CN102490885A - Rollover movement control method of multi-joint dolphin robot - Google Patents

Abstract

The invention discloses a rollover movement control method of a multi-joint dolphin robot. A control method and achieving steps of front rollover movements and rear rollover movements of the dolphin robot are provided by performing theoretical analysis and system research on the front rollover movements and the rear rollover movements of the dolphin robot and combining a propulsion mechanism of movements of a dolphin. Due to the fact that the front rollover movements and the rear rollover movements of the dolphin robot belong to pitching movements of the dolphin, first the pitching movements of the dolphin are analyzed and divided into a bending stage and an stretching stage, the bending stage and the stretching stage are respectively analyzed, a calculation formula of a joint turning angle and a movement path of joints during the pitching movements are provided, and movements of pitching joints of the dolphin robot are controlled. The rollover movement control method of the multi-joint dolphin robot can accurately control a pitch angle of the dolphin robot during the movements, and achieves accuracy of pitching movement control of the dolphin robot.

Description

A kind of tumbling motion control method of multi-joint robotic dolphin

Technical field

The present invention relates to the bionics field, especially a kind of method of tumbling motion control of multi-joint robotic dolphin.

Background technology

Dolphin as a kind of marine mammal, has mirable natatory skill and drag reduction ability.When dolphin moves about, rely on swinging up and down and the cooperation of pectoral fin of caudal peduncle and tail fin, the momentary velocity of swimming is up to 11m/s.When dolphin changed kinematic velocity and direction, skin can produce the effect that fold suppresses turbulent flow, thereby reduces the resistance of water greatly, and the average propulsion coefficient of dolphin is reached between 0.75～0.90.In addition, dolphin has superpower manoevreability and the alerting ability of turning to, and its deflection angle can reach 561.6 °/s, radius of rotation even can be less than 0.2 height.In view of the good mobility of dolphin, flexibility and high efficiency, has excellent application value in the monitoring in dangerous, narrow, complicated underwater environment, detective, attack, salvage and the maintenance.

The research of biomimetic robotic dolphin has comprised multidisciplinary cross-cutting issues such as biology, hydrodynamics, automatic guidance, materialogy and Robotics, and form and mechanism more complicated still are in the starting stage in the world.At present, domestic and international many experts, scholar and linked groups conduct a research to propelling mechanism, drag reduction mechanism and the motion control of robotic dolphin.The two joint robotic dolphins that Nakashima makes, pectoral fin and tail fin have 1 degree of freedom respectively.Dlgangil has successively made four joint robotic dolphins and five joint robotic dolphins.Wherein, four joint robotic dolphins provide power with pneumatics, and the pectoral fin of five joint robotic dolphins and tail fin have 2 degree of freedom respectively.Fish team is devoted to study propulsion capability and the maneuverability property that dolphin moves about always.The successful solution of " Gray ' s Paradox " problem helps us that propelling mechanism, drag reduction mechanism and the motion control of dolphin have been had darker understanding.A lot of viewpoints think why dolphin has so surprising characteristic, and reason and its luffing through the high flexible of the asymmetric swing achievements of tail fin have relation.But, so far, the research of dolphin luffing also being in the starting stage, the influence that luffing produces also needs further research.

Summary of the invention

The tumbling motion control method that the purpose of this invention is to provide a kind of multi-joint robotic dolphin is to solve the three-dimensional motion control problem of biomimetic robotic dolphin.This method to dolphin before roll under water, the back tumbling motion carries out systematic study and theoretical analysis, with preceding roll, the luffing of back under the tumbling motion be divided into crooked stage and stretching, extension stage, sets up the model that moves about in stretching, extension stage.Simultaneously, provide roll before the robotic dolphin, the control method and the performing step of back tumbling motion.

The tumbling motion control method of a kind of multi-joint robotic dolphin proposed by the invention; It is characterized in that said tumbling motion comprises preceding tumbling motion and back tumbling motion, two kinds of motions are by facing upward and nutation fundamental operation combination completion; In the process of rolling of robotic dolphin; The pitch angle through robotic dolphin is set and the pivot angle in each pitching joint, alternately carry out face upward, the nutation action, the barycenter of adjustment robotic dolphin and the relative position of centre of buoyancy; Obtain corresponding tumbling rate and steering torque, to accomplish tumbling motion.

The present invention has realized accurately with flexibly controlling the robotic dolphin luffing; Forward roll campaign and two kinds of actions of backward roll campaign of initiative robotic dolphin; Reach 360 ° of rotations in the robotic dolphin vertical plane surface, the high mobility and the alerting ability of the luffing of verifier dolphin.Simultaneously, the pitch angle of the pitch control subsystem algorithm accuracy control robotic dolphin on the go among the present invention obtains the particularity that the robotic dolphin luffing is controlled.

Description of drawings

Fig. 1 is the biomimetic robotic dolphin structural representation.

Fig. 2 is that the phase analysis scheme drawing is stretched in the biomimetic robotic dolphin luffing.

Fig. 3 is the experiment video interception of rolling before the biomimetic robotic dolphin.

Fig. 4 is the experiment video interception of rolling behind the biomimetic robotic dolphin.

The specific embodiment

For making the object of the invention, technical scheme and advantage clearer, below in conjunction with specific embodiment, and with reference to accompanying drawing, to further explain of the present invention.

One, the physical construction of biomimetic robotic dolphin

Fig. 1 is the biomimetic robotic dolphin structural representation; As shown in Figure 1, biomimetic robotic dolphin comprises rigidity leading portion health 2, has the flexible back segment health 6 in a plurality of pitching joint, tail fin 14, pectoral fin sheet 10, dorsal fin sheet 3, control circuit board 9, gyroscope 11, pressure sensor 12, infrared detector 8, moving slider 1, counterweight copper billet 4, driftage joint 5, pitching joint 7, caudal peduncle 13.

In the said biomimetic robotic dolphin, leading portion health 2 links to each other with the flexible back segment health 6 with a plurality of joints; Leading portion health 2 inside are hollow structure, and set inside contains moving slider 1, control circuit board 9, power module, gyroscope 11, counterweight copper billet 4; The leading portion health 2 anterior infrared detectors 8 of installing are used for keeping away barrier, and left side setting pressure sensor 12 is used for measuring the pressure of water, and upside is installed source switch; Comprise a servomotor in the moving slider 1, be used to drive pitching joint J4, the center of gravity that is used for regulating robotic dolphin; Pectoral fin sheet 10 and dorsal fin sheet 3 are installed on the both sides and the upside of leading portion health 2 respectively, play equilibrium activity; Back segment health 6 comprises a driftage joint 5 and three pitching joint 7 (J ₁, J ₂And J ₃), drive by DC machine; The yawing rotation of driftage joint 5 control robotic dolphins; Pitching joint 7 produces the propulsive force that robotic dolphin moves about, the luffing of control robotic dolphin; Caudal peduncle 13 connects the back segment health 6 and tail fin 14 of robotic dolphin; Tail fin 14 swings up and down the generation propulsive force with the back segment health; All joints adopt aluminum alloy framework to link to each other; Fish-skin is the waterproof fish-skin.

The three-dimensional dimension of this biomimetic robotic dolphin is about (L * W * H): 560mm * 240mm * 160mm.Total weight is about: 3.29kg.

Below in conjunction with accompanying drawing a kind of tumbling motion control method of multi-joint robotic dolphin is provided detailed explanation.

Two, robotic dolphin tumbling motion control

The tumbling motion of robotic dolphin belongs to the luffing of dolphin, so the present invention at first analyzes the luffing of dolphin.Characteristic based on the dolphin elevating movement is divided into crooked stage and stretching, extension stage with elevating movement.The crooked stage is meant that each pitching joint of robotic dolphin bends towards the health homonymy, and body shape is c-shaped.The time that this stage continues is shorter, and mainly being increases luffing angle.The stretching, extension stage is meant that the health of robotic dolphin reverts to the straight line form by bending shape.This stage considers that the recoil that turns to can have a negative impact to pitch angle, and the present invention takes to slow down the rate of stretch, prolongs the measure of stretching time length.

Robotic dolphin is pitching in water, relies on the swing of back segment health and tail fin that power is provided.Back segment health on the go must receive the drag effect of the water that arranges.When the dolphin constant airspeed, the size of suffered resistance is directly proportional with the active area of water.Therefore, for the drag effect of water in reducing to move, should make the active area of water minimum.Theoretically, the cross-sectional plane of back segment health is the smallest cross-sectional of water active area, this means that each pitching joint must move along the axis of body section at its place.But the pitching joint cooperatively interacts, mutual restriction.Therefore, this method is also infeasible in reality.

The measure that the present invention takes is for making current active joint J _iThe adjacent segment J of back _I+1The edge

The direction motion.So, obtain constraint condition:

$\left\{\begin{array}{c}\frac{x_{i+1}^{\′}-x_i}{x_i-x_{i+1}}=\frac{z_{i+1}^{\′}-z_i}{z_i-z_{i+1}}\\ {(x_{i+1}^{\′}-x_i^{\′})}^2+{(z_{i+1}^{\′}-z_i^{\′})}^2=l_i^2\end{array}\right.,$

Wherein, (x _i, z _i) the preceding coordinate of expression joint Ji rotation, (x _I+1, z _I+1) expression joint J _I+1Coordinate before rotating, (x ' _i, z ' _i) expression joint J _iCoordinate after the rotation, (x ' _I+1, z ' _I+1) expression joint J _I+1Coordinate after the rotation, l _iExpression joint J _iWith joint J _I+1Between distance.

According to this constraint condition, obtain rotary joint J _iRotational angle θ ' _i:

Wherein, J _I-1' expression joint J _I-1Loca after the rotation, J ' _iExpression joint J _iLoca after the rotation, J _I+1' expression joint J _I+1Loca after the rotation,

Posterior joint section J ' is rotated in expression _iJ _I+1' at the cooresponding vector of system of axes,

Posterior joint section J is rotated in expression _I-1' J ' _iCooresponding vector in system of axes,

The expression vector

Length, i.e. joint segments J ' _iJ _I+1' length,

Represent vectorial J _I-1' J ' _iLength, i.e. joint segments J _I-1' J ' _iLength.

According to above-mentioned condition, just can control the motion in each pitching joint of robotic dolphin, realize the luffing of robotic dolphin.As shown in Figure 2: in Fig. 2 a, at first, pitching joint J ₁Rotate at full speed as the active joint, and other pitching joints J ₂, J ₃Then, follow its adjacent last joint J respectively as passive joint ₁, J ₂Rotate, the angle of rotation is determined by above-mentioned formula.In Fig. 2 b, joint segments J ₁J ₂Move to horizontality, keep stretching, pitching joint J ₁Stop operating.In Fig. 2 b to Fig. 2 f, joint J ₂Replace joint J ₁As the active joint rotation, its posterior joint J ₃Follow joint J as passive joint ₂Rotate.In Fig. 2 g, joint segments J ₂J ₃Move to horizontality, keep stretching, pitching joint J ₂Stop operating joint J ₃Replace J ₂As the active joint rotation, until horizontality.

The tumbling motion of robotic dolphin of the present invention, preceding tumbling motion that comprises dolphin and back tumbling motion, therefore designed respectively roll before the robotic dolphin, the control method of back tumbling motion.Said preceding tumbling motion and back tumbling motion are by facing upward and nutation fundamental operation combination completion.In the process of rolling of robotic dolphin; The pitch angle through robotic dolphin is set and the pivot angle in each pitching joint, alternately carry out face upward, the nutation action, the barycenter of adjustment robotic dolphin and the relative position of centre of buoyancy; Obtain corresponding tumbling rate and steering torque, to accomplish tumbling motion.

(1) tumbling motion before the robotic dolphin

Fig. 3 is the experiment video interception of tumbling motion before the robotic dolphin, and as shown in Figure 3, the preceding tumbling motion control method of robotic dolphin further may further comprise the steps:

Step 1.1, shown in Fig. 3 a to Fig. 3 c, robotic dolphin begins level and is statically placed in the bottom, before carrying out during tumbling motion; At first all pitching joints are swung to the back side being no more than under the prerequisite of limit angles simultaneously rapidly, the robotic dolphin head is faced upward rapidly, then use pitch control subsystem algorithm of the present invention; Make dolphin through behind several oscillation periods, rise rapidly, advance integral body upwards to travel forward with 45 ° pitch angle; It is water-bed that robotic dolphin is broken away from, and moves to the middle part in pond, conveniently carries out ensuing action; Avoid scratching with water-bed, wherein, the limit angles in pitching joint is a pitching joint maximum rotation angle; Be the maximum angle that the pitching joint can be rotated, it sets three of robotic dolphin rotary joint J among the present invention according to the parameter character of joint steering wheel and the restriction of robotic dolphin action itself ₁, J ₂And J ₃Corner restriction be set to respectively: 80 °, 65 ° and 65 °;

Step 1.2, shown in Fig. 3 d, behind the middle part, arrival pond, robotic dolphin uses same pitch control subsystem algorithm, and nutation obtains-45 ° pitch angle immediately, guarantees that simultaneously robotic dolphin still has certain distance apart from the bottom;

Step 1.3, shown in Fig. 3 e, three pitching joints of robotic dolphin are crooked to the back side slightly, and angle of bend is respectively 20 °, 30 °, 40 °, increases the distance that tail fin is struck when the outside of belly is flapped, for the bigger nose-down pitching moment that needs in the step 1.4 is prepared;

Step 1.4; Shown in Fig. 3 f to Fig. 3 g; Robotic dolphin with maximal rate to crooked all the pitching joints of the outside of belly; By the warming-up exercise in the step 1.3, produce very large nose-down pitching moment, make dolphin in the extremely short time; The angle of pitch is above-90 °; At this moment, the barycenter CM of robotic dolphin and centre of buoyancy CB counter-rotating, dolphin begins lift-over forward simultaneously;

Step 1.5 is shown in Fig. 3 h to Fig. 3 i, at this moment; By the bigger cireular frequency that produced during nutation rapidly just now, and the extra nose-down pitching moment that brings of barycenter CM and centre of buoyancy CB counter-rotating, dolphin is rolled before further; When approaching-270 ° of the pitch angle of robotic dolphin; The barycenter CM of robotic dolphin and centre of buoyancy CB be reversed to once more barycenter down, the centre of buoyancy is in last normal condition, at this moment, robotic dolphin stretches its afterbody; Use pitch control subsystem algorithm of the present invention to continue the nutation motion, further reduce pitch angle;

Step 1.6, shown in Fig. 3 j to Fig. 3 k, in the process of rolling after this, robotic dolphin utilizes acquired turning velocity, continues to bend the body and roll, and is in vertical state up to head;

Step 1.7, last shown in Fig. 3 l, robotic dolphin makes physical recovery arrive horizontality through further luffing adjustment pitch angle, and swims out of forward or stop, and accomplishes once preceding tumbling motion.

According to observed data, can learn that the crooked time length of robotic dolphin health is about t _Tuck≈ 0.666 ± 0.122s, the angle of rotation of its tail fin and time relation formula are:

β _front＝1726.4t ³-1724.7t ²+255，t∈[0，0.666]。

In the process of before whole, rolling, the suffered moment of robotic dolphin meets following equality:

$J_D\stackrel{\·\·}{\mathrm{\θ}}=M_F^{\′}+M_f^{\′}+M_G$

$M_F^{\′}=\left\{\begin{array}{c}-\frac{1}{8}\mathrm{\ρ}{\stackrel{\·}{\mathrm{\ψ}}}^2\{W_p{C}_c{L_p}^4+W_c{C}_F[{(L_p+L_c)}^4-{L_p}^4\left]\right\},t\∈[t_0,t_0+t_{\mathrm{tuck}}]\\ 0,t>t_0+t_{\mathrm{tuck}}\end{array}\right.$

$M_f^{\′}=\left\{\begin{array}{c}-\frac{1}{8}\mathrm{sign}\left(\stackrel{\·}{\mathrm{\θ}}\right){\stackrel{\·}{\mathrm{\θ}}}^2\mathrm{\ρ}{W}_a{C}_c{L_a}^4,t\∈[t_0,t_0+t_{\mathrm{tuck}}]\\ -\frac{1}{16}\mathrm{sign}\left(\stackrel{\·}{\mathrm{\θ}}\right){\stackrel{\·}{\mathrm{\θ}}}^2\mathrm{\ρ}(W_a{C}_c{L_a}^4-2W_c{C}_F{L_p}^4),t>t_0+t_{\mathrm{tuck}}\end{array}\right.,$

$M_G=\left\{\begin{array}{c}{\mathrm{mgd}}_{0}t\cos \left(\stackrel{\·}{\mathrm{\θ}}\right)/t_{\mathrm{tuck}},t\∈[t_0,t_0+t_{\mathrm{tuck}}]\\ {\mathrm{mgd}}_0\cos \left(\stackrel{\·}{\mathrm{\θ}}\right),t>t_0+t_{\mathrm{tuck}}\end{array}\right.$

Wherein, J _DThe rotor inertia of expression robotic dolphin,

The angular acceleration of expression robotic dolphin, M ' _FExpression impulse force moment, M ' _fThe expression resistance torque, M _GThe moment that expression barycenter CM and centre of buoyancy CB difference produce, ρ representes water tightness,

The cireular frequency that the expression impulse force produces, W _pThe width of expression back of the body abdomen swing part, C _cExpression cylinder suffered drag coefficient in water, L _pThe length of expression robotic dolphin back of the body abdomen swing part, W _cExpression tail fin width, C _FExpression square planar suffered drag coefficient in water, L _cThe tail fin chord length of expression robotic dolphin, t ₀The expression robotic dolphin crooked time opening of health, t _TuckThe crooked time length of expression robotic dolphin health,

The cireular frequency of expression robotic dolphin, W _aExpression robotic dolphin front body projection width, L _aExpression robotic dolphin front body length, m representes the quality of robotic dolphin, d ₀Ultimate range between expression barycenter CM and centre of buoyancy CB.

(2) tumbling motion behind the robotic dolphin

The back tumbling motion of robotic dolphin is with respect to the difficulty more of preceding rolling.Reason is because the varying in weight of first health of robotic dolphin and second health, and causes dolphin gravity also different in the effect of preceding rolling, play in the tumbling motion of back.During tumbling motion, in 270 ° of initial rotary courses, gravity is the resistance of tumbling motion always behind the robotic dolphin.Therefore, robotic dolphin relies on the propulsive force of self to realize preceding 270 ° rotation this moment fully.

Fig. 4 is the experiment video interception of tumbling motion behind the robotic dolphin, and is as shown in Figure 4, and the back tumbling motion control method of robotic dolphin further may further comprise the steps:

Step 2.1; Shown in Fig. 4 a to Fig. 4 e, swing to the back side being no more than under the prerequisite of limit angles rapidly in all pitching joints of robotic dolphin, and the robotic dolphin head is faced upward rapidly; Then use pitch control subsystem algorithm of the present invention; Dolphin is through behind several oscillation periods, move to depth of water central authorities and the most at last pitch angle be increased to 90 °, robotic dolphin is rendered as attitude straight up at this moment;

Step 2.2, shown in Fig. 4 f to Fig. 4 h, the pitching joint J of robotic dolphin ₁Sharply, make the barycenter CM of robotic dolphin be positioned at the back side one side of its centre of buoyancy CB, still keep enough static stabilities under the topsy-turvydom that robotic dolphin makes progress at the outside of belly, the back side is downward thereby make to crooked 50 ° of outside of belly direction;

Step 2.3, shown in Fig. 4 i, at this moment, the pitching joint J of robotic dolphin ₂As the active joint in the pitch control subsystem algorithm; The motion of proceeding to face upward; Surpass 220 ° up to pitch angle, then, robotic dolphin slightly stretches all pitching joints to the outside of belly; Increase the distance that tail fin is struck when flap in the back side, for the bigger nose-up pitching moment that needs in step 2.4 and the step 2.5 is prepared;

Step 2.4, shown in Fig. 4 j to Fig. 4 k, robotic dolphin towards all pitching joints of back side swing, makes the health rotation that comes back rapidly with maximum speed;

Step 2.5, shown in Fig. 4 l to Fig. 4 m, by the extra nose-up pitching moment that reverses and bring in the cireular frequency and the barycenter centre of buoyancy of accumulation in step 2.3 and the step 2.4, the quick lift-over of robotic dolphin reaches 360 ° up to pitch angle;

Step 2.6 is shown in Fig. 4 n, after pitch angle arrives 360 °; Must stretch each pitching joint immediately; Make pitch angle remain on 360 °, otherwise dolphin can be further under the nose-up pitching moment that barycenter CM and centre of buoyancy CB are produced lift-over to 450 ° pitch angle, thereby make the backward roll failure;

Step 2.7 shown in Fig. 4 o, after robotic dolphin reverts to horizontality, is swum out of or is stopped, and accomplishes a backward roll campaign.

According to observed data, can learn that the crooked time length of robotic dolphin health is about t _Tuck≈ 0.575 ± 0.118s, the angle of rotation of its tail fin and time relation are:

β _back＝1893.6t ³-1633.2t ²+180，t∈[0，0.575]。

Above-described specific embodiment; The object of the invention, technical scheme and beneficial effect have been carried out further explain, and institute it should be understood that the above is merely specific embodiment of the present invention; Be not limited to the present invention; All within spirit of the present invention and principle, any modification of being made, be equal to replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (10)

1. the tumbling motion control method of a multi-joint robotic dolphin; It is characterized in that said tumbling motion comprises preceding tumbling motion and back tumbling motion, two kinds of motions are by facing upward and nutation fundamental operation combination completion; In the process of rolling of robotic dolphin; The pitch angle through robotic dolphin is set and the pivot angle in each pitching joint, alternately carry out face upward, the nutation action, the barycenter of adjustment robotic dolphin and the relative position of centre of buoyancy; Obtain corresponding tumbling rate and steering torque, to accomplish tumbling motion.

2. method according to claim 1 is characterized in that, said multi-joint robotic dolphin comprises: rigidity leading portion health, have flexible back segment health, gyroscope, tail fin, pectoral fin sheet, the dorsal fin sheet in a plurality of pitching joint.

3. method according to claim 1 is characterized in that, said control for preceding tumbling motion further may further comprise the steps:

Step 1.1; Robotic dolphin begins level and is statically placed in the bottom; Before carrying out during tumbling motion; At first all pitching joints are swung to the back side being no more than under the prerequisite of limit angles simultaneously rapidly; The robotic dolphin head is faced upward rapidly; Then use said pitch control subsystem algorithm; Make dolphin through after several hunting periods; The angle of pitch with 45 ° rises rapidly; Advance integral body upwards to travel forward, it is water-bed that robotic dolphin is broken away from, and moves to the middle part in pond; Conveniently carry out ensuing action, avoid scratching with water-bed;

Step 1.2, behind the middle part, arrival pond, robotic dolphin uses same pitch control subsystem algorithm, and nutation obtains-45 ° pitch angle immediately, guarantees that simultaneously robotic dolphin still has certain distance apart from the bottom;

Step 1.3, all pitching joints of robotic dolphin are crooked to the back side slightly, increase the distance that tail fin is struck when the outside of belly is flapped, for the bigger nose-down pitching moment that needs in the step 1.4 is prepared;

Step 1.4; Robotic dolphin with maximal rate to crooked all the pitching joints of the outside of belly; By the warming-up exercise in the step 1.3; Produce very large nose-down pitching moment; Make dolphin in the extremely short time, the angle of pitch surpasses-90 °, at this moment; The barycenter CM of robotic dolphin and centre of buoyancy CB counter-rotating, dolphin begins lift-over forward simultaneously;

Step 1.5, by the bigger cireular frequency that produces during nutation rapidly in the step 1.4, and the extra nose-down pitching moment that brings of barycenter CM and centre of buoyancy CB counter-rotating; Dolphin is rolled before further, when approaching-270 ° of the pitch angle of robotic dolphin, the barycenter CM of robotic dolphin and centre of buoyancy CB be reversed to once more barycenter CM descend, centre of buoyancy CB is in last normal condition; At this moment; Robotic dolphin stretches its afterbody, uses said pitch control subsystem algorithm to continue the nutation motion, further reduces pitch angle;

Step 1.6, in the process of rolling after this, robotic dolphin utilizes acquired turning velocity, continues to bend the body and roll, and is in vertical state up to head;

Step 1.7, last, robotic dolphin makes physical recovery arrive horizontality through further luffing adjustment pitch angle, and swims out of forward or stop, and accomplishes once preceding tumbling motion.

4. method according to claim 1 is characterized in that, in the said preceding tumbling motion, and the angle of rotation β of robotic dolphin tail fin _FrontWith the relation of time t be:

β _front＝1726.4t ³-1724.7t ²+255，t∈[0，0.666]。

5. method according to claim 1 is characterized in that, in the said preceding tumbling motion, the suffered moment of robotic dolphin meets following equality:

$J_D\stackrel{\·\·}{\mathrm{\θ}}=M_F^{\′}+M_f^{\′}+M_G$

$M_F^{\′}=\left\{\begin{array}{c}-\frac{1}{8}\mathrm{\ρ}{\stackrel{\·}{\mathrm{\ψ}}}^2\{W_p{C}_c{L_p}^4+W_c{C}_F[{(L_p+L_c)}^4-{L_p}^4\left]\right\},t\∈[t_0,t_0+t_{\mathrm{tuck}}]\\ 0,t>t_0+t_{\mathrm{tuck}}\end{array}\right.$

$M_f^{\′}=\left\{\begin{array}{c}-\frac{1}{8}\mathrm{sign}\left(\stackrel{\·}{\mathrm{\θ}}\right){\stackrel{\·}{\mathrm{\θ}}}^2\mathrm{\ρ}{W}_a{C}_c{L_a}^4,t\∈[t_0,t_0+t_{\mathrm{tuck}}]\\ -\frac{1}{16}\mathrm{sign}\left(\stackrel{\·}{\mathrm{\θ}}\right){\stackrel{\·}{\mathrm{\θ}}}^2\mathrm{\ρ}(W_a{C}_c{L_a}^4-2W_c{C}_F{L_p}^4),t>t_0+t_{\mathrm{tuck}}\end{array}\right.,$

$M_G=\left\{\begin{array}{c}{\mathrm{mgd}}_{0}t\cos \left(\stackrel{\·}{\mathrm{\θ}}\right)/t_{\mathrm{tuck}},t\∈[t_0,t_0+t_{\mathrm{tuck}}]\\ {\mathrm{mgd}}_0\cos \left(\stackrel{\·}{\mathrm{\θ}}\right),t>t_0+t_{\mathrm{tuck}}\end{array}\right.$

Wherein, J _DThe rotor inertia of expression robotic dolphin,

The angular acceleration of expression robotic dolphin, M ' _FExpression impulse force moment, M ' _fThe expression resistance torque, M _GThe moment that expression barycenter CM and centre of buoyancy CB difference produce, ρ representes water tightness,

The cireular frequency that the expression impulse force produces, W _pThe width of expression back of the body abdomen swing part, C _cExpression cylinder suffered drag coefficient in water, L _pThe length of expression robotic dolphin back of the body abdomen swing part, W _cExpression tail fin width, C _FExpression square planar suffered drag coefficient in water, L _cThe tail fin chord length of expression robotic dolphin, t ₀The expression robotic dolphin crooked time opening of health, t _TuckThe crooked time length of expression robotic dolphin health,

The cireular frequency of expression robotic dolphin, W _aExpression robotic dolphin front body projection width, L _aExpression robotic dolphin front body length, m representes the quality of robotic dolphin, d ₀Ultimate range between expression barycenter CM and centre of buoyancy CB.

6. method according to claim 1 is characterized in that, said control for the back tumbling motion further may further comprise the steps:

Step 2.1; Swing to the back side being no more than under the prerequisite of limit angles rapidly in all pitching joints of robotic dolphin; The robotic dolphin head is faced upward rapidly, then use said pitch control subsystem algorithm, dolphin is through behind several oscillation periods; Move to depth of water central authorities and the most at last pitch angle be increased to 90 °, robotic dolphin is rendered as attitude straight up at this moment;

Step 2.2, the pitching joint J of robotic dolphin ₁Sharply crooked 50 °, make the barycenter CM of robotic dolphin be positioned at the back side one side of its centre of buoyancy CB, thereby make robotic dolphin under the outside of belly makes progress the downward topsy-turvydom in the back side, still keep enough static stabilities to outside of belly direction;

Step 2.3, at this moment, the pitching joint J of robotic dolphin ₂As the active joint in the said pitch control subsystem algorithm; The motion of proceeding to face upward; Surpass 220 ° up to pitch angle, then, robotic dolphin slightly stretches all pitching joints to the outside of belly; Increase the distance that tail fin is struck when flap in the back side, for the bigger nose-up pitching moment that needs in step 2.4 and the step 2.5 is prepared;

Step 2.4, robotic dolphin towards all pitching joints of back side swing, make the health rotation that comes back rapidly with maximum speed;

Step 2.5, by the extra nose-up pitching moment that reverses and bring in the cireular frequency and the barycenter centre of buoyancy of accumulation in step 2.3 and the step 2.4, the quick lift-over of robotic dolphin reaches 360 ° up to pitch angle;

Step 2.6, pitch angle stretches each pitching joint after arriving 360 ° immediately, makes pitch angle remain on 360 °;

Step 2.7 after robotic dolphin reverts to horizontality, is swum out of or is stopped, and accomplishes a backward roll campaign.

7. method according to claim 6 is characterized in that, in the tumbling motion of said back, and the angle of rotation β of robotic dolphin tail fin _BackWith the relation of time t be:

β _back＝1893.6t ³-1633.2t ²+180，t∈[0，0.575]。

8. according to claim 1 or 3 or 6 described methods, it is characterized in that said pitch control subsystem algorithm is: pitching joint J at first ₁Rotate at full speed as the active joint, and other pitching joints J ₂, J ₃Then, follow its adjacent last joint J respectively as passive joint ₁, J ₂Rotate; Joint segments J ₁J ₂Move to horizontality, keep stretching, pitching joint J ₁Stop operating; Then, joint J ₂Replace joint J ₁As the active joint rotation, its posterior joint J ₃Follow joint J as passive joint ₂Rotate; Joint segments J ₂J ₃Move to horizontality, keep stretching, pitching joint J ₂Stop operating; Last joint J ₃Replace J ₂As the active joint rotation, until horizontality.

9. method according to claim 8 is characterized in that, each rotary joint J _iRotational angle θ ' _iFor:

Wherein, J _I-1' expression joint J _I-1Loca after the rotation, J ' _iExpression joint J _iLoca after the rotation, J _I+1' expression joint J _I+1Loca after the rotation,

Posterior joint section J ' is rotated in expression _iJ _I+1' at the cooresponding vector of system of axes,

Posterior joint section J is rotated in expression _I-1' J ' _iCooresponding vector in system of axes, The expression vector

Length, i.e. joint segments J ' _iJ _I+1' length,

The expression vector

Length, i.e. joint segments J _I-1' J ' _iLength.

10. according to claim 3 or 6 described methods, it is characterized in that said limit angles is the maximum angle that the pitching joint can be rotated, it is set according to the parameter character of joint steering wheel and the restriction of robotic dolphin action itself.

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