if the spacecraft target position P r (x r ,y r ,z r ) is not blocked by any basic geometric unit B i Any face of F i j Only when the target position is blocked, δ(x, y, z) = 1, that is, the target position is visible. Therefore, there is no need to traverse every face of every basic geometric unit. As long as it is detected that the target position is blocked by a face, δ(x, y, z) = 0.
[0180] S6: By taking (x, y, z) in the obstacle repulsion potential field formula (24) as the robot's current position coordinate ξ(t), the robot's obstacle repulsion term U is obtained o (t)==F(ξ(t)), so as to design the following motion control law for the robot (the point P(x,y,z) is taken as the current position coordinate ξ(t) of the robot):
[0181] U(t)=δ(ξ(t))(-D 21 ξ(t)-D 22 ζ(t)-k p ξ(t)-k v ζ(t))+U o (t) (32)
[0182] Among them, δ(ξ(t)) is the target position occlusion determination function shown in formula (30).
[0183] S7: Based on the control law formula (32) and the parameter values set in S1, the robot obstacle avoidance motion simulation is performed under the dynamic model shown in formula (13). The simulation time is set to 40000s. The results are as follows: Figure 6 to Figure 9 As shown in . It can be found that under the action of the designed control law, the robot can successfully cross the obstacle and converge to the target position with high accuracy, and the amplitude of the control amount is also within the appropriate level. In contrast, the simulation results without considering the occlusion of the target position (that is, δ(ξ(t)) is always 1) are shown in Figure 10-11 As shown in the figure, it can be found that the robot is trapped in the local area near the obstacle and cannot successfully reach the target position.
[0184] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.
Claims
1. A spatial assembly obstacle avoidance method combining natural forces and artificial potential fields, characterized in that: The following steps are involved: Get the robot's dynamic model, initial position, target position, and obstacles The structure and parameter values of the obstacles Decompose into several basic geometric units The union of; Based on obstacles The basic geometric unit , classical artificial potential function form and point to basic geometric unit The distance to the obstacle Construct a repulsive potential function and apply it to the obstacle The repulsive potential function is used to find the gradient and obtain the obstacle repulsive potential field; Based on obstacles The geometric structure of the robot, the current and target positions of the robot, and the design of a target position occlusion detection algorithm for the robot; Combined obstacles The repulsive potential field and target position occlusion detection algorithm are used to design motion control laws for the robot; The target position occlusion detection algorithm is: in, is the basic geometric unit of the obstacle Occlusion detection function for the target position, is the number of basic geometric units, ; Said It can be expressed as: in, is the basic geometric unit of the obstacle No. Face Occlusion detection function for the target position, The basic geometric unit The number of faces, , the target position is Take when blocked , otherwise take .
2. The method for avoiding obstacles in a space assembly combining natural forces and artificial potential fields according to claim 1, characterized in that: The dynamic model of the robot is: in, for The robot position vector at the moment, for The robot velocity vector at the moment, is the robot open-loop dynamics function, for The amount of robot control at the moment.
3. The method for avoiding obstacles in a space assembly combining natural forces and artificial potential fields according to claim 1, characterized in that: The obstacles Decompose into The union of basic geometric units: Among them, each basic geometric unit They are all convex geometric bodies. is the number of basic geometric units, , its Face It is expressed in the following general form, , The basic geometric unit Number of faces: The first equation is The surface equation, The inequality is No. The constraints generated by the edges, , for The number of edges.
4. The method for avoiding obstacles in a space assembly combining natural forces and artificial potential fields according to claim 1, characterized in that: The obstacle The repulsive potential function can be expressed as follows: in, is the basic geometric unit of the obstacle The repulsive potential function, is the number of basic geometric units, .
5. The method for avoiding obstacles in a space assembly combining natural forces and artificial potential fields according to claim 4, characterized in that: The basic geometric unit of the obstacle The repulsive potential function is: in, For point To basic geometric units The distance For the collision avoidance detection distance threshold, at a known point In basic geometric units The nearest neighbor point on coordinate The following formula is used to calculate: 。 6. The method for avoiding obstacles in a space assembly combining natural forces and artificial potential fields according to claim 1, characterized in that: The obstacle repelling potential field is: in, is the basic geometric unit of the obstacle The repulsive potential field, is the number of basic geometric units, .
7. The method for avoiding obstacles in a space assembly combining natural forces and artificial potential fields according to claim 6, characterized in that: Said By the corresponding potential function Point The negative gradient of the coordinates is obtained in the form of: in, For point To basic geometric units The distance is the obstacle repulsion potential coefficient, For the collision avoidance detection distance threshold, click To basic geometric units Distance At the point The gradient at is: Known Points In basic geometric units The nearest neighbor point on coordinate hour, Calculated as follows: 。 8. The method for avoiding obstacles in a space assembly combining natural forces and artificial potential fields according to claim 1, characterized in that: The motion control law is: in, is the position feedback coefficient, is the speed feedback coefficient, is the desired position of the robot, is the target position occlusion determination function, The obstacle repelling potential field at the robot's current position The value of Use The three components are replaced.
Citation Information
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