CN104932511A - Fourier expansion based Gyro stabilizer and realization method thereof - Google Patents

Abstract

The invention provides a Fourier expansion based gyro stabilizer and a realization method thereof, relates to the technical field of robot control, and aims at solving the control difficulty caused by narrow angle range of procession force torque of gyros and non-linear relation between the procession force torque and procession force angle when a dual-gyro stabilizer is used to maintain stable attitude of a single-wheel robot. The gyro stabilizer comprises a lower connecting piece, an upper connecting piece and two groups of gyros, each group is composed of multiple gyros, self rotation of each gyro is driven by an independent motor, in each group, procession of the gyro at a middle position is driven by a procession motor, and procession of gyros in the surrounding is transmitted by groups of synchronous pulleys of fixed transmission ratio. The stabilizer and realization method are used for attitude stabilization of single-wheel robot system as well as attitude adjustment of small aircrafts and satellites.

Description

Based on gyrostabilization unit and its implementation of Fourier expansion

Technical field

The present invention relates to a kind of gyrostabilization unit for adjusting controlled component pose, being specifically related to a kind of gyrostabilization unit based on Fourier expansion, relating to technical field of robot control.

Background technology

What current one-wheel robot system problem the most difficult was exactly side to attitude is stable, and great majority utilize inertia to take turns the moment of reaction of acceleration and deceleration or gyroscopic procession moment to maintain the lateral balance of one-wheel robot system.

Feature based on the stabilising arrangement of inertia wheel is the transient equilibrium of the moment of reaction maintenance system that the acceleration and deceleration by controlling inertia wheel produce, advantage is that the moment of torsion produced is large, class one-wheel robot system can be made fast to return to steady state (SS), shortcoming is exactly that inertia is large, structure bulky, start-up time are long, commutation can cause system to shake to cause system stability to reduce, and the working capability finite under state of saturation.

The stabilising arrangement principle of single gyro is the transient equilibrium that the moment of torsion produced by the precession effect of gyro maintains class one-wheel robot system, advantage is that inertia is little, easy to adjust, and shortcoming can produce perturbed force to make class one-wheel robot system system generation pitching producing trimming moment while.The stabilising arrangement (if publication number is the patent of CN 103488178A) of double tops can eliminate this disturbance torque, therefore, in practical application, and normal employing double tops scheme.

Based on the double tops stabilising arrangement of gyroscopic procession effect, although the stable of system can be maintained near equilibrium point, when external disturbance moment is too large, counterbalance effect is then so not good.It is significantly shortcoming that double tops stabilising arrangement based on gyroscopic procession effect exists two, first, be the relation of cosine between gyroscopic procession moment active constituent (trimming moment) and precession angle, precession moment active constituent is rapid decay along with the increase of precession angle.In time reaching 90 degree, the vanishing of precession moment active constituent, namely reach capacity state, out of trim effect, thus the reach greatly reducing balance device.The second, the varies with cosine rule of gyroscopic procession moment active constituent is nonlinear, which again increases the difficulty of control, improves the requirement to drive motor.

Summary of the invention

The present invention is for solving double tops stabilising arrangement when maintaining the attitude stability of one-wheel robot system, there is gyroscopic procession moment loading angular range narrow, and between precession moment and precession angle, nonlinear relationship causes the problem controlling difficulty, and then a kind of gyrostabilization unit based on Fourier expansion and its implementation are proposed.

The present invention is the technical scheme taked that solves the problem:

Gyrostabilization unit based on Fourier expansion of the present invention comprises lower web member, two groups of gyroscopes that upper connector is identical with structure; Two groups of gyroscopes are arranged symmetrically with and the two is linked together by lower web member, upper connector; Often organize gyroscope to comprise lower supporting plate, upper backup pad, precession motor and be installed on the multiple single gyro instrument between lower supporting plate and upper backup pad; Each single gyro instrument rotates along the single gyro instrument turning axle perpendicular to lower supporting plate, upper backup pad, and the rotor of each single gyro instrument rotates along the rotor turning axle perpendicular to single gyro instrument turning axle; In multiple single gyro instrument, with the single gyro instrument turning axle of one of them single gyro instrument for axis, precession motor drives one of them single gyro instrument described to rotate along single gyro instrument turning axle by the first gear train; Remaining single gyro instrument with described axis for benchmark circumference uniform setting, and be all connected by the second gear train with one of them single gyro instrument described, under the drive of one of them single gyro instrument described, remaining single gyro instrument all rotates with respective single gyro instrument turning axle; Two precession motors in two groups of gyroscopes, its velocity of rotation moment keeps equal and opposite in direction, and direction is contrary; Two lower supporting plates are connected by lower web member, and two upper backup pads are connected by upper connector.

Each single gyro instrument comprises bracing frame, lower support axle, upper back shaft, spinning motor, shaft coupling, rotor, rotor bearing and two the back shaft bearings be packed in by screw on bracing frame; Rotor is arranged on bracing frame by rotor bearing, spinning motor and rotor are positioned at bracing frame, the output shaft of spinning motor is connected with the rotating shaft of rotor by shaft coupling, to be positioned at below bracing frame and connected lower support axle is arranged on lower supporting plate by a back shaft bearing, to be positioned at above bracing frame and connected upper back shaft is arranged on upper backup pad by another back shaft bearing; Lower support axle and upper back shaft are coaxially provided as single gyro instrument turning axle.

Described first gear train is bevel-gear sett; Described second gear train comprises N to synchronous pulley and N bar Timing Belt, the value of N is identical with the quantity of the single gyro instrument of the uniform setting of circumference, the driving pulley of often pair of synchronous pulley is installed on the single gyro instrument turning axle of the single gyro instrument being in location mid-shaft, the driven pulley one_to_one corresponding of often pair of synchronous pulley is arranged on the single gyro instrument turning axle of the single gyro instrument of circumferential uniform setting, and often pair of synchronous pulley realizes being rotationally connected by a Timing Belt.

Further restriction: often organize containing four single gyro instrument in gyroscope, being distributed as of four single gyro instrument: a single gyro instrument is in circle centre position, its excess-three single gyro instrument is circumferentially uniformly distributed.

Further restriction: often organize containing seven single gyro instrument in gyroscope, being distributed as of seven single gyro instrument: a single gyro instrument is in circle centre position, all the other six single gyro instrument are circumferentially uniformly distributed.

Further restriction: described upper connector is rectangular slab, upper connector is connected by screw two upper backup pads; Described lower web member is quadra, and its upper side frame is connected by screw two lower supporting plates, and its lower frame has some threaded holes, for being connected with controlled parts.

Further restriction: described lower supporting plate has a rectangular recess, motor cabinet can move about left and right in this groove.

Further restriction: three pairs of synchronous pulleys, its ratio of gear is respectively 3:1,5:1 and 7:1.

Further restriction: the ratio of gear of the multiple single gyro instrument often organized in gyroscope is respectively: middle single gyro instrument and the gyrostatic ratio of gear of surrounding n-th are (2n+1): 1.

An implementation method for the above-mentioned gyrostabilization unit based on Fourier expansion, the process of described method is as follows:

Effective precession moment that step one, single gyro rotor D precession produce is:

τ _good＝Acosθ＝2I _zω _yω _zcos(ω _yt)

The precession moment of one group of gyrorotor C generation is:

τ＝A ₁cosθ ₁+A ₂cosθ ₂+A ₃cosθ ₃+A ₄cosθ ₄+…

In formula, A represents amplitude, I _zrepresent moment of inertia, ω _yrepresent angular velocity of precession, ω _zrepresent spin velocity, the subscript 1,2,3 of each parameter ... represent in one group of gyroscope containing the 1st single gyro instrument, the 2nd single gyro instrument ...,

Step 2, regulate the angular velocity of precession ω of each cosine function _ywith amplitude A, obtain a square wave function in (-pi/2, pi/2) interval; Angular velocity of precession ω _yas follows with the regulative mode of amplitude A:

(1), angular velocity of precession ω _yadjustment:

Regulate each gyrorotor D angular velocity of precession ω _ymeet following ratio relation:

θ ₁:θ ₂:θ ₃:θ ₄…＝ω _y1:ω _y2:ω _y3:ω _y4…＝1:3:5:7…

Above-mentioned ratio relation is realized by ratio of gear;

(2), the adjustment of amplitude A:

Amplitude A=2I _zω _yω _z, based on moment of inertia I _zbe inconvenient to regulate, regulate each rotor ω _yω _zratio be:

${\mathrm{\ω}}_{y1}{\mathrm{\ω}}_{z1}:{\mathrm{\ω}}_{y2}{\mathrm{\ω}}_{z2}:{\mathrm{\ω}}_{y3}{\mathrm{\ω}}_{z3}:{\mathrm{\ω}}_{y4}{\mathrm{\ω}}_{z4}\·\·\·=1:-\frac{1}{3}:\frac{1}{5}:-\frac{1}{7}\·\·\·$

Realize the adjustment of amplitude A;

By ω _y1: ω _y2: ω _y3: ω _y4=1:3:5:7 ..., obtain the spin velocity ω of each rotor _zshould meet:

${\mathrm{\ω}}_{z1}:{\mathrm{\ω}}_{z2}:{\mathrm{\ω}}_{z3}:{\mathrm{\ω}}_{z4}\·\·\·=1:-\frac{1}{9}:\frac{1}{25}:-\frac{1}{49}\·\·\·$

Wherein, the negative sign in formula represents the spin velocity ω of rotor _zdirection is contrary.

The corresponding single gyro instrument often organized in gyroscope of step 3, each Fourier series, is made the resultant moment that obtains level and smooth to Fourier coefficient revise.

The invention has the beneficial effects as follows:

1, the present invention can provide effective precession moment, more efficiently can realize attitude stabilization and the adjustment of the systems such as one-wheel robot; Solving double tops stabilising arrangement when maintaining the attitude stabilization of one-wheel robot system, there is gyroscopic procession moment loading angular range narrow, and between precession moment and precession angle, nonlinear relationship causes the problem controlling difficulty.

2, the present invention devises the stabilising arrangement that two groups of gyroscopes instead of existing double tops, and often group gyroscope is made up of the single gyroscope of some quantity (at least two), by will often multiple single gyrostatic precession moment superposition in group, make the effect angular range of total synthesis effective torque wider, expand the effect angle of gyrostabilization unit, compared with existing gyrostabilization unit, the present invention within the scope of larger operating angle, can provide the effective torque needed for stable (balance) controlled parts.The present invention is not easy to reach failure state (failure state as shown in Figure 8), more has practicality.

3, compared with existing double tops stabilising arrangement, the proportionate relationship of the present invention by utilizing the Fourier series improved to determine the proportionate relationship of the angular velocity of precession often organizing each single gyro instrument in gyroscope and the spin velocity of each single gyro instrument, make the effective precession moment of synthesis of the present invention more level and smooth within the scope of operating angle, reduce the requirement to precession motor, working control is more prone to;

4, two groups of gyroscopes of the present invention are that specular is arranged, and the structure of all single gyro instrument is identical, present invention employs modular design philosophy thus, makes actual production, application and safeguards convenient.

5, the present invention may be used for lateral balance control (attitude stabilization for one-wheel robot system) of one-wheel robot, realize the balance of one-wheel robot, in addition, this device also can be applicable to the pose adjustment of small aircraft and satellite, has wide application scenarios.

Accompanying drawing explanation

Fig. 1 is that (coordinate system is set to: the axis of rotation direction of single gyro instrument is z-axis for the spatial structure of the gyrostabilization unit based on Fourier expansion of the present invention, the turning axle in single gyro instrument precession direction is y-axis, x-axis is vertical with z-axis with y-axis, meet the right-hand rule), Fig. 2 is the vertical view (concealing upper connector B and upper backup pad 2) of Fig. 1, Fig. 3 is one group of gyrostatic three-dimensional structure diagram, Fig. 4 is single gyrostatic perspective view, Fig. 5 often organizes gyroscope to comprise multiple gyrostatic distribution schematic diagram, Fig. 6 is a single gyroscopic precession effect principle schematic diagram (precession certain angle θ), Fig. 7 is double tops instrument precession effect principle schematic (being also two groups of gyroscopic precession effect principle schematic diagram), Fig. 8 is double tops stabilising arrangement failure state schematic diagram, Fig. 9 is the graph of relation between the effective precession moment of double tops instrument stabilising arrangement and precession angle, Figure 10 is the relation curve comparison diagram (often organizing in gyroscope situation when comprising 4 single gyro instrument) between effective precession moment of producing of apparatus of the present invention and precession angle, in Figure 11: topmost figure is square wave function, middle graph is Fourier expansion (4 function superposition), and figure is Fourier expansion (40 function superposition) bottom, Figure 12 is that this application of installation is in the schematic diagram of one-wheel robot system.

Embodiment

Embodiment one: composition graphs 1-Fig. 5 illustrates present embodiment, the gyrostabilization unit based on Fourier expansion described in present embodiment, is characterized in that: described gyrostabilization unit comprises lower web member A, the upper connector B two group gyroscope Cs identical with structure; Two groups of gyroscope C are arranged symmetrically with and the two is linked together by lower web member A, upper connector B;

Often organize gyroscope C to comprise lower supporting plate 1, upper backup pad 2, precession motor 3 and be installed on the multiple single gyro instrument D between lower supporting plate 1 and upper backup pad 2; Each single gyro instrument D rotates along the single gyro instrument turning axle perpendicular to lower supporting plate 1, upper backup pad 2, and the rotor 18 of each single gyro instrument D rotates along the rotor turning axle perpendicular to single gyro instrument turning axle; Precession motor 3 is arranged on lower supporting plate 1 by motor cabinet 4; The rotor turning axle of multiple single gyro instrument D all be arranged in parallel;

In multiple single gyro instrument D, with the single gyro instrument turning axle of one of them single gyro instrument D for axis, precession motor 3 drives described one of them single gyro instrument D to rotate along single gyro instrument turning axle by the first gear train; Remaining single gyro instrument D with described axis for benchmark circumference uniform setting, and be all connected by the second gear train with described one of them single gyro instrument D, under the drive of described one of them single gyro instrument D, remaining single gyro instrument D all rotates with respective single gyro instrument turning axle;

Two precession motors 3 in two groups of gyroscope C, its velocity of rotation moment keeps equal and opposite in direction, and direction is contrary.Setting like this, just can make the pitching disturbance torque produced cancel out each other.

Two lower supporting plates 1 are connected by lower web member A, and two upper backup pads 2 are connected by upper connector B.

Each gyrostatic rotation is driven by motor independent separately, and in one group of gyroscope, the gyrostatic precession being positioned at centre position is driven by a precession motor, the synchronous belt pulley transmission that the gyrostatic precession around distributed is fixed by several groups of ratio of gear.Motor output shaft is connected with armature spindle by shaft coupling.Rotor can make High Rotation Speed around self axis of symmetry.Meanwhile, single gyroscope can rotate around vertical direction, i.e. precession.

Embodiment two: composition graphs 1-Fig. 5 illustrates present embodiment, in present embodiment, each single gyro instrument D comprises bracing frame 12, lower support axle 13, upper back shaft 14, spinning motor 15, shaft coupling 17, rotor 18, rotor bearing 19 and two the back shaft bearings 20 be packed in by screw 16 on bracing frame 12; Rotor 18 is arranged on bracing frame 12 by rotor bearing 19, and spinning motor 15 and rotor 18 are positioned at bracing frame 12, and the output shaft of spinning motor 15 is connected with the rotating shaft of rotor 18 by shaft coupling 17, thus makes rotor 18 High Rotation Speed.To be positioned at below bracing frame 12 and connected lower support axle 13 is arranged on lower supporting plate 1 by a back shaft bearing 20, to be positioned at above bracing frame 12 and connected upper back shaft 14 is arranged on upper backup pad 2 by another back shaft bearing 20; Lower support axle 13 and upper back shaft 14 are coaxially provided as single gyro instrument turning axle.Other composition and annexation identical with embodiment one.

Motor 15 described in present embodiment is fixed on bracing frame 12 by screw 16, and motor 15 output shaft is connected by the rotating shaft of shaft coupling 17 with rotor 18, rotor 18 High Rotation Speed under the drive of motor 15; The rotating shaft two ends of rotor 18 are provided with pair of bearings 19, rotor 18 is fixed on bracing frame 12 by bearing 19, the weight of rotor 18 is all born by the pair of bearings 19 at its two ends, setting like this, motor 15 moments of torsion rotated can be ensured, and the Action of Gravity Field do not born from rotor 18, thus improve the life-span of motor 15.Present embodiment support frame as described above 12 is fixed on lower supporting plate 1 and upper backup pad 2 by the bearing 20 at lower support axle 13 and upper back shaft 14 two ends, thus whole single gyro instrument D can be made to rotate around vertical direction (in figure y-axis), namely produces precession.

Embodiment three: composition graphs 1-Fig. 5 illustrates present embodiment, in present embodiment, described first gear train is bevel-gear sett 5; Described second gear train comprises N to synchronous pulley and N bar Timing Belt, the value of N is identical with the quantity of the single gyro instrument D of the uniform setting of circumference, the driving pulley of often pair of synchronous pulley is installed on the single gyro instrument turning axle of the single gyro instrument D being in location mid-shaft, the driven pulley one_to_one corresponding of often pair of synchronous pulley is arranged on the single gyro instrument turning axle of the single gyro instrument D of circumferential uniform setting, and often pair of synchronous pulley realizes being rotationally connected by a Timing Belt.Other composition and annexation identical with embodiment one or two.

Embodiment four: composition graphs 1-Fig. 3 illustrates present embodiment, in present embodiment, often organize containing four single gyro instrument D in gyroscope C, four single gyro instrument D are distributed as: a single gyro instrument D is in circle centre position, and its excess-three single gyro instrument D is circumferentially uniformly distributed.Described second gear train comprises three pairs of synchronous pulleys, 6,7,8 and three Timing Belts 9,10,11.

Special instruction, the single gyro instrument D often organizing gyroscope C is not limited only to 4, and the quantity of the gyroscope D comprised in a group is more, and effect is better.During multiple gyroscope D, also can take this strategy; Setting like this, can make compact conformation, reduces and taken up space.

Other composition and annexation and embodiment one, two or three identical.

Embodiment five: composition graphs 5 illustrates present embodiment, in present embodiment, often organize containing seven single gyro instrument D in gyroscope C, seven single gyro instrument D are distributed as: a single gyro instrument D is in circle centre position, and all the other six single gyro instrument D are circumferentially uniformly distributed.Other composition and annexation and embodiment one, two or three identical.

Embodiment six: composition graphs 1-Fig. 2 illustrates present embodiment, in present embodiment, described upper connector B is rectangular slab, and upper connector B is connected by screw two upper backup pads 2; Described lower web member A is quadra, and its upper side frame is connected by screw two lower supporting plates 1, and its lower frame has some threaded holes, for being connected with controlled parts (by stabilizing means).Controlled parts are one-wheel robot, small aircraft, satellite, Double-wheel self-balancing car such as.

Other composition and annexation and embodiment one, two, three, four or five identical.

Embodiment seven: composition graphs 1 illustrates present embodiment, in present embodiment, described lower supporting plate 1 has a rectangular recess, motor cabinet 4 can move about left and right in this groove, thus can the gap of cone governor gear 5, setting like this, is conducive to the drive gap reducing bevel gear 5, improves transmission accuracy.

Other composition and annexation and embodiment one, two, three, four, five or six identical.

Embodiment eight: composition graphs 1 illustrates present embodiment, in present embodiment, three pairs of synchronous pulleys 6,7,8, its ratio of gear is respectively 3:1,5:1 and 7:1.Other composition and annexation identical with embodiment four.

Embodiment nine: composition graphs 5 illustrates present embodiment, in present embodiment, the ratio of gear of the multiple single gyro instrument D often organized in gyroscope C is respectively: middle single gyro instrument and the gyrostatic ratio of gear of surrounding n-th are (2n+1): 1; Setting like this, meets the scale-up factor relation in Fourier expansion formula.

Other composition and annexation identical with embodiment one.

Embodiment ten: composition graphs 1 ~ 5 illustrates present embodiment, and present embodiment is the implementation method of the gyrostabilization unit based on Fourier expansion in above-mentioned embodiment, and the process of described method is as follows:

Effective precession moment that step one, single gyro rotor D precession produce is:

τ _good＝Acosθ＝2I _zω _yω _zcos(ω _yt)

The precession moment of one group of gyrorotor C generation is:

τ＝A ₁cosθ ₁+A ₂cosθ ₂+A ₃cosθ ₃+A ₄cosθ ₄+…

In formula, A represents amplitude, I _zrepresent moment of inertia, ω _yrepresent angular velocity of precession, ω _zrepresent spin velocity, the subscript 1,2,3 of each parameter ... represent in one group of gyroscope C containing the 1st single gyro instrument D, the 2nd single gyro instrument D ...,

Step 2, regulate the angular velocity of precession ω of each cosine function _ywith amplitude A, obtain a square wave function in (-pi/2, pi/2) interval; Angular velocity of precession ω _yas follows with the regulative mode of amplitude A:

(1), angular velocity of precession ω _yadjustment:

Regulate each gyrorotor D angular velocity of precession ω _ymeet following ratio relation:

θ ₁:θ ₂:θ ₃:θ ₄…＝ω _y1:ω _y2:ω _y3:ω _y4…＝1:3:5:7…

Above-mentioned ratio relation is realized by ratio of gear;

(2), the adjustment of amplitude A:

Amplitude A=2I _zω _yω _z, based on moment of inertia I _zbe inconvenient to regulate, regulate the ω of each rotor 18 _yω _zratio is:

${\mathrm{\ω}}_{y1}{\mathrm{\ω}}_{z1}:{\mathrm{\ω}}_{y2}{\mathrm{\ω}}_{z2}:{\mathrm{\ω}}_{y3}{\mathrm{\ω}}_{z3}:{\mathrm{\ω}}_{y4}{\mathrm{\ω}}_{z4}\·\·\·=1:-\frac{1}{3}:\frac{1}{5}:-\frac{1}{7}\·\·\·$

Realize the adjustment of amplitude A;

By ω _y1: ω _y2: ω _y3: ω _y4=1:3:5:7 ..., obtain the spin velocity ω of each rotor 18 _zshould meet:

${\mathrm{\ω}}_{z1}:{\mathrm{\ω}}_{z2}:{\mathrm{\ω}}_{z3}:{\mathrm{\ω}}_{z4}\·\·\·=1:-\frac{1}{9}:\frac{1}{25}:-\frac{1}{49}\·\·\·$

Wherein, the negative sign in formula represents the spin velocity ω of rotor 18 _zdirection is contrary.

The corresponding single gyro instrument D often organized in gyroscope C of step 3, each Fourier series, is made the resultant moment that obtains level and smooth to Fourier coefficient revise.

Implementation method for the gyrostabilization unit based on Fourier expansion is set forth as follows again:

Gyroscopic procession effect illustrates:

Composition graphs 6-Fig. 9, is described gyroscopic procession effect.Fig. 6 is single gyro precession effect principle schematic.In figure, ω _zbe the spin velocity of gyro, driven by disc type electric machine at a high speed.ω _yfor angular velocity of precession, driven by the motor of outside.From the precession effect of gyro, produce a moment of torsion τ perpendicular to gyroscopic procession angular velocity and spin velocity _x, and meet following mathematical relation:

${\stackrel{\→}{\mathrm{\τ}}}_x=I_z*{\stackrel{\→}{\mathrm{\ω}}}_y\×{\stackrel{\→}{\mathrm{\ω}}}_z$

Wherein, I _zrepresent the rotation moment of inertia of gyrorotor.

The active constituent of precession moment along the longitudinal direction, i.e. x ₀direction.When it turns over certain angle θ, the active constituent size of precession moment is: τ _good=τ _x* cos θ.Meanwhile, also a disturbance torque τ can be produced at left and right directions _bad=τ _x* sin θ.This disturbance torque is harmful, and the balance for the lateral balance of class one-wheel robot is a disturbance torque.Adopt double tops, this interference can be eliminated.

Fig. 7 is double tops precession effect principle schematic.When two gyro senses of rotation are contrary, and when precession direction is contrary, its gyroscopic procession resultant moment direction produced is

τ _good＝2τ*cosθ＝2I _zω _yω _zcosθ

The direction of resultant moment along the longitudinal direction, i.e. x-axis direction, and the disturbance torque of left and right directions is cancelled out each other.

In above-mentioned formula, I _zdefinite value, ω _zbe gyro rotational velocity, rotating speed is higher, remains unchanged in working control.So above formula can be written as:

τ _good＝A ₀ω _ycosθ

Wherein, A ₀=2I _zω _z, be definite value.So, the size of the effective torque of generation and ω _yrelevant with θ.When θ=90 °, τ _good=A ₀ω _ycos θ=0, that is, now, effective precession moment is 0, and stabilising arrangement is ineffective.Stabilising arrangement failure state as shown in Figure 8

Work as ω _yduring for definite value, i.e. angular velocity of precession one timing, the relation of effective precession moment and θ meets

τ _good＝A ₁cosθ

In formula, A ₁=2I _zω _zω _y.Effective precession moment τ _goodbe cosine relation with the pass of θ, as shown in Figure 9.As seen from the figure, when θ increases time, effective precession moment is decayed rapidly, this greatly reduces the effective range of stabilising arrangement; Meanwhile, this nonlinear relation turn increases the difficulty of control to a great extent.Above 2 points, make gyrostabilization unit be very restricted in actual use.In order to solve above-mentioned two problems, the gyrostabilization unit effect angle proposed based on Fourier expansion is expanded and precession moment smoothing apparatus.

Fourier expansion explanation

In conjunction with Figure 11, Fourier expansion is described.If Figure 11 is the square wave function shown in upper figure, its equation is:

$f\left(x\right)=1,-\frac{\mathrm{\π}}{2}\≤x\≤\frac{\mathrm{\π}}{2}$

Can be obtained by Fourier expansion, above-mentioned equation can be write as a series of cosine function and:

$g\left(x\right)=\frac{4}{\mathrm{\π}}[\cos x-\frac{1}{3}\cos 3x+\frac{1}{5}\cos 5x-\frac{1}{7}\cos 7x+\frac{1}{9}\cos 9x-\·\·\·],-\frac{\mathrm{\π}}{2}\≤x\≤\frac{\mathrm{\π}}{2}$

Cosine function quantity used is more, and Approximation effect is better, and it launches effect as shown in the figure below of figure and Figure 11 in Figure 11.Wherein the middle figure of Figure 11 is the Overlay of 4 cosine functions, and figure below of Figure 11 is the Overlay of 40 cosine functions.

The explanation of balance device principle

Composition graphs 9-Figure 12, is described the principle of work of balance device.As described in embodiment one, effective precession moment that single gyrorotor D precession produces is:

τ _good＝Acosθ＝2I _zω _yω _zcos(ω _yt)

The precession moment of one group of gyrorotor C generation is

τ＝A ₁cosθ ₁+A ₂cosθ ₂+A ₃cosθ ₃+A ₄cosθ ₄+…

By above formula compared with the Fourier expansion formula in specific embodiment two, known, as long as suitably regulate the angular velocity of precession ω of each cosine function _ywith amplitude A, a square wave function in (-pi/2, pi/2) interval just can be obtained.Angular velocity of precession ω _yas follows with the regulative mode of amplitude A:

(1) angular velocity of precession ω _yadjustment:

From embodiment two,

θ ₁:θ ₂:θ ₃:θ ₄…＝ω _y1:ω _y2:ω _y3:ω _y4…＝1:3:5:7…

Therefore, as long as regulate each gyrorotor D angular velocity of precession ω _ymeet above-mentioned ratio relation.This ratio relation, by synchronous pulley 6,7,8, mechanical mechanism ensures aforementioned proportion relation by ratio of gear.

(2) adjustment of amplitude A:

From embodiment two, amplitude A=2I _zω _yω _z, due to moment of inertia I _zbe inconvenient to regulate, as long as therefore regulate each rotor ω _yω _zratio be:

${\mathrm{\ω}}_{y1}{\mathrm{\ω}}_{z1}:{\mathrm{\ω}}_{y2}{\mathrm{\ω}}_{z2}:{\mathrm{\ω}}_{y3}{\mathrm{\ω}}_{z3}:{\mathrm{\ω}}_{y4}{\mathrm{\ω}}_{z4}\·\·\·=1:-\frac{1}{3}:\frac{1}{5}:-\frac{1}{7}\·\·\·$

Just can realize.

By known in (1), ω _y1: ω _y2: ω _y3: ω _y4=1:3:5:7 ..., so the spin velocity ω of each rotor D _zshould meet:

${\mathrm{\ω}}_{z1}:{\mathrm{\ω}}_{z2}:{\mathrm{\ω}}_{z3}:{\mathrm{\ω}}_{z4}\·\·\·=1:-\frac{1}{9}:\frac{1}{25}:-\frac{1}{49}\·\·\·$

Wherein, the negative sign in formula represents the spin velocity ω of rotor D _zdirection is contrary.

Because Fourier series has by infinite multinomial, each corresponding apparatus of the present invention often organizes a single gyro instrument D in gyroscope C, and the quantity of single gyro instrument D used in actual use can not reach infinite multiple, directly according to Fourier coefficient configuration ω _yω _zeffective precession moment smooth effect of obtaining of ratio bad, as shown in figure in Figure 11.So, in actual use, to be revised Fourier coefficient.The basic skills revised is on the basis of former Fourier coefficient, finely tunes coefficient, the resultant moment obtained is tried one's best level and smooth.Here often organizes gyroscope C when containing 4 single gyro instrument D, the one group of experience ratio provided:

ω _y1ω _z1:ω _y2ω _z2:ω _y3ω _z3:ω _y4ω _z4＝1:-0.265:0.09:-0.021

The effective precession moment Changing Pattern obtained is as shown in Figure 10 solid line.As can be seen from curve, the effective precession moment obtained is basic in the angular range of-60 degree to+60 degree keeps constant, and the relation as shown in Figure 9 between the effective precession moment of double tops instrument stabilising arrangement and precession angle, when-60 degree or+60 are spent, effective precession moment has decayed to original half.Therefore, the gyrostabilization unit effect angle based on Fourier expansion of the present invention expands the operating angle bandwidth greatly can widening former gyrostabilization unit with precession moment smoothing apparatus, and gyrostabilization unit can be worked in larger angular range.Meanwhile, in this angular range, effective precession moment remains unchanged substantially, and this greatly reduces again in practical application, to the performance requirement of precession motor 3, control is more prone to.

Figure 12 is the structural representation that the present invention is arranged on one-wheel robot, and the present invention has larger operating angle bandwidth of operation and level and smooth moment, effectively can realize the lateral balance of one-wheel robot.Apparatus of the present invention also can be applicable to the aspects such as the pose adjustment of small aircraft and satellite.

Claims (10)

1. based on the gyrostabilization unit of Fourier expansion, it is characterized in that: described gyrostabilization unit comprises lower web member (A), two groups of gyroscopes (C) that upper connector (B) is identical with structure; Two groups of gyroscopes (C) are arranged symmetrically with and the two is linked together by lower web member (A), upper connector (B);

Often organize gyroscope (C) to comprise lower supporting plate (1), upper backup pad (2), precession motor (3) and be installed on the multiple single gyro instrument (D) between lower supporting plate (1) and upper backup pad (2); Each single gyro instrument (D) is rotated along the single gyro instrument turning axle perpendicular to lower supporting plate (1), upper backup pad (2), and the rotor (18) of each single gyro instrument (D) rotates along the rotor turning axle perpendicular to single gyro instrument turning axle;

In multiple single gyro instrument (D), with the single gyro instrument turning axle of one of them single gyro instrument (D) for axis, precession motor (3) drives one of them single gyro instrument (D) described to rotate along single gyro instrument turning axle by the first gear train; Remaining single gyro instrument (D) with described axis for benchmark circumference uniform setting, and be all connected by the second gear train with one of them single gyro instrument (D) described, under the drive of one of them single gyro instrument (D) described, remaining single gyro instrument (D) all rotates with respective single gyro instrument turning axle;

Two precession motors (3) in two groups of gyroscopes (C), its velocity of rotation moment keeps equal and opposite in direction, and direction is contrary;

Two lower supporting plates (1) are connected by lower web member (A), and two upper backup pads (2) are connected by upper connector (B).

2. the gyrostabilization unit based on Fourier expansion according to claim 1, is characterized in that: each single gyro instrument (D) comprises bracing frame (12), lower support axle (13), upper back shaft (14), the spinning motor (15) be packed in by screw (16) on bracing frame (12), shaft coupling (17), rotor (18), rotor bearing (19) and two back shaft bearings (20), rotor (18) is arranged on bracing frame (12) by rotor bearing (19), spinning motor (15) and rotor (18) are positioned at bracing frame (12), the output shaft of spinning motor (15) is connected with the rotating shaft of rotor (18) by shaft coupling (17), be positioned at bracing frame (12) below and connected lower support axle (13) is arranged on lower supporting plate (1) by a back shaft bearing (20), be positioned at bracing frame (12) top and connected upper back shaft (14) is arranged on upper backup pad (2) by another back shaft bearing (20), lower support axle (13) and upper back shaft (14) are coaxially provided as single gyro instrument turning axle.

3. the gyrostabilization unit based on Fourier expansion according to claim 2, is characterized in that: described first gear train is bevel-gear sett (5); Described second gear train comprises N to synchronous pulley (6,7,8) and N bar Timing Belt (9,10,11), the value of N is identical with the quantity of the single gyro instrument (D) of the uniform setting of circumference, the driving pulley of often pair of synchronous pulley is installed on the single gyro instrument turning axle of the single gyro instrument (D) being in location mid-shaft, the driven pulley one_to_one corresponding of often pair of synchronous pulley is arranged on the single gyro instrument turning axle of the single gyro instrument (D) of circumferential uniform setting, and often pair of synchronous pulley realizes being rotationally connected by a Timing Belt.

4. the gyrostabilization unit based on Fourier expansion according to claim 1,2 or 3, it is characterized in that: often organize in gyroscope (C) containing four single gyro instrument (D), four single gyro instrument (D) are distributed as: a single gyro instrument (D) is in circle centre position, and its excess-three single gyro instrument (D) is circumferentially uniformly distributed.

5. the gyrostabilization unit based on Fourier expansion according to claim 1,2 or 3, it is characterized in that: often organize in gyroscope (C) containing seven single gyro instrument (D), seven single gyro instrument (D) are distributed as: a single gyro instrument (D) is in circle centre position, and all the other six single gyro instrument (D) are circumferentially uniformly distributed.

6. the gyrostabilization unit based on Fourier expansion according to claim 1,2 or 3, it is characterized in that: described upper connector (B) is rectangular slab, upper connector (B) is connected by screw two upper backup pads (2); Described lower web member (A) is quadra, and its upper side frame is connected by screw two lower supporting plates (1), and its lower frame has some threaded holes, for being connected with controlled parts.

7. the gyrostabilization unit based on Fourier expansion according to claim 6, is characterized in that: described lower supporting plate (1) has a rectangular recess, and motor cabinet (4) can move about left and right in this groove.

8. the gyrostabilization unit based on Fourier expansion according to claim 4, is characterized in that: three pairs of synchronous pulleys (6,7,8), its ratio of gear is respectively 3:1,5:1 and 7:1.

9. the gyrostabilization unit based on Fourier expansion according to claim 1,2 or 3, is characterized in that: the ratio of gear often organizing the multiple single gyro instrument (D) in gyroscope (C) is respectively: middle single gyro instrument and the gyrostatic ratio of gear of surrounding n-th are (2n+1): 1.

10. based on an implementation method for the gyrostabilization unit of Fourier expansion, it is characterized in that: the process of described method is as follows:

Effective precession moment that step one, single gyro rotor D precession produce is:

τ _good＝Acosθ＝2I _zω _yω _zcos(ω _yt)

The precession moment that one group of gyrorotor (C) produces is:

τ＝A ₁cosθ ₁+A ₂cosθ ₂+A ₃cosθ ₃+A ₄cosθ ₄+…

In formula, A represents amplitude, I _zrepresent moment of inertia, ω _yrepresent angular velocity of precession, ω _zrepresent spin velocity, the subscript 1,2,3 of each parameter ... represent in one group of gyroscope (C) containing the 1st single gyro instrument (D), the 2nd single gyro instrument (D) ...,

Step 2, regulate the angular velocity of precession ω of each cosine function _ywith amplitude A, obtain a square wave function in (-pi/2, pi/2) interval; Angular velocity of precession ω _yas follows with the regulative mode of amplitude A:

(1), angular velocity of precession ω _yadjustment:

Regulate each gyrorotor D angular velocity of precession ω _ymeet following ratio relation:

θ ₁:θ ₂:θ ₃:θ ₄…＝ω _y1:ω _y2:ω _y3:ω _y4…＝1:3:5:7…

Above-mentioned ratio relation is realized by ratio of gear;

(2), the adjustment of amplitude A:

Amplitude A=2I _zω _yω _z, based on moment of inertia I _zbe inconvenient to regulate, regulate the ω of each rotor (18) _yω _zratio is:

${\mathrm{\ω}}_{y1}{\mathrm{\ω}}_{z1}:{\mathrm{\ω}}_{y2}{\mathrm{\ω}}_{z2}:{\mathrm{\ω}}_{y3}{\mathrm{\ω}}_{z3}:{\mathrm{\ω}}_{y4}{\mathrm{\ω}}_{z4}\·\·\·=1:-\frac{1}{3}:\frac{1}{5}:-\frac{1}{7}\·\·\·$

Realize the adjustment of amplitude A;

By ω _y1: ω _y2: ω _y3: ω _y4=1:3:5:7 ..., obtain the spin velocity ω of each rotor (18) _zshould meet:

${\mathrm{\ω}}_{z1}:{\mathrm{\ω}}_{z2}:{\mathrm{\ω}}_{z3}:{\mathrm{\ω}}_{z4}\·\·\·=1:-\frac{1}{9}:\frac{1}{25}:-\frac{1}{49}\·\·\·$

Wherein, the negative sign in formula represents the spin velocity ω of rotor (18) _zdirection is contrary;

Step 3, each Fourier series correspondence often organize a single gyro instrument (D) in gyroscope (C), are made the resultant moment that obtains level and smooth to Fourier coefficient revise.