Shape control method

Abstract

To provide a shape control method for deforming a filament into a desired shape.SOLUTION: A shape control method S11 performs: a basic rotation / vibration process S12 in which an end of a filament is vibrated in a direction along a reference axis while rotating the end of the filament around the reference axis; and a same position process S13 for a prescribed direction for so controlling that the filament is located at a same position in the direction along the reference axis when the filament is located in the prescribed direction around the reference axis.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to a shape control method. [Background technology]

[0002] Conventionally, a propulsion method that extends multiple electrically charged tethers (wires, linear bodies) from a spacecraft and utilizes the repulsive force between them and charged particles in the solar wind is called an electric sail. Separately, a device that connects multiple spacecraft with tethers is called a tether system (see, for example, Non-Patent Documents 1 and 2). Tethers can be used for tether propulsion, which utilizes the interaction between the electric current flowing through the tether and the planet's magnetic field (Lorentz force). Other uses of tethers include accelerating a spacecraft by detaching the tip of a rapidly rotating tether, or conversely, rotobata, which uses the tip of a tether to capture and decelerate an object coming from outside. [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] Marco Bassetto, Lorenzo Niccolai, Alessandro A. Quarta, Giovanni. Mengali, “A comprehensive review of Electric Solar Wind Sail concept and its applications”, Progress in Aerospace Sciences, 128 (2022), p. 1-27, 2022. [Non-patent document 2] MP Cartmell and DJ McKenzie, “A review of space tether research”, Progress in Aerospace Sciences, 44 (2008), p. 1-21 Summary of the Invention [Problem to be solved by the invention]

[0004] However, because tethers are flexible structures, they must be tensioned in some way and used in a linearly stretched state. If the shape of a tether could be changed to a curved surface in an inertial frame, its applications would be further expanded, but such technology does not exist.

[0005] The present invention has been made in view of the above problems, and has an object to provide a shape control method for deforming a linear object into a desired shape. [Means for solving the problem]

[0006] In order to solve the above problems, the present invention proposes the following means. (1) Aspect 1 of the present invention is a shape control method that includes a basic rotation / vibration process for rotating an end of a linear body around a reference axis while vibrating the end of the linear body in a direction along the reference axis, and a uniform position process for a predetermined orientation for controlling the linear body so that it is positioned in the same position in a direction along the reference axis when the linear body is positioned in a predetermined orientation around the reference axis. In this invention, a basic rotation / vibration process is performed, rotating the end of the linear body around a reference axis while vibrating the end of the linear body in a direction along the reference axis. In this state, a uniform position process for a predetermined orientation is performed, and when the linear body is positioned in a predetermined orientation around the reference axis, the linear body is controlled so that it is positioned in the same position in the direction along the reference axis. Then, in an inertial system, the linear body rotating around the reference axis moves on a predetermined curved surface, and the trajectory that the linear body passes through has a constant shape. Therefore, the linear body can be deformed into a desired shape.

[0007] (2) Aspect 2 of the present invention may be a shape control method as described in (1), in which, as the basic rotation / vibration process and the same position process with respect to the predetermined direction, the displacement w(r, t) of the linear body in a direction along the reference axis is controlled so as to satisfy equation (2) obtained using equation (1). where ω0 is the angular frequency that vibrates the end of the linear body in a direction along the reference axis, A0 and α0 are constants, r and x are the coordinates of the linear body in the radial direction perpendicular to the reference axis, Ω is the rotation speed of the linear body around the reference axis, m is a natural number, t is time, and H n (ω0) is the frequency response function of the linear body, and Φ n (x) is the nth eigenfunction of the linear field.

[0008]

number

[0009] In this invention, the inventors have intensively studied a method for controlling the shape of a linear body when the end of the linear body is rotated around a reference axis and vibrated in a direction along the reference axis, based on a known equation of motion and a general solution of free vibration for the linear body. As a result, by controlling the displacement w(r, t) to satisfy equation (2) obtained using equation (1) as a basic rotation / vibration process and an identical position process with respect to a predetermined direction, it is possible to deform the linear body into a certain shape with equation (2) as a predetermined curved surface.

[0010] (3) Aspect 3 of the present invention may be a shape control method as described in (1), in which, as the basic rotation / vibration process and the same position process with respect to the predetermined direction, the displacements w(r, t) of the multiple linear bodies arranged around the reference axis in a direction along the reference axis are controlled so as to satisfy equation (4) obtained using equation (3). where ω0 is the angular frequency that vibrates the end of the linear body in a direction along the reference axis, A0 and α0 are constants, r and x are coordinates of the linear body in a direction perpendicular to the reference axis, m is a natural number, θ is the coordinate of each linear body around the reference axis, t is time, and H n (ω0) is the frequency response function of the linear body, and Φ n (x) is the nth eigenfunction of the linear field.

[0011]

number

[0012] In this invention, the inventors have intensively studied a method for controlling the shape of a linear body when the ends of multiple linear bodies are rotated around a reference axis while vibrating the ends of multiple linear bodies in a direction along the reference axis, based on a known equation of motion and a general solution of free vibration for the linear body. As a result, by controlling the displacement w(r, θ, t) to satisfy equation (4) obtained using equation (3) as the basic rotation / vibration process and the same position process with respect to a predetermined direction, it is possible to control multiple linear bodies into a certain shape with equation (4) as a predetermined curved surface.

[0013] (4) Aspect 4 of the present invention is a shape control method that includes a basic rotation / vibration process for rotating an end of a linear body around a reference axis while vibrating the end of the linear body in a direction along the reference axis, and an identical position process for a shifted position for controlling the position of the linear body in a direction along the reference axis when the linear body is arranged in a predetermined orientation around the reference axis to be equal to the position of the linear body in a direction along the reference axis when the linear body is further rotated around the reference axis to a position shifted by one rotation plus a displacement angle. In this invention, a basic rotation / vibration process is performed, rotating the end of the linear body around a reference axis while vibrating the end of the linear body in a direction along the reference axis. In this state, a matching process is performed for the shifted position, and the position of the linear body in a direction along the reference axis when the linear body is arranged in a predetermined direction around the reference axis is controlled to be equal to the position of the linear body in a direction along the reference axis when the linear body is further rotated around the reference axis to a position shifted by one rotation plus a displacement angle. Then, in an inertial system, the linear body rotating around the reference axis moves on a predetermined curved surface rotating around the reference axis at a predetermined speed, and the trajectory traveled by the linear body becomes a fixed shape rotating around the reference axis. Therefore, the linear body can be deformed into a desired shape. [Effects of the Invention]

[0014] The shape control method of the present invention can deform a linear object into a desired shape. [Brief explanation of the drawings]

[0015] [Figure 1] 1 is a perspective view of a plurality of linear bodies whose shapes are controlled by a shape control method according to an embodiment of the present invention, when the linear bodies are rotated around a reference axis. [Figure 2] 10 is a flowchart showing the shape control method. [Figure 3] 10 is a perspective view of a plurality of linear bodies when they are rotated around a reference axis and vibrated in a direction along the reference axis. FIG. [Figure 4] FIG. 2 is a diagram illustrating an x-axis and a z-axis defined for a linear body. [Figure 5] 10A and 10B are diagrams illustrating the balance conditions of forces acting on minute line elements of a linear body. DETAILED DESCRIPTION OF THE INVENTION

[0016] Hereinafter, one embodiment of a shape control method according to the present invention will be described with reference to FIGS.

[0017] [1. A specified curved surface on which multiple linear bodies move] In this shape control method, for example, the shapes of a plurality of linear bodies 100 shown in Fig. 1 are controlled. Fig. 1 shows an example of a shape control device 1 that controls the shapes of a plurality of linear bodies 100. Note that the configuration of shape control device 1 is not limited as long as it can rotate the ends of a plurality of linear bodies 100 around a reference axis O1 or vibrate them in a direction along the reference axis O1.

[0018] Here, in a linear body in its natural state (flattened) without external forces, the direction in which it has the longest dimension is called the longest direction, and the direction in which it has the shortest dimension is called the shortest direction. The directions perpendicular to the longest and shortest directions are called the orthogonal directions. For example, the linear body referred to here means a shape in which the length in the orthogonal direction is 1 to 10 times the length in the shortest direction, and the length in the longest direction is 2 or more times the length in the orthogonal direction. The linear body also includes so-called strip-shaped objects (strips).

[0019] For example, linear body 100 is formed in a linear shape from polyimide resin. For example, linear body 100 is a rope (tether). It is preferable that a conductive member is embedded in linear body 100. In this case, a spacecraft using the shape control device can be used as an electric sail. If the width of the linear body is relatively wide, it is preferable that the outer surface of the linear body is provided with a coating or the like having a relatively high reflectivity. In this case, the spacecraft can be used as a heliogyro (a space helicopter) by propelling it by reflecting sunlight with the linear body.

[0020] In the shape control method, the ends of a plurality of linear bodies 100 are rotated around a reference axis O1. The plurality of linear bodies 100 are arranged around the reference axis O1. It is preferable that the plurality of linear bodies 100 are arranged at equal angles around the reference axis O1. Hereinafter, when the plurality of linear bodies 100 are to be distinguished from one another, they may be referred to as linear bodies 100A, 100B, 100C, ... around the reference axis O1. When viewed from the direction along the reference axis O1, the angular difference between linear body 100B, 100C, . . . and linear body 100A about the reference axis O1 is defined as θ B ,θ C ,... as stipulated. Shape control device 1 holds the ends of a plurality of linear bodies 100. As shown in FIG. 1, in an inertial system, when ends of multiple linear bodies 100 are rotated around reference axis O1, predetermined curved surface S1 along which multiple linear bodies 100 move becomes a flat surface. Hereinafter, when viewing multiple linear bodies 100 from a direction along reference axis O1, a direction perpendicular to reference axis O1 will be referred to as a radial direction, and a direction going around reference axis O1 will be referred to as a circumferential direction.

[0021] As shown in Figure 2, in this shape control method S11, in the basic rotation / vibration step S12, in an inertial system, the ends of multiple linear bodies 100 are rotated in a predetermined direction around a reference axis O1 while vibrating the ends of the linear bodies 100 in a direction along the reference axis O1. In this shape control method S11, when the basic rotation / vibration process S12 is performed, in the same position process S13 relative to a predetermined orientation, when the linear body 100A is positioned in a predetermined orientation around the reference axis O1 in an inertial system, the linear body 100A is controlled so that it is positioned in the same position in the direction along the reference axis O1 regardless of its radial position, regardless of the rotation speed of the linear body 100A around the reference axis O1. 3, in the inertial frame, linear body 100A rotating about reference axis O1 moves on predetermined curved surface S5, and the path traveled by linear body 100A has a fixed shape. In the inertial frame, predetermined curved surface S5 is stationary. For example, the predetermined curved surface S5 has two peaks S6 and two valleys S7 in the inertial system. At the peaks S6, the predetermined curved surface S5 protrudes toward a first side in the direction along the reference axis O1. At the valleys S7, the predetermined curved surface S5 protrudes toward a second side opposite to the first side in the direction along the reference axis O1.

[0022] Furthermore, for linear bodies 100B, 100C, ..., in a standing wave angle difference same position step S14 (see FIG. 2), an angle difference θ is calculated in the predetermined direction around reference axis O1 on predetermined curved surface S5 with respect to the position of linear body 100A on predetermined curved surface S5 at a predetermined time in the inertial system. B ,θ C , ...and control linear bodies 100B, 100C, ...to be placed at the rotated positions, respectively. In the shape control method S11, the basic rotation / vibration step S12, the same position step S13 relative to a predetermined direction, and the standing wave angle difference same position step S14 are carried out simultaneously.

[0023] The waveform of a plurality of linear bodies 100 passing on a predetermined curved surface S5 that is stationary in an inertial system is called a standing wave. In an inertial system, multiple linear bodies 100 rotating around reference axis O1 may move on a predetermined curved surface rotating at a predetermined speed around reference axis O1. In an inertial system, when the entire shape of linear bodies 100 passes through a predetermined curved surface rotating around reference axis O1, the waveform of multiple linear bodies 100 is called a quasi-standing wave. A method for controlling the shape of linear body 100 taking into consideration the equation of motion of linear body 100 will be described below.

[0024] 2. Shape control method of a linear body taking into account the equation of motion of the linear body [2.1. Equation of motion of a linear body] In the units of length and the like described below, SI units such as "m" are preferably used for length. As shown in Fig. 4, for one linear body 100, the x-axis is defined as the longitudinal direction of the linear body 100. The first end of the linear body 100 is defined as the origin of the x-axis, and the direction from the first end to the second end of the linear body 100 is defined as the positive direction of the x-axis. In other words, x is the coordinate in the direction perpendicular to the (set) reference axis O1 of the linear body 100. The z-axis is defined as the direction perpendicular to the x-axis and parallel to the reference axis O1. The length of linear body 100 is defined as L. The rotational speed of linear body 100 about the z-axis (reference axis O1) is defined as Ω. The linear density of linear body 100 is defined as ρ. The tension of linear body 100 at position x is defined as T(x), and the displacement of linear body 100 in the z direction is defined as w(x, t), where t is time (clock time). First, tension T(x) acting on linear body 100 when linear body 100 is not displaced (w=0) is found.

[0025] As shown in FIG. 5, the balance condition of the force acting on minute wire element 101 of linear body 100 for length Δx in the x-axis direction is expressed as in equation (11).

[0026]

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[0027] Considering the limit of △x→0 in equation (11), we obtain equation (12).

[0028]

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[0029] When a boundary condition is applied to equation (12) such that tension T(x)=0 at the second end (x=L) of linear body 100, equation (13) is obtained.

[0030]

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[0031] Next, it is assumed that the displacement w is infinitesimal for the linear body 100, and therefore the tension T(x) remains unchanged. In this case, the force F in the z direction acting on the infinitesimal line element 101 is z is obtained by equation (14).

[0032]

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[0033] Therefore, the equation of motion of the minute line element 101 is equation (15), that is, equation (16) obtained by modifying equation (15).

[0034]

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[0035] [2.2. General solution for free vibration of a linear body] Assume that displacement w(x,t) of linear body 100 is the product of Φ(x), which is a function of position x, and q(t), which is a function of time t, and can be expressed as w(x,t) = Φ(x)q(t) by separating x and t. Φ(x) is an eigenfunction that represents the natural vibration mode shape. Then, equation (19) and equation (20) obtained by modifying equation (19) are obtained.

[0036]

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[0037] The tension T(x) depends on x. Therefore, the left side of equation (20) depends only on time t, and the right side of equation (20) depends only on x. Therefore, based on the method of separation of variables, both sides of equation (20) can be treated as constants. This constant can be expressed as -ω 2 Then, equations (21) and (22) are obtained.

[0038]

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[0039] Here, (x / L) is defined as the non-dimensional position x^ (the symbol "^" above the symbol "x"), and (ω / Ω) is defined as the non-dimensional angular frequency ω^. Substituting equation (13), position x^, and angular frequency ω^ into equation (22), equations (23) and (24) are obtained.

[0040]

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[0041] Here, 2(ω^) 2 If we set = n(n+1), equation (24) coincides with the Legendre differential equation. Therefore, the eigenfunction Φ(x) can be written as a Legendre polynomial. The Legendre polynomial is 2(ω^) 2 It takes various values ​​depending on the value of . In order for the Legendre polynomial to have a finite value at x^=1 (the second end of the linear body 100), n must be an integer greater than or equal to 0. From this condition, the natural frequency ω^ n is determined discretely, and the nth-order eigenfunction Φ n (x^) is obtained by equation (27).

[0042]

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[0043] From the above, the general solution for the displacement w(x, t) of linear body 100 rotating around the z-axis is given by equation (28). n ,B n is an integral constant determined from the initial conditions.

[0044]

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[0045] An important property is that the eigenfunctions (Legendre polynomials) have the orthogonality property expressed by equation (29). mn is the Kronecker delta.

[0046]

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[0047] [2.3. Shape control of linear bodies: response to external inputs] Assume that an external force F(x, t) is applied to linear body 100 at position x and time t. External force F(x, t) is an external force in the z-axis direction per unit length in the x-axis direction. In this case, the equation of motion of linear body 100 is given by equation (32).

[0048]

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[0049] The eigenfunction Φ(x) is assumed to be the same as that of the free vibration of the linear body 100 in [2.2], and the modal coordinate q(t) is assumed to be an unknown. Then, equation (33) is obtained. Substituting equation (33) into equation (32), equation (34) is obtained.

[0050]

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[0051] On both sides of equation (34), Φ m Multiplying by (x^) and integrating over the interval [0,1] with respect to the position x^, we extract only one mode due to the orthogonality of the eigenfunctions, yielding equation (35). However, M ~ n , F ~ n are the n-th order generalized mass and generalized force, respectively, and are expressed by equations (36) and (37).

[0052]

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[0053] Therefore, when an external force F(x,t) is given, equation (35) is written as the modal coordinate q n By solving (t) and superimposing it with the eigenfunction, the displacement w(x, t) of linear body 100 as a response can be obtained. The displacement w(x, t) will be explained below.

[0054] [2.4. Shape control of linear body: Control side] Assume that a periodic input F0(t) expressed by equation (40) is applied to a first end (x=0) of linear body 100 rotating about the z axis. Here, A0 and α0 are constants, and ω0 is the angular frequency that vibrates the end of linear body 100 in the direction along reference axis O1.

[0055]

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[0056] Let us assume that the generalized force F(x,t) = δ(x)F0(t) is expressed using the Dirac delta function. ~ n is expressed by equation (42).

[0057]

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[0058] Here, the frequency response function of the single-degree-of-freedom system (35) is expressed as H n (ω). In this case, the response in the modal coordinates is expressed by equation (43). However, H n (ω0) is the frequency response function corresponding to the angular frequency ω0.

[0059]

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[0060] Therefore, displacement w(x, t) of linear body 100 is expressed by equation (44).

[0061]

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[0062] Here, the amplification factor G ω0 Let (x) be expressed by equation (45). In this case, the displacement w(x,t) is expressed by equation (46).

[0063]

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[0064] Here, a cylindrical coordinate system r-θ-z in inertial space is defined. r is a coordinate with the z-axis as the origin in a direction perpendicular to the (set) reference axis O1 of linear body 100. θ is a coordinate of each linear body 100 about reference axis O1. Linear body 100 rotates around the z-axis at a rotational speed Ω. Assume that linear body 100 passes through position θ=0 at time t=0. A first end (base) of linear body 100 is excited at a certain angular rotation frequency ω0=mΩ. This excitation and F(x, t) in the z-axis direction correspond to basic rotation / vibration step S12. The deformation response of linear body 100 is expressed by equation (49).

[0065]

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[0066] Here, since θ=Ωt, displacement w(r, θ, t) of linear body 100 when passing through position θ is expressed by equation (50).

[0067]

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[0068] Therefore, if m is a natural number, the term sin(mθ+α0) on the right side of equation (50) becomes a waveform (standing wave) that closes in one revolution around the z-axis with respect to position θ. Equation (50) where m is a natural number corresponds to the same position step S13 for a predetermined direction. That is, the displacement w(r, θ, t) of linear body 100 in the inertial space (inertial system) is constant regardless of time t. In other words, linear body 100 is moved by G ω0 It vibrates and deforms while tracing a stationary wave front in inertial space, expressed as (r)A0sin(mθ+α0).

[0069] [3. Summary of shape control methods] [3.1. Standing Waves] In a shape control method S11 for controlling the shape of multiple linear bodies 100, as a basic rotation / vibration process S12 and a same position process S13 for a predetermined direction, the displacement w(r, θ, t) of the multiple linear bodies 100 in the direction along the reference axis O1 is controlled so as to satisfy equation (50) obtained using equation (45). In addition, in the shape control method for controlling the shape of a single linear body 100A, as the basic rotation / vibration process S12 and the same position process S13 for a predetermined direction, the displacement w(r, t) of the linear body 100A in the direction along the reference axis O1 is controlled so as to satisfy equation (49) obtained using equation (45).

[0070] [3.2. Quasi-standing wave] In this case, in the shape control method, while performing the basic rotation / vibration step S12, a uniform position step for the displaced position is performed to control, in an inertial system, the position of linear body 100A in the direction along reference axis O1 when linear body 100A is arranged in a predetermined orientation around reference axis O1 for each linear body 100, so that the position of linear body 100A in the direction along reference axis O1 when linear body 100A is further rotated around reference axis O1 to a position displaced by one rotation plus a displacement angle is equal to each other. Here, the displacement angle is, for example, a predetermined angle equal to or greater than -180° and less than 180°. By controlling in this manner, linear body 100A moves on a predetermined curved surface that rotates at a predetermined speed around reference axis O1 (hereinafter, this predetermined curved surface will be referred to as a rotating curved surface). Furthermore, for linear bodies 100B, 100C, ..., in the quasi-standing wave angular difference same position step, in the inertial system, the angular difference in the predetermined direction around reference axis O1 on the curved surface of rotation is calculated as (θ B + displacement angle), (θ C + displacement angle), linear bodies 100B, 100C, etc. are controlled to be positioned at the rotated positions.

[0071] In the case of a quasi-standing wave, m is a non-integer value (real number) in equations (49) and (50).

[0072] 4. Spacecraft Operation Using Shape Control Devices A spacecraft can be constructed using a shape control device 1 that can perform the shape control method of this embodiment. In the spacecraft, a shape control method is performed while passing an electric current through conductive members embedded in the plurality of linear bodies 100, thereby deforming the plurality of linear bodies 100 into a desired shape. When the spacecraft is affected by a magnetic field such as that of the sun, the plurality of linear bodies 100 are subjected to a Lorentz force, thereby changing the direction in which the spacecraft moves. For example, spacecraft can capture space debris and collect samples from small celestial bodies.

[0073] 5. Effects of this embodiment As described above, in shape control method S11 of the present embodiment, linear body 100A is subjected to basic rotation / vibration step S12, and then to identical position step S13 for a predetermined orientation. As a result, in an inertial system, linear body 100A rotating around reference axis O1 moves on a predetermined curved surface, and the path traveled by linear body 100A has a constant shape. Therefore, linear body 100A can be deformed into a desired shape.

[0074] For linear body 100A, in basic rotation / vibration step S12 and identical position step S13 with respect to a predetermined orientation, displacement w(r, t) of linear body 100A in a direction along reference axis O1 is controlled to satisfy equation (49) obtained using equation (45). The inventors have extensively studied, based on known equations of motion and a general solution of free vibration for linear body 100, methods for controlling the shape of linear body 100 when the end of linear body 100 is rotated around reference axis O1 while vibrating the end of linear body 100 in a direction along reference axis O1. As a result, by controlling displacement w(r, t) to satisfy equation (49) obtained using equation (45), linear body 100 can be deformed into a certain shape with equation (49) as a predetermined curved surface.

[0075] For the plurality of linear bodies 100, as the basic rotation / vibration step S12 and the same position step S13 with respect to a predetermined orientation, the displacements w(r, θ, t) of the plurality of linear bodies 100 in the direction along the reference axis O1 are controlled to satisfy equation (50) obtained using equation (45). The inventors have extensively studied, based on a known equation of motion and a general solution of free vibration for the linear body 100, a method for controlling the shape of the linear body 100 when the ends of the plurality of linear bodies 100 are rotated around the reference axis O1 while vibrating the ends of the plurality of linear bodies 100 in the direction along the reference axis O1. As a result, by controlling the displacements w(r, θ, t) to satisfy equation (50) obtained using equation (45), the plurality of linear bodies 100 can be controlled to have a constant shape with equation (50) as a predetermined curved surface.

[0076] In the quasi-standing wave shape control method, a same-position step is performed for the shifted positions while performing the basic rotation / oscillation step S12. Then, in an inertial system, multiple linear bodies 100 rotating around a reference axis O1 move on a predetermined curved surface rotating around the reference axis O1 at a predetermined speed, and the trajectory traversed by multiple linear bodies 100 forms a constant shape rotating around the reference axis O1. Therefore, multiple linear bodies 100 can be deformed into a desired shape.

[0077] Although one embodiment of the present invention has been described in detail above with reference to the drawings, the specific configuration is not limited to this embodiment, and configuration changes, combinations, deletions, etc. are also included within the scope that does not deviate from the gist of the present invention. For example, in the above embodiment, when the shape control method is performed, it is not necessary to use the equations (49) and (50). The shape control method may be performed on one linear body 100. In this case, in the shape control method, the standing wave angle difference same position step S14 and the quasi-standing wave angle difference same position step are not performed.

[0078] A linear object equipped with light-emitting elements such as LEDs (Light Emitting Diodes) may be deformed. The color or brightness of the light-emitting elements, i.e., the pattern, may be changed while the linear object is being deformed, and the linear object may be used as a 3D monitor. Alternatively, 3D projection mapping using an external light source may be performed on a linear object deformed into a desired shape. Wind power generation may be performed using multiple linear bodies. The shape control device may be used to make the flight path of a UAV (Unmanned Aerial Vehicle) more three-dimensional, and the power generation efficiency in controlling the UAV may be improved. [Explanation of symbols]

[0079] 100 linear body O1 Reference Axis S11 Shape control method S12 Basic rotation and vibration process S13 Same position process for a given direction

Claims

1. a basic rotation / vibration step of rotating an end of a linear body around a reference axis while vibrating the end of the linear body in a direction along the reference axis; a uniform positioning step for controlling the linear object so that the linear object is disposed at the same position in a direction along the reference axis when the linear object is disposed in a predetermined direction around the reference axis; A shape control method.

2. 2. The shape control method according to claim 1, wherein the basic rotation / vibration process and the same position process with respect to the specified orientation control the displacement w(r, t) of the linear body in a direction along the reference axis so as to satisfy equation (2) obtained using equation (1). However, ω ０ is the angular frequency at which the end of the linear body vibrates in a direction along the reference axis, and A ０ , α ０ is a constant, r and x are coordinates of the linear body in a direction perpendicular to the reference axis, Ω is the rotation speed of the linear body around the reference axis, m is a natural number, t is time, and H ｎ (ω ０ ) is the frequency response function of the linear body, and Φ ｎ (x) is the nth-order eigenfunction of the linear body. [Equation 1]

3. 2. The shape control method according to claim 1, wherein, as the basic rotation / vibration process and the same position process with respect to the specified orientation, the displacements w(r, θ, t) of the multiple linear bodies arranged around the reference axis in a direction along the reference axis are controlled so as to satisfy equation (4) obtained using equation (3). However, ω ０ is the angular frequency at which the end of the linear body vibrates in a direction along the reference axis, and A ０ , α ０ is a constant, r and x are coordinates of the linear body in a direction perpendicular to the reference axis, m is a natural number, θ is a coordinate of each linear body around the reference axis, t is time, and H ｎ (ω ０ ) is the frequency response function, and Φ ｎ (x) is an nth-order eigenfunction. [Equation 2]

4. a basic rotation / vibration step of rotating an end of a linear body around a reference axis while vibrating the end of the linear body in a direction along the reference axis; an identical position process for the shifted position, which controls the position of the linear body in the direction along the reference axis when the linear body is arranged in a predetermined orientation around the reference axis to be equal to the position of the linear body in the direction along the reference axis when the linear body is further rotated around the reference axis to a position shifted by one rotation plus a displacement angle; A shape control method.

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