Calculation method and related device for feasible arm angle range of 7-DOF robotic arm

Abstract

The present application provides a method for calculating the feasible arm angle range of a 7-DOF manipulator and a related device, relating to the field of robot motion control. In this method, the 7 joints of the manipulator are respectively referred to as the nth joint, where the larger the n value is, the closer to the end of the manipulator, and n is a positive integer ≤ 7. The electronic device obtains the target parameter in the stationary point expression of the first arm angle function, wherein the first arm angle function characterizes the constraint relationship between the joint angle of the i-th joint of the manipulator and the arm angle, i∈{1,3,5,7}; according to the function curve under each relationship between the target parameter and the preset threshold, the feasible arm angle range of each joint that avoids the joint limit and singular condition is determined, wherein the preset threshold Δ=1e‑8. In this way, the feasible arm angle range of each joint of the manipulator under different conditions is determined.

Description

Technical Field

[0001] The present application relates to the field of robot motion control, and more specifically, to a method for calculating the feasible arm angle range of a 7-DOF robotic arm and related devices. Background Art

[0002] Compared with the 6-DOF manipulator, the 7-DOF manipulator has higher flexibility. While completing the given task, it can prevent joints from exceeding the limit, avoid strange configurations, and avoid obstacles. Figure 1 As shown in the figure, the elbow of a 7-DOF manipulator can rotate about a line SW. Point S represents the shoulder joint, the first joint connected to the base, which allows the manipulator to rotate in the horizontal plane. Point W represents the wrist joint, typically the wrist joint of the manipulator, the joint closest to the end effector, which controls wrist rotation. Point E represents the elbow joint, typically the intermediate joint between the shoulder joint S and the wrist joint W. Point B represents the base, typically the base joint of the manipulator, which connects the manipulator to the external environment. The base provides a fixed reference point for the manipulator and may contain one or more revolute joints, allowing the manipulator to be positioned in space. For a 7-DOF manipulator, the redundant degrees of freedom of the 7-DOF manipulator can be represented by the arm angle (i.e., the angle ψ between plane S E W and plane B SW ). Therefore, the redundant nature of the 7-DOF manipulator can be fully exploited by controlling the arm angle.

[0003] A common approach in the prior art involves introducing arm angles during the inverse solution process and calculating the mapping relationship between arm angles and joint angles. By controlling the arm angles, a 7-DOF manipulator can prevent joint limits and avoid singular configurations. However, prior art only briefly describes the mapping relationship between joint angles and arm angle space, without detailed research into the feasible range of arm angles under joint limit and singular configuration avoidance conditions. Summary of the Invention

[0004] In order to overcome at least one of the deficiencies in the prior art, the present application provides a method and related apparatus for calculating the feasible arm angle range of a 7-DOF robotic arm, specifically comprising:

[0005] In a first aspect, the present application provides a method for calculating a feasible arm angle range of a 7-DOF manipulator, wherein the seven joints of the manipulator are respectively referred to as n-th joints, where a larger value of n indicates a position closer to the end of the manipulator, and n is a positive integer ≤ 7. The method comprises:

[0006] Obtaining a target parameter in a stationary point expression of a first arm angle function, wherein the first arm angle function represents a constraint relationship between a joint angle of an i-th joint of the robotic arm and an arm angle, i∈{1,3,5,7};

[0007] The feasible arm angle range of each joint that avoids joint limits and singular conditions is determined based on the function curve under each relationship between the target parameter and the preset threshold, wherein the preset threshold Δ=1e-8.

[0008] In conjunction with an optional implementation manner of the first aspect, determining a feasible arm angle range for each joint that avoids joint limits and singular conditions based on a function curve under each relationship between the target parameter and the preset threshold, includes:

[0009] If the target parameter is greater than the preset threshold, and the joint angle of the i-th joint is within the interval [-ππ], then the maximum and minimum values of the first arm angle function are calculated;

[0010] Obtaining a first function curve of the first arm angle function according to a magnitude relationship between the minimum joint angle and the maximum joint angle of the i-th joint and the maximum and minimum values of the first arm angle function;

[0011] Calculating a first arm angle corresponding to the first arm angle function and the minimum joint angle and the maximum joint angle of the i-th joint;

[0012] Taking the first arm angle as an interval endpoint, a feasible range of the arm angle of the i-th joint under the constraint of the first function curve is determined.

[0013] In conjunction with the optional implementation manner of the first aspect, determining the feasible arm angle range for each joint that avoids joint limits and singular conditions based on the function curves under each relationship between the target parameter and the preset threshold value further includes:

[0014] If the target parameter is greater than the preset threshold and the joint angle of the i-th joint is outside the interval [-ππ], then calculating the local maximum and local minimum of the first arm angle function;

[0015] Obtaining a second function curve of the first arm angle function according to a relationship between the minimum joint angle, the maximum joint angle of the i-th joint, and the local maximum value and the local minimum value of the first arm angle function;

[0016] Calculating a first arm angle corresponding to the first arm angle function and the minimum joint angle and the maximum joint angle of the i-th joint;

[0017] Taking the first arm angle as the interval endpoint, determine the feasible range of the arm angle of the i-th joint under the constraint of the second function curve.

[0018] In conjunction with an optional implementation manner of the first aspect, determining a feasible arm angle range for each joint that avoids joint limits and singular conditions based on a function curve under each relationship between the target parameter and the preset threshold, includes:

[0019] If the target parameter is less than the negative preset threshold, calculating the first arm angle corresponding to the first arm angle function and the minimum joint angle and the maximum joint angle of the i-th joint;

[0020] Obtaining a third function curve of the first arm angle function according to the relationship between the minimum joint angle, the maximum joint angle, and the interval [-π π] of the i-th joint;

[0021] Taking the first arm angle as the interval endpoint, determine the feasible range of the arm angle of the i-th joint under the constraint of the third function curve.

[0022] In conjunction with an optional implementation manner of the first aspect, determining a feasible arm angle range for each joint that avoids joint limits and singular conditions based on a function curve under each relationship between the target parameter and the preset threshold, includes:

[0023] If the target parameter is greater than the negative preset threshold and less than the preset threshold, a singular arm angle of the first arm angle function at a singular stationary point is obtained, and an arm angle exclusion interval of the i-th joint is obtained according to the singular arm angle;

[0024] Obtaining a fourth function curve of the first arm angle function according to the relationship between the minimum joint angle, the maximum joint angle, and the interval [-π π] of the i-th joint and the mutation angle corresponding to the i-th joint and the singular arm angle;

[0025] Calculating a first arm angle corresponding to the first arm angle function and the minimum joint angle and the maximum joint angle of the i-th joint;

[0026] Taking the first arm angle as the interval endpoint, determine the feasible range of the arm angle of the i-th joint under the constraint of the fourth function curve.

[0027] In combination with the optional implementation manner of the first aspect, the arm angle exclusion interval The calculation expression is:

[0028]

[0029] δ=1e-6.

[0030] In conjunction with the optional implementation manner of the first aspect, the method further includes:

[0031] If the cosine value of the joint angle of the j-th joint is not 0, obtain the second arm angle corresponding to the second arm angle function and the minimum joint angle and the maximum joint angle of the j-th joint, wherein the second arm angle function represents the constraint relationship between the joint angle of the j-th joint of the robotic arm and the arm angle, j∈{2,6};

[0032] Obtaining a function curve of the second arm angle function according to a magnitude relationship between the minimum joint angle and the maximum joint angle of the j-th joint and the maximum value and the minimum value of the second arm angle function;

[0033] According to the function curve of the second arm angle and the second arm angle function, the feasible arm angle range of the j-th joint is obtained.

[0034] In a second aspect, the present application further provides a device for calculating a feasible arm angle range of a 7-DOF manipulator, wherein the seven joints of the manipulator are respectively referred to as n-th joints, where a larger value of n indicates a position closer to the end of the manipulator, and n is a positive integer ≤ 7. The device comprises:

[0035] a parameter acquisition module, configured to acquire target parameters in a stationary point expression of a first arm angle function, wherein the first arm angle function represents a constraint relationship between the joint angle of the i-th joint of the robotic arm and the arm angle, i∈{1,3,5,7};

[0036] The arm angle range module is used to determine the feasible arm angle range of each joint to avoid joint limits and singular conditions based on the function curve under each relationship between the target parameter and the preset threshold, wherein the preset threshold Δ=1e-8.

[0037] In conjunction with the optional implementation manner of the second aspect, the arm angle range module is further specifically configured to:

[0038] If the target parameter is greater than the preset threshold, and the joint angle of the i-th joint is within the interval [-ππ], then the maximum and minimum values of the first arm angle function are calculated;

[0039] Obtaining a first function curve of the first arm angle function according to a magnitude relationship between the minimum joint angle and the maximum joint angle of the i-th joint and the maximum and minimum values of the first arm angle function;

[0040] Calculating a first arm angle corresponding to the first arm angle function and the minimum joint angle and the maximum joint angle of the i-th joint;

[0041] Taking the first arm angle as an interval endpoint, a feasible range of the arm angle of the i-th joint under the constraint of the first function curve is determined.

[0042] In conjunction with the optional implementation manner of the second aspect, the arm angle range module is further specifically configured to:

[0043] If the target parameter is greater than the preset threshold and the joint angle of the i-th joint is outside the interval [-ππ], then calculating the local maximum and local minimum of the first arm angle function;

[0044] Obtaining a second function curve of the first arm angle function according to a relationship between the minimum joint angle, the maximum joint angle of the i-th joint, and the local maximum value and the local minimum value of the first arm angle function;

[0045] Calculating a first arm angle corresponding to the first arm angle function and the minimum joint angle and the maximum joint angle of the i-th joint;

[0046] Taking the first arm angle as the interval endpoint, determine the feasible range of the arm angle of the i-th joint under the constraint of the second function curve.

[0047] In conjunction with the optional implementation manner of the second aspect, the arm angle range module is further specifically configured to:

[0048] If the target parameter is less than the negative preset threshold, calculating the first arm angle corresponding to the first arm angle function and the minimum joint angle and the maximum joint angle of the i-th joint;

[0049] Obtaining a third function curve of the first arm angle function according to the relationship between the minimum joint angle, the maximum joint angle, and the interval [-π π] of the i-th joint;

[0050] Taking the first arm angle as the interval endpoint, determine the feasible range of the arm angle of the i-th joint under the constraint of the third function curve.

[0051] In conjunction with the optional implementation manner of the second aspect, the arm angle range module is further specifically configured to:

[0052] If the target parameter is greater than the negative preset threshold and less than the preset threshold, a singular arm angle of the first arm angle function at a singular stationary point is obtained, and an arm angle exclusion interval of the i-th joint is obtained according to the singular arm angle;

[0053] Obtaining a fourth function curve of the first arm angle function according to the relationship between the minimum joint angle, the maximum joint angle, and the interval [-π π] of the i-th joint and the mutation angle corresponding to the i-th joint and the singular arm angle;

[0054] Calculating a first arm angle corresponding to the first arm angle function and the minimum joint angle and the maximum joint angle of the i-th joint;

[0055] Taking the first arm angle as the interval endpoint, determine the feasible range of the arm angle of the i-th joint under the constraint of the fourth function curve.

[0056] In combination with the optional implementation manner of the second aspect, the arm angle exclusion interval The calculation expression is:

[0057]

[0058]

[0059] δ=1e-6.

[0060] In conjunction with the optional implementation manner of the second aspect, the arm angle range module is further used to:

[0061] If the cosine value of the joint angle of the j-th joint is not 0, obtain the second arm angle corresponding to the second arm angle function and the minimum joint angle and the maximum joint angle of the j-th joint, wherein the second arm angle function represents the constraint relationship between the joint angle of the j-th joint of the robotic arm and the arm angle, j∈{2,6};

[0062] Obtaining a function curve of the second arm angle function according to a magnitude relationship between the minimum joint angle and the maximum joint angle of the j-th joint and the maximum value and the minimum value of the second arm angle function;

[0063] According to the function curve of the second arm angle and the second arm angle function, the feasible arm angle range of the j-th joint is obtained.

[0064] In a third aspect, the present application further provides a storage medium storing a computer program, which, when executed by a processor, implements the method for calculating the feasible arm angle range of a 7-DOF robotic arm.

[0065] In a fourth aspect, the present application also provides an electronic device, which includes a processor and a memory, wherein the memory stores a computer program, and when the computer program is executed by the processor, the method for calculating the feasible arm angle range of the 7-DOF robotic arm is implemented.

[0066] Compared with the prior art, this application has the following beneficial effects:

[0067] The present application provides a method for calculating the feasible arm angle range of a 7-DOF manipulator and a related device. In this method, the 7 joints of the manipulator are respectively referred to as the nth joint, and the larger the n value is, the closer to the end of the manipulator, and n is a positive integer ≤ 7. The electronic device obtains the target parameter in the stationary point expression of the first arm angle function, wherein the first arm angle function characterizes the constraint relationship between the joint angle of the i-th joint of the manipulator and the arm angle, i∈{1,3,5,7}; according to the relationship between the target parameter and the preset threshold, the feasible arm angle range of each joint is calculated to avoid the joint limit and the singular condition under each relationship, wherein the preset threshold Δ=1e-8. In this way, the feasible arm angle range of each joint of the manipulator under different conditions is determined. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following is a brief introduction to the drawings required for use in the embodiments. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without paying any creative work.

[0069] Figure 1 A schematic diagram of the arm angle provided in an embodiment of the present application;

[0070] Figure 2 One of the mapping relationship function diagrams between the angles of joints 1, 3, 5, and 7 and the arm angle provided in an embodiment of the present application;

[0071] Figure 3 This is the second function diagram of the mapping relationship between the angles of joints 1, 3, 5, and 7 and the arm angle provided in an embodiment of the present application;

[0072] Figure 4 This is the third function diagram of the mapping relationship between the angles of joints 1, 3, 5, and 7 and the arm angle provided in the embodiment of the present application;

[0073] Figure 5 Schematic diagram of the mapping relationship between the angles of joints 2 and 4 and the arm angle provided in an embodiment of the present application;

[0074] Figure 6 A flowchart of a method for calculating the feasible arm angle range of a 7-DOF robotic arm provided in an embodiment of the present application;

[0075] Figure 7-14 A schematic diagram of the arm angle range provided in an embodiment of the present application;

[0076] Figure 15 A schematic diagram of the structure of a device for calculating the feasible arm angle range of a 7-DOF robotic arm provided in an embodiment of the present application;

[0077] Figure 16 A schematic diagram of the structure of an electronic device provided in an embodiment of the present application.

[0078] Icons: 11- parameter acquisition module; 12- arm angle range module; 21- memory; 22- processor; 23- communication unit; 24- system bus. DETAILED DESCRIPTION

[0079] To make the objectives, technical solutions, and advantages of the embodiments of the present application more clear, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Generally, the components of the embodiments of the present application described and shown in the drawings herein can be arranged and designed in various different configurations.

[0080] Therefore, the following detailed description of the embodiments of the present application provided in the accompanying drawings is not intended to limit the scope of the present application for protection, but merely represents selected embodiments of the present application. All other embodiments obtained by persons of ordinary skill in the art based on the embodiments in the present application without creative work are within the scope of protection of the present application.

[0081] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings.

[0082] In the description of this application, it should be noted that the terms "comprises," "includes," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, article, or apparatus comprising a series of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or apparatus comprising the element.

[0083] Based on the above statement, as introduced in the background technology, the common method in the prior art is to introduce the arm angle in the inverse solution process, calculate the mapping relationship between the arm angle and each joint angle, and by controlling the arm angle, the 7-DOF robotic arm can prevent joint over-limit and avoid singular configuration.

[0084] For example, the seven joints of the robotic arm are referred to as n-th joints, where n≤7. A larger n value indicates a position closer to the end of the robotic arm. Under this premise, the mapping relationship between the arm angle and each joint angle is divided into the following three categories:

[0085] (1) The angle of the fourth joint is not related to the arm angle:

[0086]

[0087] Among them, d se is the length of connecting rod SE, d sw is the length of connecting rod SW, d ew is the length of the connecting rod EW.

[0088] (2) The mapping between the angles of joints 1, 3, 5, and 7 and the arm angle can be expressed as an inverse tangent function:

[0089] θ i (ψ)=atan2(a n sinψ+b n cosψ+c n ,a d sinψ+b d cosψ+c d )(2)

[0090] Among them, a n ,b n ,c n ,a d ,b d ,c d are the coefficients in the inverse solution expressions for joints 1, 3, 5, and 7.

[0091] Assume u = a n sinψ+b n cosψ+c n , v=a d sinψ+b d cosψ+c d , by differentiating both sides of formula (2) with respect to ψ, we can obtain:

[0092]

[0093] Among them, a t =c n b d -b n c d , b t =a n c d -c n a d , c t =a n b d -b n a d Using the universal substitution formula, we can get the stationary point of formula (3):

[0094]

[0095] According to a t 2 +b t 2 -c t 2 The relationship between and 0 can be divided into three cases.

[0096] See Figure 2 , when a t 2 +b t 2 -c t 2 When >0, Equation (4) has two stationary points. Figure 2 (a) shows that when the joint angle θ i When between [-ππ], the function curve changes continuously. Figure 2 (b) shows that when the joint angle θ i When it exceeds π or -π, the function atan2() maps the joint angle to [-ππ], and the function curve suddenly changes. Figure 2 (a) indicates Figure 2 The local image marked with symbol a in , similarly, Figure 2 (b) indicates Figure 2 It should be noted that the meaning of the same expression form in the following text is the same as this, and will not be repeated in the following text.

[0097] See Figure 3 , when a t 2 +b t 2 -c t 2 When <0, there is no stationary point in equation (4). Figure 3 (a) shows the angle θ when the joint i When between [-ππ], the function curve changes continuously; Figure 3 (b) shows the joint angle θ i When the value exceeds π or -π, the function curve changes suddenly because the function atan2() maps the joint angle to between [-ππ].

[0098] like Figure 4 As shown, when a t 2 +b t 2 -c t 2 = 0, Equation (4) has a singular arm angle. At the singular arm angle, the function curve suddenly changes.

[0099] In addition, the mapping relationship between the angles of joints 2 and 6 and the arm angle can be expressed as an inverse cosine function:

[0100] θ i (ψ)=arccos(asinψ+bcosψ+c)(5)

[0101] Where a, b, and c are the coefficients in the inverse solution expressions of joints 2 and 6.

[0102] Assuming m = asinψ + bcosψ + c, and differentiating both sides of equation (5) with respect to ψ, we can obtain:

[0103]

[0104] See Figure 5 , Figure 5 (a) shows that when sinθ i When ≠0, Equation (6) has two stationary points; Figure 5 (b) shows that when sinθ i When =0, Equation (6) has one stationary point.

[0105] Therefore, the existing technology only briefly introduces the mapping relationship between joint angles and arm angle space, and does not study in detail the feasible range of arm angles under joint limit and singular conditions.

[0106] Based on the discovery of the above technical problems, the inventors have proposed the following technical solutions after creative work to solve or improve the above problems. It should be noted that the defects existing in the solutions in the above prior art are the results obtained by the inventors after practice and careful research. Therefore, the discovery process of the above problems and the solutions proposed in the embodiments of this application below for the above problems should all be the contributions made by the inventors to this application in the process of invention and creation, and should not be understood as technical contents known to those skilled in the art.

[0107] In view of the technical problems discovered above, this embodiment provides a method for calculating the feasible arm angle range of a 7-DOF robotic arm. In this method, the 7 joints of the robotic arm are respectively referred to as the nth joint, and the larger the n value is, the closer to the end of the robotic arm is, and n is a positive integer ≤ 7. The electronic device obtains the target parameter in the stationary point expression of the first arm angle function, wherein the first arm angle function characterizes the constraint relationship between the joint angle of the i-th joint of the robotic arm and the arm angle, i∈{1,3,5,7}; according to the relationship between the target parameter and the preset threshold, the feasible arm angle range of each joint is calculated to avoid the joint limit and the singular condition under each relationship, wherein the preset threshold Δ=1e-8. In this way, the feasible arm angle range of each joint of the robotic arm is determined.

[0108] It should be noted that the electronic device implementing this method may include, but is not limited to, a mobile terminal, a tablet computer, a laptop computer, a desktop computer, and a control device integrated with the robotic arm body. The mobile terminal, tablet computer, laptop computer, desktop computer, etc., as a host computer, communicates with the robotic arm to control the robotic arm.

[0109] To make the solution provided by this embodiment clearer, the following takes the control device of the robot arm as an example, and combines Figure 6 Each step of the method is described in detail. However, it should be understood that the operations in the flowchart can be implemented in a non-sequential order, and steps that have no logical contextual relationship can be reversed or implemented simultaneously. In addition, those skilled in the art can add one or more other operations to the flowchart, or remove one or more operations from the flowchart, guided by the content of this application. Figure 6 As shown, the method includes:

[0110] S1, obtain the target parameters in the stationary point expression of the first arm angle function.

[0111] Among them, the first arm angle function represents the constraint relationship between the joint angle of the i-th joint of the robotic arm and the arm angle, i∈{1,3,5,7}.

[0112] In this embodiment, the relationship between the 1st, 3rd, 5th, and 7th joint angles and the arm angle is called the first arm angle function, which is the inverse tangent function shown in formula (2). Based on the inverse tangent function shown in formula (2), the stationary point expression of the first arm angle function shown in formula (3) can be obtained:

[0113]

[0114] In this embodiment, a in the above expression is t 2 +b t 2 -c t 2 The result of the calculation is called the target parameter.

[0115] Based on the above implementation of the target parameters, continue to refer to Figure 6 The method for calculating the feasible arm angle range of a 7-DOF manipulator provided in this embodiment further includes:

[0116] S2, based on the function curve under each relationship between the target parameter and the preset threshold, determines the feasible arm angle range of each joint to avoid the joint limit and singular conditions.

[0117] Wherein, the preset threshold value Δ=1e-8. In this embodiment, based on the relationship between the target parameter and the preset threshold value, three situations can be divided into: the target parameter is greater than the preset threshold value, the target parameter is less than the negative preset threshold value, and the target parameter is greater than the negative preset threshold value and less than the preset threshold value. The above three situations are described below.

[0118] Case 1:

[0119] If the target parameter is greater than a preset threshold and the joint angle of the i-th joint is within the interval [-π π], the control device calculates the maximum and minimum values of the first arm angle function; according to the size relationship between the minimum joint angle and the maximum joint angle of the i-th joint and the maximum and minimum values of the first arm angle function, the first function curve of the first arm angle function is obtained; the first arm angle corresponding to the first arm angle function and the minimum joint angle and the maximum joint angle of the i-th joint is calculated; and the first arm angle is used as the endpoint of the interval to determine the feasible range of the arm angle of the i-th joint under the constraints of the first function curve.

[0120] For example, when the joint angle θ i When the value is between [-ππ], the function curve of the first arm angle function is called the first function curve, which is in a continuously changing style. The function values at the stationary point are the maximum values θ max and the minimum value θ min According to θ max ,θ min and the upper limit of the i-th joint Lower limit The relationship between , the feasible range of the arm angle of the i-th joint is divided into the following five cases:

[0121] (1) and

[0122] At this point, the upper and lower limits of the joint intersect with the function curve. Using the universal substitution formula for the first arm angle function, we can obtain the following expression for the first arm angle function:

[0123]

[0124] Where a p =(c d -b d )tanθ i +b n -c n , b p =2(a d tanθ i -a n ), c p =(b d +c d )tanθ i -b n -c n .

[0125] Will and Substituted into formula (7), the first arm angle function is calculated to obtain the first arm angle corresponding to the minimum joint angle and maximum joint angle of the i-th joint, including the first arm angle corresponding to the minimum joint angle and and exist Left side; maximum joint angle corresponds to and and exist Left side. Figure 7 As shown, there are four possible situations and the feasible arm angle range Ψ of the i-th joint in each situation. i .

[0126]

[0127] (2) and

[0128] At this point, the lower limit of the joint intersects the first function curve. Substituted into formula (7), the first arm angle function corresponding to the minimum joint angle of the i-th joint is calculated, including and and exist Left side. According to the maximum point θ max Intersection and The relationship between the feasible arm angle range Ψ i The calculation can be divided into three cases. Figure 8 The feasible arm angle range Ψ of the i-th joint in three possible cases is shown in i .

[0129]

[0130] (3) and

[0131] At this time, the joint upper limit intersects with the first function curve, similar to case (2). Substituted into formula (7), the first arm angle function corresponding to the maximum joint angle of the i-th joint is calculated, including and and exist Left side. According to the minimum point θ min Intersection and The relationship between the feasible arm angle range Ψ i The calculation of can be divided into three cases. The feasible arm angle range Ψ of the i-th joint i for:

[0132]

[0133] (4) and

[0134] At this time, the upper and lower limits of the joint do not intersect with the first function curve, and the feasible arm angle range of the i-th joint is Ψ i =[-ππ].

[0135] (5) or

[0136] The feasible arm angle range of the i-th joint is an empty set, that is,

[0137] The above embodiment describes the case where the joint angle of the i-th joint is within the interval [-π π]. The following describes the case where the target parameter is greater than the preset threshold and the joint angle of the i-th joint is outside the interval [-π π]. In this case, the control device calculates the local maximum and local minimum of the first arm angle function; obtains the second function curve of the first arm angle function based on the size relationship between the minimum joint angle and the maximum joint angle of the i-th joint and the local extreme value and the local extreme value of the first arm angle function; calculates the first arm angle corresponding to the first arm angle function and the minimum joint angle and the maximum joint angle of the i-th joint; uses the first arm angle as the endpoint of the interval to determine the feasible range of the arm angle of the i-th joint under the constraints of the second function curve.

[0138] For example, since the function atan2() (first arm angle function) maps the joint angle to [-ππ], when the joint angle θ i When the joint angle θ exceeds -π or π, the function curve of the first arm angle function will suddenly change. i When it is outside the interval [-ππ], the function curve of the first arm angle function is called the second function curve, which is consistent with the joint angle θ i Compared with the interval [-ππ], the function curve at this time will undergo a sudden change, resulting in the function value at the stationary point not being the maximum value θ max and the minimum value θ min , but a local maximum and local minima according to and and the upper limit of the i-th joint and lower limit The size relationship between them, the feasible arm angle range Ψ of joint i i The calculation can be divided into the following 6 cases:

[0139] (1) and

[0140] At this time, the upper limit of the joint intersects with the upper half of the second function curve, and the lower limit of the joint intersects with the lower half of the second function curve. Therefore, and Substituted into formula (7), the first arm angle function corresponding to the minimum joint angle and maximum joint angle of the i-th joint is calculated, including the first arm angle corresponding to the minimum joint angle and and exist Left side; corresponds to the maximum joint angle and and exist Left side. Figure 9 The figure shows the six possible situations, and the feasible arm angle range Ψ of the i-th joint in the six situations is i for:

[0141]

[0142] It is worth noting that according to θ i (π) and The size relationship between them or according to θ i (π) and The size relationship between them, the feasible arm angle range Ψ i The calculation of can be divided into two cases, Figure 9 (b)(c)(e)(f) shows only one possible scenario.

[0143] (2) and

[0144] The joint upper limit intersects with the upper half of the second function curve, according to θ i (π) and The size relationship between them, the feasible arm angle range Ψ i The calculation of can be divided into two cases. At this time, the feasible arm angle range Ψ of the i-th joint i for:

[0145]

[0146] (3) and

[0147] The upper and lower limits of the joint intersect with the upper half of the second function curve. At this time, the feasible arm angle range of the i-th joint is i for:

[0148]

[0149] (4) and

[0150] The upper and lower limits of the joint intersect with the lower half of the second function curve. At this time, the feasible arm angle range of the i-th joint is i for:

[0151]

[0152] (5) and

[0153] The lower limit of the joint intersects the lower half of the second function curve, according to θ i (π) and The size relationship between them, the feasible arm angle range Ψ i The calculation of can be divided into two cases. At this time, the feasible arm angle range Ψ of the i-th joint i for:

[0154]

[0155] (6) and

[0156] The upper and lower limits of the joint do not intersect with the function curve. At this time, the feasible arm angle range of the i-th joint is Ψ i is an empty set, that is

[0157] Case 2:

[0158] If the target parameter is less than the negative preset threshold, the control device calculates the first arm angle corresponding to the first arm angle function and the minimum joint angle and maximum joint angle of the i-th joint; according to the size relationship between the minimum joint angle, maximum joint angle of the i-th joint and the interval [-ππ], the third function curve of the first arm angle function is obtained; taking the first arm angle as the endpoint of the interval, the feasible range of the arm angle of the i-th joint under the constraints of the third function curve is determined.

[0159] For example, when the joint angle θ i When the angle is between [-ππ], the function curve of the first arm angle function is called the third function curve, which changes continuously. At this time, the upper and lower limits of the joint intersect with the third function curve, so and Substituted into formula (7), the first arm angle function corresponding to the minimum joint angle and maximum joint angle of the i-th joint is calculated, including ψ corresponding to the minimum joint angle l , and ψ corresponding to the maximum joint angle u .like Figure 10 As shown, if the function is a monotonically increasing function, the feasible arm angle range is Ψ i =[ψl ψ u ]; If the function is a monotonically decreasing function, the feasible arm angle range is Ψ i =[ψ u ψ l ].

[0160] When the joint angle θ i When the joint angle is outside the interval [-ππ], the third function curve will suddenly change because the atan2 (first arm angle function) function maps the joint angle to [-ππ]. At this time, the upper and lower limits of the joint intersect with the third function curve. and Substituted into formula (7), the first arm angle function corresponding to the minimum joint angle and maximum joint angle of the i-th joint is calculated, including ψ corresponding to the minimum joint angle l , and ψ corresponding to the maximum joint angle u When the functions on the left and right sides of the mutation are monotonically increasing functions, according to θ i (π) and the upper and lower limits of the joint The size relationship between them, the feasible arm angle range Ψ i The calculation of can be divided into three cases. Figure 11 As shown in the figure, there are three possible situations, and the feasible arm angle range Ψ of the i-th joint in the three situations is shown in the figure. i for:

[0161]

[0162] Similarly, we can get the feasible arm angle range Ψ when the functions on the left and right sides of the mutation are monotonically decreasing functions: i .

[0163] Case 3:

[0164] If the target parameter is greater than the negative preset threshold and less than the preset threshold, the control device obtains the singular arm angle of the first arm angle function at the singular stationary point, and obtains the arm angle exclusion interval of the i-th joint based on the singular arm angle; according to the size relationship between the minimum joint angle, the maximum joint angle of the i-th joint and the interval [-π π] and the mutation angle corresponding to the i-th joint and the singular arm angle, the fourth function curve of the first arm angle function is obtained; the first arm angle corresponding to the first arm angle function and the minimum joint angle and the maximum joint angle of the i-th joint is calculated; the first arm angle is used as the endpoint of the interval to determine the feasible range of the arm angle of the i-th joint under the constraints of the fourth function curve.

[0165] In this embodiment, the arm angle exclusion interval is expressed as The two endpoints of the interval are calculated as follows:

[0166]

[0167] For example, if the target parameter is greater than a negative preset threshold and less than a preset threshold, the first arm angle function has a singular stationary point. At this singular stationary point, the same arm angle corresponds to two joint angles. The value of the arm angle at the singular stationary point is expressed as ψ sing , at this time, the feasible range of the arm angle of the i-th joint must be In addition to the above, the feasible range of arm angles in different situations is explained in detail below.

[0168] (A) When the first arm angle function is an increasing function and the singular arm angle is not at ±π, the feasible arm angle range Ψ is determined by whether the fourth function curve intersects the upper and lower limits of the joint. i The calculation can be divided into the following four cases:

[0169] (1) Figure 12 As shown, the singular arm angle at the joint θ i The mutation is -π. According to whether the function curve intersects with the upper and lower limits of the joint, the feasible arm angle range Ψ of the i-th joint can be obtained. i . Figure 12 (a) shows one of the possible situations in the following situation, in which the feasible arm angle range Ψ of the i-th joint i =[-π ψ u ]∪[ψ l π],

[0170]

[0171] (2) Joint θ at the singular arm angle i When the value of suddenly changes to π, the arm angle range Ψ can be obtained according to whether the fourth function curve intersects with the upper and lower limits of the joint i . Figure 12 (b) shows one of the possible situations below, in which the feasible arm angle range of joint i is

[0172]

[0173] (3) Joint θ at the singular arm angle i When the value of mutates to π, if the joint angle θ i When it exceeds -π or π, the function curve will mutate again. When the mutation is on the left side of the singular arm angle, the arm angle range Ψ can be obtained based on whether the fourth function curve intersects with the upper and lower limits of the joint. i . Figure 12 (c) shows one of the possible situations below, where the feasible range of arm angles is

[0174]

[0175] (4) Joint θ at the singular arm angle i When the value of mutates to π, if the joint angle θ i When it exceeds -π or π, the function curve will mutate again. When the mutation is on the right side of the singular arm angle, the arm angle range Ψ can be obtained based on whether the fourth function curve intersects with the upper and lower limits of the joint. i . Figure 12 (d) shows one of the possible situations below, where the feasible range of arm angles is

[0176]

[0177] (B) The first arm angle function is an increasing function and when the singular arm angle is at ±π, the feasible arm angle range Ψ is determined by whether the function curve intersects the upper and lower limits of the joint. i The calculation can be divided into the following two cases:

[0178] (1) When the joint angle θ i When the value is between [-ππ], the function curve changes continuously. The arm angle range Ψ can be obtained according to whether the function curve intersects with the upper and lower limits of the joint. i . Figure 12 (e) shows one of the possible situations under the following circumstances, in which the feasible arm angle range Ψ i =[ψ l ψ u ].

[0179]

[0180] (2) When the joint angle θ i When it exceeds -π or π, the function curve suddenly changes. According to whether the function curve intersects with the upper and lower limits of the joint, the arm angle range Ψ can be obtained. i . Figure 12 (f) shows one of the possible situations under the following circumstances, in which the feasible arm angle range Ψ i =[-π+δ ψ u ]∪[ψ l π-δ].

[0181]

[0182] (C) Similarly, we can obtain the feasible arm angle range Ψ when the first arm angle function is a decreasing function i , this embodiment will not be described in detail.

[0183] The above embodiment introduces the feasible arm angle range of the i-th joint, i∈{1,3,5,7}. The following introduces the feasible arm angle range of the j-th joint, j∈{2,6}. Therefore, the method for calculating the feasible arm angle range of the 7-DOF manipulator provided in this embodiment also includes:

[0184] If the sine value of the joint angle of the j-th joint is not 0, the control device obtains the second arm angle corresponding to the second arm angle function and the minimum joint angle and maximum joint angle of the j-th joint, wherein the second arm angle function characterizes the constraint relationship between the joint angle and the arm angle of the j-th joint of the robotic arm, j∈{2,6}; according to the size relationship between the minimum joint angle, maximum joint angle of the j-th joint and the maximum value and minimum value of the second arm angle function, the function curve of the second arm angle function is obtained; according to the second arm angle and the function curve of the second arm angle function, the feasible arm angle range of the j-th joint is obtained.

[0185] For example, the second arm angle function that characterizes the relationship between the angles of the second and sixth joints and the arm angle is an arccosine function, and its expression is as follows:

[0186] θ i (ψ)=arccos(asinψ+bcosψ+c)(9)

[0187] Assuming m = asinψ + bcosψ + c, differentiating both sides of the second arm angle function with respect to ψ yields:

[0188]

[0189] (1) Based on the expression of the second arm angle function above, when sinθ i ≠0, the second arm angle function has two stationary points, and the function values at the stationary points are the maximum value θ max and the minimum value θ min Using the universal substitution formula, we can get the stationary point expression of the second arm angle function:

[0190]

[0191] Using the universal substitution formula, we can also get the following expression for the second arm angle function:

[0192]

[0193] Will and Substituting into formula (12), we can get the intersection of the upper and lower limits of the joint and the second arm angle function curve. max ,θ min and The size relationship between them, the feasible arm angle range Ψ iThe calculation of can be divided into 5 cases. The specific method is the same as the first arm angle function. The feasible arm angle Ψ is obtained when the two stationary point images change continuously. i The calculation method is the same as Figure 13 One possible scenario is shown.

[0194] (2) Based on the expression of the second arm angle function above, when sinθ i = 0, the second arm angle function has one stationary point and one singular point, and the singular point is a singular configuration of the manipulator. i = 0, the arm angle value ψ at the singular point can be obtained according to the following expression sing :

[0195]

[0196] When θ i =π, the arm angle value ψ at the singular point can be obtained according to the following expression sing :

[0197]

[0198] According to formula (11), the arm angle value ψ0 at the stationary point can be obtained. sing and ψ0 are respectively brought into equation (9), and the corresponding joint angle θ can be obtained. sing and θ0, according to θ sing and the size of θ0 will be θ sing and θ0 is set to the maximum value θ max and the minimum value θ min Finally, according to θ max ,θ min and The size relationship between them, the feasible arm angle range Ψ i The calculation of can be divided into 5 cases. The specific method is the same as the first arm angle function. The feasible arm angle Ψ is obtained when the two stationary point images change continuously. i The calculation method is the same as that of , which will not be described in detail in this embodiment. Figure 14 One possible scenario is shown.

[0199] Based on the same inventive concept as the method for calculating the feasible arm angle range of a 7-DOF manipulator provided in this embodiment, this embodiment also provides a device for calculating the feasible arm angle range of a 7-DOF manipulator, which includes at least one software function module that can be stored in the memory 21 or solidified in the electronic device in the form of software. The processor 22 in the electronic device is used to execute the executable module stored in the memory 21. For example, the software function modules and computer programs included in the device. Please refer to Figure 15 Functionally, the device can include:

[0200] A parameter acquisition module 11 is used to obtain target parameters in a stationary point expression of a first arm angle function, wherein the first arm angle function represents the constraint relationship between the joint angle of the i-th joint of the robotic arm and the arm angle, i∈{1,3,5,7};

[0201] The arm angle range module 12 is used to determine the feasible arm angle range of each joint to avoid joint limits and singular conditions based on the function curve under each relationship between the target parameter and the preset threshold, wherein the preset threshold Δ=1e-8.

[0202] In this embodiment, the parameter acquisition module 11 is used to implement Figure 6 In step S1, the arm angle range module 12 is used to implement Figure 6 For a detailed introduction to each of the above modules, please refer to the specific implementation of the corresponding step. In view of the fact that the method provided in this embodiment has the same inventive concept, the above modules can also be used to implement other steps or sub-steps of the method, and this embodiment will not go into details about this.

[0203] In addition, the functional modules in each embodiment of the present application can be integrated together to form an independent part, or each module can exist independently, or two or more modules can be integrated to form an independent part.

[0204] It should also be understood that if the above embodiments are implemented in the form of software function modules and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, or part of the technical solution, can be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present application.

[0205] Therefore, this embodiment further provides a storage medium, which is a computer-readable storage medium. The storage medium stores a computer program, which, when executed by a processor, implements the calculation of the feasible arm angle range of the 7-DOF manipulator provided in this embodiment. The storage medium can be a USB flash drive, a mobile hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk, among other media that can store program code.

[0206] This embodiment provides an electronic device for implementing a method for calculating the feasible arm angle range of a 7-DOF manipulator. Figure 16As shown, the electronic device may include a processor 22 and a memory 21. In addition, the memory 21 stores a computer program, and the processor implements the method for calculating the feasible arm angle range of the 7-DOF manipulator provided in this embodiment by reading and executing the computer program corresponding to the above embodiment in the memory 21.

[0207] Continue to see Figure 16 The electronic device further includes a communication unit 23. The memory 21, the processor 22 and the communication unit 23 are electrically connected to each other directly or indirectly via a system bus 24 to achieve data transmission or interaction.

[0208] The memory 21 may be an information recording device based on any electronic, magnetic, optical or other physical principles, for recording execution instructions, data, etc. In some embodiments, the memory 21 may be, but is not limited to, a volatile memory, a non-volatile memory, a storage drive, etc.

[0209] In some embodiments, the volatile memory may be a random access memory (RAM); in some embodiments, the non-volatile memory may be a read-only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), a flash memory, etc.; in some embodiments, the storage drive may be a magnetic disk drive, a solid-state drive, any type of storage disk (such as a CD, DVD, etc.), or a similar storage medium, or a combination thereof.

[0210] The communication unit 23 is used to send and receive data through a network. In some embodiments, the network may include a wired network, a wireless network, a fiber optic network, a telecommunications network, an intranet, the Internet, a local area network (LAN), a wide area network (WAN), a wireless local area network (WLAN), a metropolitan area network (MAN), a wide area network (WAN), a public switched telephone network (PSTN), a Bluetooth network, a ZigBee network, or a near field communication (NFC) network, or any combination thereof. In some embodiments, the network may include one or more network access points. For example, the network may include a wired or wireless network access point, such as a base station and / or a network switching node, through which one or more components of the service request processing system can connect to the network to exchange data and / or information.

[0211] The processor 22 may be an integrated circuit chip having signal processing capabilities, and the processor may include one or more processing cores (e.g., a single-core processor or a multi-core processor). By way of example only, the processor may include a central processing unit (CPU), an application-specific integrated circuit (ASIC), an application-specific instruction set processor (ASIP), a graphics processing unit (GPU), a physical processing unit (PPU), a digital signal processor (DSP), a field programmable gate array (FPGA), a programmable logic device (PLD), a controller, a microcontroller unit, a reduced instruction set computer (RISC), or a microprocessor, or any combination thereof.

[0212] I understand. Figure 16The structure shown is for reference only. Figure 16 More or fewer components than shown, or with Figure 16 Different configurations shown. Figure 16 The components shown may be implemented in hardware, software, or a combination thereof.

[0213] It should be understood that the devices and methods disclosed in the above embodiments may also be implemented in other ways. The device embodiments described above are merely illustrative. For example, the flowcharts and block diagrams in the accompanying drawings show the possible architectures, functions, and operations of the devices, methods, and computer program products according to multiple embodiments of the present application. In this regard, each box in the flowchart or block diagram may represent a module, a program segment, or a portion of code, and the module, program segment, or a portion of code contains one or more executable instructions for implementing the specified logical functions. It should also be noted that in some alternative implementations, the functions marked in the boxes may also occur in an order different from that marked in the accompanying drawings. For example, two consecutive boxes may actually be executed substantially in parallel, or they may sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or flowchart, and the combination of boxes in the block diagram and / or flowchart, may be implemented using a dedicated hardware-based system that performs the specified functions or actions, or may be implemented using a combination of dedicated hardware and computer instructions.

[0214] The above are merely various embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of this application. Therefore, the scope of protection of this application should be based on the scope of protection of the claims.

Claims

1. A method for calculating the feasible arm angle range of a 7-DOF manipulator, characterized in that: The seven joints of the robotic arm are respectively referred to as joint, The larger the value, the closer to the end of the robot arm. A positive integer, the method comprising: Obtain the target parameter in the stationary point expression of the first arm angle function, wherein the first arm angle function represents the first The constraint relationship between the joint angle and the arm angle of the joint, ; The stationary point expression of the first arm angle function is: Where, Indicates a stationary point. , , , are the coefficients in the inverse expressions of the 1st, 3rd, 5th and 7th joints, is the target parameter; According to the function curve under each relationship between the target parameter and the preset threshold, the feasible arm angle range of each joint to avoid the joint limit and singular condition is determined, wherein the preset threshold , which includes: If the target parameter is greater than the preset threshold, and the The joint angle of the joint is in the interval When it is within , the maximum and minimum values of the first arm angle function are calculated; According to The relationship between the minimum joint angle, the maximum joint angle and the maximum and minimum values of the first arm angle function is obtained, and the first function curve of the first arm angle function in 5 cases is obtained, wherein the maximum value of the first arm angle function at the stationary point , minimum value With the said Upper limit of joint , lower limit The five situations in between include: Case 1, and ; Case 2, and ; Case 3, and ; Case 4, and ; Case 5, or ; Calculate the first arm angle function and the The first arm angle corresponding to the minimum joint angle and the maximum joint angle of the joint; Taking the first arm angle as the interval endpoint, determine the The feasible range of the arm angle of the joint under the constraint of the first function curve; If the target parameter is greater than the preset threshold, and the The joint angle of the joint is in the interval When the first arm angle function is outside the range of , the local maximum and local minimum of the first arm angle function are calculated, wherein the first The joint angle of the joint exceeds When , the function curve of the first arm angle function will suddenly change; According to The relationship between the minimum joint angle, the maximum joint angle and the local maximum and local minimum of the first arm angle function is obtained to obtain the second function curve of the first arm angle function under 6 conditions, wherein the local maximum of the first arm angle function at the stationary point is , local minimum With the said Upper limit of joint and lower limit The six situations include: Case 1, and ; Case 2, and ; Case 3, and ; Case 4, and ; Case 5, and ; Case 6, and ; Calculate the first arm angle function and the The first arm angle corresponding to the minimum joint angle and the maximum joint angle of the joint; Taking the first arm angle as the interval endpoint, determine the The feasible range of the arm angle of the joint under the constraints of the second function curve.

2. The method for calculating the feasible arm angle range of a 7-DOF manipulator according to claim 1, characterized in that: The determining of the feasible arm angle range of each joint to avoid joint limits and singular conditions based on the function curve under each relationship between the target parameter and the preset threshold comprises: If the target parameter is less than the negative preset threshold, the first arm angle function and the first The first arm angle corresponding to the minimum joint angle and the maximum joint angle of the joint; According to the said Minimum joint angle, maximum joint angle and interval of joints , and obtain the third function curve of the first arm angle function; Taking the first arm angle as the interval endpoint, determine the The feasible range of the arm angle of the joint under the constraints of the third function curve.

3. The method for calculating the feasible arm angle range of a 7-DOF manipulator according to claim 1, characterized in that: The determining of the feasible arm angle range of each joint to avoid joint limits and singular conditions based on the function curve under each relationship between the target parameter and the preset threshold comprises: If the target parameter is greater than the negative preset threshold and less than the preset threshold, the singular arm angle of the first arm angle function at the singular stationary point is obtained, and the first arm angle function is obtained according to the singular arm angle. The arm angle exclusion interval of the joint; According to the said Minimum joint angle, maximum joint angle and interval of joints The size relationship and the The mutation angle corresponding to the joint and the singular arm angle is used to obtain a fourth function curve of the first arm angle function; Calculate the first arm angle function and the The first arm angle corresponding to the minimum joint angle and the maximum joint angle of the joint; Taking the first arm angle as the interval endpoint, determine the The feasible range of the arm angle of the joint under the constraints of the fourth function curve.

4. The method for calculating the feasible arm angle range of a 7-DOF manipulator according to claim 3, characterized in that: Arm angle exclusion range The calculation expression is: 。 5. The method for calculating the feasible arm angle range of a 7-DOF manipulator according to claim 1, characterized in that: The method further comprises: Jordi If the cosine value of the joint angle is not 0, the second arm angle function is obtained. The second arm angle corresponding to the minimum joint angle and the maximum joint angle of the joint, wherein the second arm angle function represents the second arm angle of the robot arm The constraint relationship between the joint angle and the arm angle of the joint, ; According to the said The relationship between the minimum joint angle and the maximum joint angle of the joint and the maximum and minimum values of the second arm angle function is used to obtain a function curve of the second arm angle function; According to the function curve of the second arm angle and the second arm angle function, the second arm angle function is obtained. The range of possible arm angles for the joint.

6. A device for calculating the feasible arm angle range of a 7-DOF manipulator, characterized in that: The seven joints of the robotic arm are respectively referred to as joint, The larger the value, the closer it is to the end of the robotic arm. A positive integer, the device comprises: The parameter acquisition module is used to obtain the target parameters in the stationary point expression of the first arm angle function, wherein the first arm angle function represents the first The constraint relationship between the joint angle and the arm angle of the joint, ; The stationary point expression of the first arm angle function is: Where, Indicates a stationary point. , , , are the coefficients in the inverse expressions of the 1st, 3rd, 5th and 7th joints, is the target parameter; The arm angle range module is used to determine the feasible arm angle range of each joint to avoid joint limits and singular conditions based on the function curve under each relationship between the target parameter and the preset threshold, wherein the preset threshold , this step includes: If the target parameter is greater than the preset threshold, and the The joint angle of the joint is in the interval When it is within , the maximum and minimum values of the first arm angle function are calculated; According to The relationship between the minimum joint angle, the maximum joint angle and the maximum and minimum values of the first arm angle function is obtained, and the first function curve of the first arm angle function in 5 cases is obtained, wherein the maximum value of the first arm angle function at the stationary point , minimum value With the said Upper limit of joint , lower limit The five situations include: Case 1, and ; Case 2, and ; Case 3, and ; Case 4, and ; Case 5, or ; Calculate the first arm angle function and the The first arm angle corresponding to the minimum joint angle and the maximum joint angle of the joint; Taking the first arm angle as the interval endpoint, determine the The feasible range of the arm angle of the joint under the constraint of the first function curve; If the target parameter is greater than the preset threshold, and the The joint angle of the joint is in the interval When the first arm angle function is outside the range of , the local maximum and local minimum of the first arm angle function are calculated, wherein the first The joint angle of the joint exceeds When , the function curve of the first arm angle function will suddenly change; According to The relationship between the minimum joint angle, the maximum joint angle and the local maximum and local minimum of the first arm angle function is obtained to obtain the second function curve of the first arm angle function under 6 conditions, wherein the local maximum of the first arm angle function at the stationary point is , local minimum With the said Upper limit of joint and lower limit The six situations include: Case 1, and ; Case 2, and ; Case 3, and ; Case 4, and ; Case 5, and ; Case 6, and ; Calculate the first arm angle function and the The first arm angle corresponding to the minimum joint angle and the maximum joint angle of the joint; Taking the first arm angle as the interval endpoint, determine the The feasible range of the arm angle of the joint under the constraints of the second function curve.

7. A storage medium, characterized in that: The storage medium stores a computer program, and when the computer program is executed by the processor, it implements the method for calculating the feasible arm angle range of a 7-degree-of-freedom robotic arm according to any one of claims 1 to 5.

8. An electronic device, characterized in that: The electronic device includes a processor and a memory, the memory stores a computer program, and when the computer program is executed by the processor, the method for calculating the feasible arm angle range of a 7-degree-of-freedom robotic arm described in any one of claims 1 to 5 is implemented.

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