Rigid body rotation motion design method based on singular mixed quaternion spline

Abstract

The invention discloses a rigid body rotation motion design method based on a singular mixed quaternion spline curve. The rigid body rotation motion design method comprises the following steps: S1, defining a cumulative form of a parameter-containing quartic interpolation spline curve deployment function based on a Bernstein primary function and a singular mixed function; s2, setting key frame data in the rotating motion process of n + 1 rigid bodies, and obtaining a second-order continuous parameter-containing singular mixed quaternion interpolation spline curve; and S3, setting specific values of the global parameters and the local parameters to obtain a rotational motion track of any point on the rigid body so as to complete the rotational motion design of the rigid body. According to the method, the second-order continuous rigid body motion attitude can be constructed by only needing given key frame data, a control vertex does not need to be adjusted, the global shape and the local shape of the curve can be adjusted at the same time by only changing the values of the global parameters and the local parameters, and the operation difficulty is reduced; complex calculation is not needed, the rigid body rotation motion posture can be directly designed according to requirements, and the operation efficiency is improved.

Description

Technical Field

[0001] The invention relates to the technical field of computer animation and simulation, and in particular to a rigid body rotation motion design method based on a singular mixed quaternion spline curve. Background Art

[0002] In the field of computer animation design and robot path planning, the planning problem of the target object's motion trajectory has attracted much attention. In the existing technologies involving the planning of the target object's motion trajectory, there are many spline curves with good properties in Euclidean space, such as classic spline curves such as Bézier and B-spline. Based on this, researchers have proposed a variety of methods for constructing unit quaternion interpolation spline curves, such as direct construction method and local construction method. However, these methods have limitations to varying degrees in application. For example, some methods lack flexibility in regulating the shape of spline curves, so their application scope is limited; some methods need to solve nonlinear equations through iteration to obtain the position information of key frames, making the calculation more complicated. Other methods need to set the position information and guide vector information of key frames in advance, and the corresponding conditions should be met to ensure the smoothness of rigid body rotation. Summary of the invention

[0003] The present invention provides a method for designing rigid body rotational motion based on singular mixed quaternion spline curves, so as to overcome the technical problems existing in the prior art in the fields of computer animation design and robot path planning, such as lack of flexibility in regulating the shape of spline curves, more complex calculations, and the need to set the position information and guide vector information of key frames in advance, while satisfying corresponding conditions to ensure the smoothness of the rigid body rotational motion.

[0004] In order to achieve the above object, the technical solution of the present invention is:

[0005] A method for designing rigid body rotational motion based on singular mixed quaternion spline curves, the specific steps comprising:

[0006] S1: Define the cumulative form of the parameterized quartic interpolation spline curve adjustment function based on the Bernstein basis function and the singular mixing function;

[0007] S2: setting key frame data of n+1 rigid body rotational motion processes, and obtaining a second-order continuous parameter-containing singular mixed quaternion interpolation spline curve according to the cumulative form of the key frame data and the parameter-containing quartic interpolation spline curve deployment function;

[0008] S3: setting specific values ​​of global parameters and local parameters in the parametric singular hybrid quaternion interpolation spline curve to obtain the rotational motion trajectory of any point on the rigid body, thereby completing the rigid body rotational motion design.

[0009] Furthermore, in S1, the process of defining the cumulative form of the parameterized quartic interpolation spline curve adjustment function based on the Bernstein basis function and the singular mixing function is as follows:

[0010] The deployment function of the quartic singular hybrid interpolation spline curve is defined based on the Bernstein basis function and is expressed as:

[0011]

[0012] Where: i represents the i-th segment of the spline curve, and i=1,2,…,n; C i,0 (t), C i,1 (t), C i,2 (t) and C i,3 (t) represent the adjustment functions of the i-th segment of the spline curve; α1, α2, …, α n+1 represents the local parameter, α is the global parameter, and α∈(0,1);

[0013] is a quartic Bernstein basis function, l represents the index of the basis function, and l = 0, 1, ..., 4; t represents the time required to generate the i-th segment of the spline curve, and i = 1, 2, ..., n, n is the total number of segments of the spline curve;

[0014] Among them, the time t is segmented to define the second-order continuous singular mixing function R(t), which is expressed as:

[0015]

[0016] Where t0 represents the time required to generate the first i-1 segments of the spline curve;

[0017] Based on the adjustment function of the quartic singular hybrid interpolation spline curve and the second-order continuous singular hybrid function, the cumulative form of the parameter-containing quartic interpolation spline curve adjustment function is defined, which is expressed as:

[0018]

[0019] in, Based on the deployment function C i,j (t), the cumulative form of j = 0, 1, 2, 3.

[0020] Furthermore, in S2, key frame data of n+1 rigid body rotational motion processes are set, and the process of obtaining a second-order continuous parameterized singular mixed quaternion interpolation spline curve is as follows according to the cumulative form of the key frame data and the parameterized quartic interpolation spline curve deployment function:

[0021] S21: Set the key frame data of the n+1 rigid body rotation process to the unit quaternion sequence q1, q2, ..., q k ,…,q n+1 , which is the interpolation point sequence of rigid body rotation motion; key frame data q0 and q are added at the beginning and end of the unit quaternion sequence respectively. n+2 , and let q0=q1,q n+2 =q n+1 , get n+3 rigid body rotation motion key frame data;

[0022] Among them, q k =(w k ,x k ,y k ,z k ), k = 0, 1, ..., n + 2, qk represents the unit quaternion corresponding to the kth key frame data in the process of rigid body rotation; w k ,x k ,y k ,z k are the four real rotation components of the unit quaternion corresponding to the kth key frame data; n+3 represents the total number of interpolation points of rigid body rotation motion;

[0023] S22: constructing the i-th singular mixed quaternion curve according to the cumulative form of n+3 rigid body rotation motion key frame data and the parameter-containing quartic interpolation spline curve adjustment function;

[0024] S23: Obtain a second-order continuous parameter-containing singular mixed quaternion interpolation spline curve according to the i-th singular mixed quaternion curve.

[0025] Further, in S22, the i-th singular mixed quaternion curve constructed according to the cumulative form of n+3 rigid body rotation motion key frame data and the parameter-containing quartic interpolation spline curve adjustment function is expressed as:

[0026]

[0027] In the formula, is the key frame data of the given i-th singular hybrid quaternion curve; Based on the deployment function C i,j (t), the cumulative form of j = 0, 1, 2, 3.

[0028] Further, in S23, the second-order continuous parameter-containing singular mixed quaternion interpolation spline curve obtained according to the i-th singular mixed quaternion curve is expressed as:

[0029] Q(t)=Q i (t-i+1),i=1,2,…,n.

[0030] Further, in S3, specific values ​​of global parameters and local parameters in the parametric singular hybrid quaternion interpolation spline curve are set to obtain the rotational motion trajectory of any point on the rigid body, thereby completing the process of rigid body rotational motion design as follows:

[0031] S31: Select specific values ​​of global parameters and local parameters, and bring in the parameter-containing singular mixed quaternion spline curve Q(t), so as to obtain the posture corresponding to time t during the rigid body rotational motion;

[0032] S32: Establish a moving coordinate system on the rigid body, establish a global coordinate system in the three-dimensional Euclidean space where the rigid body moves, and obtain the point coordinates of any point A on the rigid body after rotation, expressed as:

[0033] u(t)=(0,p2(t))=Q(t)·(0,p1(t))·Q -1 (t)

[0034] Wherein, the symbol “·” represents quaternion multiplication; p1(t) represents the position coordinate of A at time t in the moving coordinate system, p1(t) = (x1(t), y1(t), z1(t)), x1(t), y1(t), z1(t) respectively correspond to the positions on the x-axis, y-axis and z-axis in the moving coordinate system; p2(t) represents the position coordinate of A at time t in the global coordinate system after rotational motion, p2(t) = (x2(t), y2(t), z2(t)), x2(t), y2(t), z2(t) respectively correspond to the positions on the x-axis, y-axis and z-axis in the global coordinate system after rotational motion;

[0035] S33: By obtaining the point coordinates u(t) obtained by the singular mixed quaternion interpolation spline curve at all times, the rotational motion trajectory curve can be continuously drawn to complete the design of the rigid body rotational motion process.

[0036] Beneficial effects: The present invention sets key frame data in the process of n+1 rigid body rotational motion, and obtains a second-order continuous parameterized singular mixed quaternion interpolation spline curve according to the cumulative form of the key frame data and the parameterized quartic interpolation spline curve adjustment function; the present invention can construct a second-order continuous rigid body motion posture without excessive restrictions when designing rigid body rotational motion, and only needs given key frame data; and there is no need to adjust the control vertices, only the values ​​of global parameters and local parameters are changed to simultaneously adjust the global and local shapes of the second-order continuous parameterized singular mixed quaternion interpolation spline curve, thereby reducing the difficulty of operation; and the present invention does not require complex calculations, and can directly design the rigid body rotational motion posture according to needs, thereby improving the computing efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0038] Figure 1 It is a flow chart of a method for designing rigid body rotational motion based on singular mixed quaternion spline curves in the present invention;

[0039] Figure 2 It is a schematic diagram of isotemporal discretization of rigid body rotational motion when global parameters and local parameters have different values ​​in an embodiment of the present invention;

[0040] Figures 3 to 7 It is a schematic diagram of the rotation motion trajectory of the center point of a rigid body when the global parameters and the local parameters have different values ​​in an embodiment of the present invention. DETAILED DESCRIPTION

[0041] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution 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. 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.

[0042] In practice, quaternions have outstanding advantages over the Euler angle method and the rotation matrix method in the representation of three-dimensional rotations. They provide information about the rotation axis and angle in the form of a four-dimensional vector consisting of a real part and three imaginary parts, which not only simplifies mathematical operations, but also significantly improves the accuracy of the numerical calculation process. The quaternion spline curve constructed on its basis can effectively handle complex motion planning and trajectory design problems, and can accurately capture its motion characteristics when applied to rigid body posture transformation. Therefore, in-depth exploration of the construction principles and characteristics of quaternion spline curves will provide more efficient and accurate solutions for fields such as robot path planning, computer animation and simulation.

[0043] Based on the above principle, this embodiment provides a rigid body rotation motion design method based on singular mixed quaternion spline curve, such as Figure 1 As shown, the specific steps include:

[0044] S1: Define the cumulative form of the parameterized quartic interpolation spline curve adjustment function based on the Bernstein basis function and the singular mixing function;

[0045] S2: setting key frame data of n+1 rigid body rotational motion processes, and obtaining a second-order continuous parameter-containing singular mixed quaternion interpolation spline curve according to the cumulative form of the key frame data and the parameter-containing quartic interpolation spline curve deployment function;

[0046] S3: setting specific values ​​of global parameters and local parameters in the parametric singular hybrid quaternion interpolation spline curve to obtain the rotational motion trajectory of any point on the rigid body, thereby completing the rigid body rotational motion design.

[0047] In a specific embodiment, in S1, the process of defining the cumulative form of the parameterized quartic interpolation spline curve adjustment function based on the Bernstein basis function and the singular mixing function is:

[0048] The deployment function of the quartic singular hybrid interpolation spline curve is defined based on the Bernstein basis function and is expressed as:

[0049]

[0050] Where: i represents the i-th segment of the spline curve, and i=1,2,…,n; C i,0 (t), C i,1 (t), C i,2 (t) and C i,3 (t) represent the adjustment functions of the i-th segment of the spline curve; α1, α2, …, α n+1 represents the local parameter, α is the global parameter, and α∈(0,1);

[0051] is a quartic Bernstein basis function, l represents the index of the basis function, and l = 0, 1, ..., 4; t represents the time required to generate the i-th segment of the spline curve, and i = 1, 2, ..., n, n is the total number of segments of the spline curve;

[0052] Among them, the time t is segmented to define the second-order continuous singular mixing function R(t), which is expressed as:

[0053]

[0054] Where t0 represents the time required to generate the first i-1 segments of the spline curve;

[0055] Based on the adjustment function of the quartic singular hybrid interpolation spline curve and the second-order continuous singular hybrid function, the cumulative form of the parameter-containing quartic interpolation spline curve adjustment function is defined, which is expressed as:

[0056]

[0057] in, Based on the deployment function C i,j(t), the cumulative form of j = 0, 1, 2, 3.

[0058] In a specific embodiment, in S2, key frame data of n+1 rigid body rotational motion processes are set, and the process of obtaining a second-order continuous parameterized singular mixed quaternion interpolation spline curve is as follows according to the cumulative form of the key frame data and the parameterized quartic interpolation spline curve deployment function:

[0059] S21: Set the key frame data of the n+1 rigid body rotation process to the unit quaternion sequence q1, q2, ..., q k ,…,q n+1 , which is the interpolation point sequence of rigid body rotation motion;

[0060] To facilitate the overall construction, key frame data q0 and q are added at the beginning and end of the above unit quaternion sequence. n+2 , and let q0=q1,q n+2 =q n+1 , get n+3 rigid body rotation motion key frame data,

[0061] Among them, q k =(w k ,x k ,y k ,z k ), k = 0, 1, ..., n + 2, qk represents the unit quaternion corresponding to the kth key frame data in the process of rigid body rotation; w k ,x k ,y k ,z k are the four real rotation components of the unit quaternion corresponding to the kth key frame data; n+3 represents the total number of interpolation points of the rigid body rotation motion.

[0062] S22: constructing the i-th singular mixed quaternion curve according to the cumulative form of n+3 rigid body rotation motion key frame data and the parameter-containing quartic interpolation spline curve adjustment function;

[0063] In a specific embodiment, in S22, the process of constructing the i-th singular mixed quaternion curve according to the cumulative form of n+3 rigid body rotation motion key frame data and the parameter-containing quartic interpolation spline curve matching function is:

[0064]

[0065] In the formula, is the key frame data of the given i-th singular hybrid quaternion curve; Based on the deployment function C i,j (t), the cumulative form of j = 0, 1, 2, 3;

[0066] In this embodiment, in order to verify that each singular mixed quaternion curve can be connected to obtain a spline curve, the constant tangential velocity of the trajectory formed by adjacent key frame data in n+3 rigid body rotation motion key frame data is obtained:

[0067]

[0068] Where: k Represents the constant tangential velocity of the rigid body rotational motion from the k-1th key frame to the kth key frame; is the unit quaternion q corresponding to the k-1th key frame data k-1 The inverse of q k-1 The inverse transformation of

[0069] According to the constant tangential velocity of the trajectory formed by the adjacent key frame data, the zero-order derivative, the first-order derivative and the second-order derivative of the i-th singular mixed quaternion curve segment at the endpoint are calculated to obtain:

[0070]

[0071] From the above results, we can see that the zero-order derivatives, first-order derivatives and second-order derivatives of adjacent singular mixed quaternion curve segments at the splicing nodes are equal, that is, Where s=1,2 represents the order of the derivative of the i-th singular mixed quaternion curve segment. Based on this condition, each curve segment can be further connected to obtain a second-order continuous parameter-containing singular mixed quaternion interpolation spline curve.

[0072] S23: Obtain a second-order continuous parameter-containing singular mixed quaternion interpolation spline curve according to the i-th singular mixed quaternion curve.

[0073] In a specific embodiment, in S23, the second-order continuous parameter-containing singular mixed quaternion interpolation spline curve obtained according to the i-th singular mixed quaternion curve is expressed as:

[0074] Q(t)=Q i (t-i+1),i=1,2,…,n.

[0075] Based on the above formula, we can know that the singular mixed quaternion interpolation spline curve Q(t) is composed of n segments Q i (t) is obtained by splicing the first and last parts in sequence.

[0076] Specifically, from the calculation results of the zero-order derivative, the first-order derivative and the second-order derivative of the i-th singular mixed quaternion curve segment at the endpoint, it can be known that the spline curve spliced ​​by these curve segments satisfies the second-order continuity property.

[0077] In a specific embodiment, in S3, the specific values ​​of the global parameters and local parameters in the parametric singular mixed quaternion interpolation spline curve are set to obtain the rotational motion trajectory of any point on the rigid body, thereby completing the process of rigid body rotational motion design:

[0078] S31: Select specific values ​​of global parameters and local parameters, and bring in the parameter-containing singular mixed quaternion spline curve Q(t), so as to obtain the posture corresponding to time t during the rigid body rotational motion;

[0079] S32: Establish a moving coordinate system on the rigid body, establish a global coordinate system in the three-dimensional Euclidean space where the rigid body moves, and obtain the point coordinates of any point A on the rigid body after rotation, expressed as:

[0080] u(t)=(0,p2(t))=Q(t)·(0,p1(t))·Q -1 (t)

[0081] Wherein, the symbol “·” represents quaternion multiplication; p1(t) represents the position coordinate of A at time t in the moving coordinate system, p1(t) = (x1(t), y1(t), z1(t)), x1(t), y1(t), z1(t) respectively correspond to the positions on the x-axis, y-axis and z-axis in the moving coordinate system; p2(t) represents the position coordinate of A at time t in the global coordinate system after rotational motion, p2(t) = (x2(t), y2(t), z2(t)), x2(t), y2(t), z2(t) respectively correspond to the positions on the x-axis, y-axis and z-axis in the global coordinate system after rotational motion;

[0082] S33: By obtaining the point coordinates u(t) obtained by the singular mixed quaternion interpolation spline curve at all times, the rotational motion trajectory curve can be continuously drawn to complete the design of the rigid body rotational motion process.

[0083] Specifically, in the embodiment of the present invention, when the local parameters are all 0.45*[1,1,1,1], the global parameters are adjusted. The experimental results are as follows: Figure 2 As shown, Figure 2 (a) to Figure 2 In (c), the global parameter α is set to 0.9, 0.5, and 0.1, respectively, corresponding to Figure 3 The blue, red and yellow curves. Figure 3 It can be seen from the figure that as the global parameter α increases, the rotational motion trajectory curve on both sides of the key frame changes from expanding outward to contracting inward. The closer α is to 1, the sharper the rotational motion trajectory curve is at the interpolation point. In particular, when α = 0.5, the trajectory curve is smoothly connected. When the global parameter is selected as 0.5, the local parameters are adjusted. The experimental results are as follows: Figure 2 As shown, Figure 2 (d) to Figure 2 (g) shows the local changes of the rigid body rotation motion when adjusting the local parameters, where the local parameters [α1, α2, α3, α4] are 0.4*[1,0,1,1], 0.4*[1,1,1,1], 0.6*[1,1,1,1], 0.6*[1,1,0,1] respectively. Figure 4 As shown, the local parameters are 2.5*[1,1,1,1], 2*[1,1,1,1] and 1.5*[1,1,1,1] corresponding to the blue curve, red curve and yellow curve respectively; Figure 5 As shown, the local parameters are -0.5*[1,1,1,1], -1*[1,1,1,1] and -1.5*[1,1,1,1] corresponding to the blue curve, red curve and yellow curve respectively; Figure 6 As shown, the local parameters are 0.6*[1,1,1,1], 0.4*[1,1,1,1] and 0.2*[1,1,1,1] corresponding to the blue curve, red curve and yellow curve respectively; Figure 7 As shown, the local parameters are 0.4*[1,2,1,1], 0.4*[1,1,1,1] and 0.4*[1,1,0,1] corresponding to the blue curve, red curve and yellow curve respectively. Figures 4 to 7 It can be seen that the smaller the local parameter, the sharper the rotation trajectory curve will be at the key frame; the larger the local parameter, the rotation trajectory curve will show obvious bulges on both sides of the key frame. Figures 3 to 7 It can be seen that when a local parameter is adjusted alone, only the trajectories of two adjacent curve segments will change, so this solution is convenient for adjusting the shape of the local curve.

[0084] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for designing rigid body rotational motion based on singular mixed quaternion spline curves, characterized in that: The specific steps include: S1: Define the cumulative form of the parameterized quartic interpolation spline curve adjustment function based on the Bernstein basis function and the singular mixing function; S2: setting key frame data of n+1 rigid body rotational motion processes, and obtaining a second-order continuous parameter-containing singular mixed quaternion interpolation spline curve according to the cumulative form of the key frame data and the parameter-containing quartic interpolation spline curve deployment function; S3: setting specific values ​​of global parameters and local parameters in the parametric singular hybrid quaternion interpolation spline curve to obtain the rotational motion trajectory of any point on the rigid body, thereby completing the rigid body rotational motion design.

2. The method for designing rigid body rotational motion based on singular mixed quaternion spline curve according to claim 1, characterized in that: In S1, the process of defining the cumulative form of the parameterized quartic interpolation spline curve adjustment function based on the Bernstein basis function and the singular mixing function is: The deployment function of the quartic singular hybrid interpolation spline curve is defined based on the Bernstein basis function and is expressed as: Where: i represents the i-th segment of the spline curve, and i=1,2,…,n; C i,0 (t), C i,1 (t), C i,2 (t) and C i,3 (t) represents the adjustment function of the i-th segment of the spline curve; α1, α2, …, α n+1 represents the local parameter, α is the global parameter, and α∈(0,1); is a quartic Bernstein basis function, l represents the index of the basis function, and l = 0, 1, ..., 4; t represents the time required to generate the i-th segment of the spline curve, and i = 1, 2, ..., n, n is the total number of segments of the spline curve; Among them, the time t is segmented to define the second-order continuous singular mixing function R(t), which is expressed as: Where t0 represents the time required to generate the first i-1 segments of the spline curve; Based on the adjustment function of the quartic singular hybrid interpolation spline curve and the second-order continuous singular hybrid function, the cumulative form of the parameter-containing quartic interpolation spline curve adjustment function is defined, which is expressed as: in, Based on the deployment function C i,j (t), the cumulative form of j = 0, 1, 2, 3.

3. The method for designing rigid body rotational motion based on singular mixed quaternion spline curve according to claim 2, characterized in that: In S2, the key frame data of n+1 rigid body rotational motion processes are set, and the process of obtaining the second-order continuous parameter-containing singular mixed quaternion interpolation spline curve is as follows according to the cumulative form of the key frame data and the parameter-containing quartic interpolation spline curve deployment function: S21: Set the key frame data of the n+1 rigid body rotation process to the unit quaternion sequence q1, q2, ..., q k ,…,q n+1 , which is the interpolation point sequence of rigid body rotation motion; key frame data q0 and q are added at the beginning and end of the unit quaternion sequence respectively. n+2 , and let q0=q1,q n+2 =q n+1 , get n+3 rigid body rotation motion key frame data; Among them, q k =(w k ,x k ,y k ,z k ), k=0,1,…,n+2,q k Represents the unit quaternion corresponding to the kth key frame data during the rigid body rotational motion; w k ,x k ,y k ,z k are the four real rotation components of the unit quaternion corresponding to the kth key frame data; n+3 represents the total number of interpolation points of rigid body rotation motion; S22: constructing the i-th singular mixed quaternion curve according to the cumulative form of n+3 rigid body rotation motion key frame data and the parameter-containing quartic interpolation spline curve adjustment function; S23: Obtain a second-order continuous parameter-containing singular mixed quaternion interpolation spline curve according to the i-th singular mixed quaternion curve.

4. The method for designing rigid body rotational motion based on singular mixed quaternion spline curve according to claim 3, characterized in that: In S22, the i-th singular mixed quaternion curve constructed according to the cumulative form of n+3 rigid body rotation motion key frame data and the parameter-containing quartic interpolation spline curve adjustment function is expressed as: In the formula, is the key frame data of the given i-th singular hybrid quaternion curve; Based on the deployment function C i,j (t), the cumulative form of j = 0, 1, 2, 3.

5. The method for designing rigid body rotational motion based on singular mixed quaternion spline curve according to claim 4, characterized in that: In S23, the second-order continuous parameter-containing singular mixed quaternion interpolation spline curve obtained according to the i-th singular mixed quaternion curve is expressed as: Q(t)=Q i (t-i+1),i=1,2,…,n。 6. The method for designing rigid body rotational motion based on singular mixed quaternion spline curve according to claim 5, characterized in that: In S3, the specific values ​​of the global parameters and local parameters in the parametric singular hybrid quaternion interpolation spline curve are set to obtain the rotational motion trajectory of any point on the rigid body, thereby completing the process of rigid body rotational motion design: S31: Select specific values ​​of global parameters and local parameters, and bring in the parameter-containing singular mixed quaternion spline curve Q(t), so as to obtain the posture corresponding to time t during the rigid body rotational motion; S32: Establish a moving coordinate system on the rigid body, establish a global coordinate system in the three-dimensional Euclidean space where the rigid body moves, and obtain the point coordinates of any point A on the rigid body after rotation, expressed as: u(t)=(0,p2(t))=Q(t)·(0,p1(t))·Q -1 (t) Wherein, the symbol "·" represents quaternion multiplication; p1(t) represents the position coordinate of A at time t in the moving coordinate system, p1(t) = (x1(t), y1(t), z1(t)), x1(t), y1(t), z1(t) respectively correspond to the positions on the x-axis, y-axis and z-axis in the moving coordinate system; p2(t) represents the position coordinate of A at time t in the global coordinate system after rotational motion, p2(t) = (x2(t), y2(t), z2(t)), x2(t), y2(t), z2(t) respectively correspond to the positions on the x-axis, y-axis and z-axis in the global coordinate system after rotational motion; S33: By obtaining the point coordinates u(t) obtained by the singular mixed quaternion interpolation spline curve at all times, the rotational motion trajectory curve can be continuously drawn to complete the design of the rigid body rotational motion process.

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