CN104943762B - Determination method for shape shifting robot attitude transformation optimal path - Google Patents

Abstract

The invention discloses a determination method for a shape shifting robot attitude transformation optimal path. According to the determination method for the shape shifting robot attitude transformation optimal path, the graph theory is introduced on the attitude control of a shape lifting robot, an attitude transformation problem is converted into a graph theory related problem, accordingly, according to the attitude transformation complexity weight minimum principle, when the optimal attitude transformation path is obtained, a control system can send a corresponding driving order to a motor of each joint of the shape shifting robot, so that the shape shifting robot can transform the joint turning angles of the shape shifting robot in sequence according to the optimal attitude transformation path, the reasonable sequence transformation of the attitude of the shape shifting robot is achieved, the interconversion between different attitudes is achieved, for different environment conditions, the attitude transformation of the shape shifting robot can be achieved stably, efficiently and reasonably, and therefore the good environmental suitability is achieved.

Description

A kind of determination method of fighter toy posture changing optimal path

Technical field

The present invention relates to fighter toy, especially a kind of displacement robot.

Background technology

Fighter toy for different complex environments, the especially research of displacement robot are more and more, and The attitude of robot deformation is also more and more.For example, there are four crawler belts with motor in a kind of displacement robot (belonging to shank), every crawler belt are all passed through an extension bar (belonging to thigh) and are connected with robot body via two movable joints, Its each movable joint all adopts Motor drive.By each, around the rotation in its joint, each shank and thigh all can be real The rotation change of existing difference angle, so as to be combined into many attitude of displacement robot, realizes its different walking manner, To adapt to the motion needs in varying environment situation.In the conversion of displacement robot pose, the change between some attitudes Change relatively easy；Conversion between some attitudes is relative complex, and some are even needed through other attitudes as intermediate conversion Attitude is realizing.For example, by certain attitude A to certain attitude B, may approach A-C-B, it is also possible to which approach A-D-F-B is transformed Journey；Rotation amplitude for causing is minimum, while ensureing that the skew of center of gravity is minimum, the energy consumption for reaching robot pose conversion is little, speed Degree is fast, the stable effect of whole fuselage, it is thus necessary to determine that from certain attitude A to the optimal conversion approach of certain attitude B.

But currently for the scientific and reasonable sex chromosome mosaicism of its posture deforming, still without a kind of scientific and effective solution.Such as A kind of what scientific and rational optimal deformation approach of the displacement robot of design in attitude change, is that we have to solution Problem certainly.

The content of the invention

The present invention is directed to scientific and rational optimal deformation approach of the displacement robot in attitude change, proposes one Plant the determination method of the fighter toy posture changing optimal path based on graph theory.

A kind of determination method of fighter toy posture changing optimal path, takes following steps：

The first step, establishes the various possible deformation attitudes of fighter toy, and takes the name on a corresponding diagram opinion summit for which Title code name (i=1,2,3, n), while, it is established that show that the summit whether various attitudes mutually directly can convert connects Logical figure；

Second step, determines each summit V_i(i=1,2,3, n) between posture changing complexity weights calculating side Method：

For the summit that can directly convert or directly connect, fortune of the complexity weights of posture changing by joint between each summit Two factors of side-play amount of dynamic angle and center of gravity are determining；

If fighter toy is from certain attitude to another kind of posture changing, relative to current pose, its 4 big leg joints The angle of rotation is respectively defined as θ_b1, θ_b2, θ_b3, θ_b4, corresponding 4 calf joint movement angles are respectively defined as θ_s1, θ_s2, θ_s3, θ_s4, the horizontal-shift component of robot body's center of gravity is X_d, the vertical shift component of center of gravity is Y_d, and take X_dMaxIt is water Square upwards maximum offset of center of gravity, Y_dMaxFor the maximum offset of center of gravity in vertical direction, then big leg joint mean motion Angle is:

In the same manner, calf joint mean motion angle is:

By variable θ_bAnd θ_sIt is normalized, even if obtain data being between 0 to 1；The method of normalized is： By the θ of gained_bAnd θ_sNumerical value is divided by 360 degree；Center of gravity horizontal and vertical offset component is respectively divided by into the maximum in all directions partially again Shifting amount, while, it is considered in vertical direction, center of gravity rises or falls the load difference to motor, Y when setting center of gravity rises_dFor just, Y when center of gravity falls_dIt is negative, then, the complexity weights of center of gravity horizontal-shift pass throughFormula represents, center of gravity vertical shift is answered Miscellaneous degree weights pass throughFormula represents that λ is between 0 and Y in formula_dMaxCertain test bit between/3；Again fuselage is risen When complexity weights somewhat tune up, by decline when complexity weights somewhat turn down, center of gravity component is synthesized into vector then P, then the mould of p vectors can be write as：

Then, according to θ during deformation_b、θ_sImpact to deformation complexity and experience, determine that each of which becomes in attitude with p Proportion shared in complexity weights is changed, constant w is used respectively₁、w₂、w₃Represent, wherein w₁、w₂、w₃Meet w₃>w₁>w₂Rule, It is last in order that computer can quickly and accurately processing data, the complexity weights of the posture changing for calculating can be amplified 100 times and round so as in rational integer range；

So, it is written as by the complexity weight computing formula for converting between various attitudes:

When one timing of body parameters, so that it may be derived from posture changing complexity weights different between each summit；Above-mentioned A kind of complexity when posture changing complexity weights represent robot from posture changing to another kind of attitude, weights are got over Low, the conversion between attitude is easier, conversely, being then more difficult to；

Represented with infinitely great symbol ∞ for the weights between summit are not directly connected；

3rd step, sets up each summit V_i(i=1,2,3, n) between weight matrix

Second step computational methods are drawn the weights between each summit, W is used_ijRepresented by summit V respectively_iConvert directly to summit V_jWhen weights, now, have the weights W of i=j on diagonal_ij=0；Setting up one accordingly has i × j (herein, i=j) individual The weight matrix W of element:

4th step, determines the minimum conversion approach of weights

First, V is set as all summit V in posture changing figure can be connected_i(i=1,2,3, set n)；Setting S_iFor mono- dynamic subset of V, S_iGather for continually adding such some summits in traversal loop：With certain V_i(i=1,2, 3, when n) being initial vertex, the current V-S of its arrival is searched for using traversal method_iIn set, the weights sum on each summit is Minimum approach, and with variable Best [V_j] (j=1,2,3, what n) special record currently can search for are pushed up from starting Point V_iTransform to any one summit V_jOptimum posture convert approach weights sum；Variable R OAD [V is used simultaneously_j] special record Summit V_jThe corresponding previous summit in its current optimum posture conversion approach, is designated as ROAD [V_j]=", is front apicad ", will be each Individual Best [V_j] (j=1,2,3, after n) being compared to each other, select that summit V with minimum weights sum_a, every time, By such a V_aIt is put into S_iIn set；

Then, the minimum conversion approach of weights is calculated, calculating process is as follows：

Step 1, initialization：Determine initial vertex V_i(i=1,2,3, n), and representative points V_end(end=1, 2, n), by initial vertex V_iIt is put into S_iIn set, now, S_i={ V_i, and by summit V_iWith each top in V set Weights between point are each placed in Best [V_j] (j=1,2,3, n) among, as initial vertex currently with each summit it Between minimum weights sum, now have, Best [V_j]=W_ij, while its each self-corresponding forward direction summit is set to into initial vertex, That is ROAD [V_j]=V_i(j=1,2,3, n)；

Step 2, the current S of comparison_iInitial vertex V in set_iWith current V-S_iConversion way in set between all summits Footpath, it is the V-S corresponding to minimum conversion approach to select each weights sum_iSummit V in set_a, V_aCorresponding conversion approach Weights sum should be Best [V_a]；

If V_a≠V_end, then by summit V_aIt is added to current S_iIn set, S is expressed as_i=S_i∪{V_a}；

If V_a=V_end, execution step 4；

Step 3, the current S of calculating_iInitial vertex V in set_iBy way of summit V_aWhen, to V-S_iEach summit V in set_j(j= 1,2,3, approach weights sum n)：Best[V_a]+W_aj, by its with originally without summit V_aEach weights sum Best[V_j] compare, if to some summits V therein_jExist：(Best[V_a]+W_aj)<Best[V_j], then update which corresponding Minimum weights are Best [V_j]=Best [V_a]+W_aj, accordingly update V_jIt is apicad ROAD [V before corresponding_j]=V_a, otherwise all Do not update；

Return to step 2, continues executing with；

Step 4, successively record representative points V_end, and by ROAD [V_end] start reverse backtracking each before apicad, directly To ROAD [V_j] it is initial vertex V_iTill, the reverse process of recorded approach is to transform to representative points by initial vertex Optimal mapping approach, algorithm terminate.

The invention has the beneficial effects as follows：

1st, after optimum posture conversion approach is obtained, control system just can be sent out to the motor in each joint of fighter toy Send corresponding drive command so that fighter toy can convert its joint rotation angle successively according to optimal mapping approach, realize which The rational sequence deformation of attitude.

2nd, Graph Theory is introduced on the gesture stability of fighter toy, posture changing problem is converted into into graph theory related Problem.So, fighter toy can be realized mutual between its different attitude according to posture deforming complexity weights minimum principle Conversion, for varying environment situation, can stablize, efficiently, reasonably realize the posture changing of fighter toy so as to very Good environmental suitability.

Description of the drawings

Fig. 1 is a displacement robot essential structure figure of the embodiment of the present invention；

Fig. 2 is the summit connected graph set up for the embodiment of the present invention；

Fig. 3 is the summit connected graph after the embodiment of the present invention adds weights；

Fig. 4 is the program flow diagram that the embodiment of the present invention finds optimal path；

Fig. 5-1 to 5-8 is the corresponding eight kinds of deformations attitude schematic diagram of the embodiment of the present invention.

In figure：001- fuselages, 002- thighs, 003- shanks.

Specific embodiment

The embodiment of the present invention is a displacement robot, and 001 length of fuselage is 648mm, and 001 width of fuselage is 450mm, 002 length of thigh is 360mm, and 003 length of shank is 262mm, takes X_dMaxWhen all trailing for robot, whole fuselage 001 is grown The a quarter of degree：473mm, takes Y_dMaxFor standing highest when whole fuselage 001 height of C.G.：622mm, while each joint Corner takes 90 ° or 45 ° of integral multiple respectively and calculates.

For finding the optimal path of robot pose deformation described in embodiment, determine that using the present invention its attitude most preferably becomes The following program of process of shape approach：

The first step, establishes the various possible 8 kinds of deformations attitudes of displacement robot, and takes a corresponding diagram opinion top for which The title code name of point, as shown in table 1, corresponding eight kinds of deformations attitude is as shown in Fig. 5-1 to 5-8；

Table 1：Attitude table corresponding with summit title

Meanwhile, according to the factors such as movement interference whether occur in deformation, by manually set up show between various attitudes be The no summit connected graph that mutually directly can be converted, summit connected graph is as shown in Fig. 2 arrow shows what is can be directly realized by figure Changing direction between different summits.

Second step, determines the computational methods of posture changing complexity weights between each summit

002 joint mean motion angle of thigh is:

In the same manner, 001 joint mean motion angle of shank is:

By variable θ_bAnd θ_sIt is normalized, even if obtain data being between 0 to 1；The method of normalized is： By the θ of gained_bAnd θ_sNumerical value is divided by 360 degree；Center of gravity horizontal and vertical offset component is respectively divided by into the maximum in all directions partially again Shifting amount, while, it is considered in vertical direction, center of gravity rises or falls the load difference to motor, Y when setting center of gravity rises_dFor just, Y when center of gravity falls_dIt is negative, then, the complexity weights of center of gravity horizontal-shift pass throughFormula represents, center of gravity vertical shift is answered Miscellaneous degree weights pass throughFormula represents that λ is between 0 and Y in formula_dMaxCertain test bit between/3；Again fuselage is risen When complexity weights somewhat tune up, by decline when complexity weights somewhat turn down, center of gravity component is synthesized into vector then P, then the mould of p vectors can be write as：

Then, according to θ during deformation_b、θ_sImpact to deformation complexity and experience, determine that each of which becomes in attitude with p Proportion shared in complexity weights is changed, constant w is used respectively₁=0.8, w₂=0.5, w₃=1.0, λ=10 expressions, robot master The horizontal-shift component X of the body weight heart_dAnd the vertical shift component Y of center of gravity_dCan be calculated by the two kinds of attitude truths for mutually converting and be obtained , it is last in order that computer can quickly and accurately processing data, the complexity weights of the posture changing for calculating can be put Big 100 times and round so as in rational integer range；

So, it is written as by the complexity weight computing formula for converting between various attitudes:

According to the body parameters given, different posture changing complexity weights can be obtained；Above-mentioned posture changing is complicated A kind of complexity when degree weights represent robot from posture changing to another kind of attitude, weights are lower, between attitude Conversion is easier, conversely, being then more difficult to.

Each posture changing complexity weights of above-mentioned calculating are counted in the summit connected graph shown in Fig. 2, after adding weights Summit connected graph it is as shown in Figure 3；

3rd step, sets up the weight matrix between each summit

Weights between each summit that second step is calculated, substitute into formula (5), it is established that following weight matrix W：

4th step, determines the minimum conversion approach of weights

First, V is set as all summit V in posture changing figure can be connected_i(i=1,2,3, set 8)；Setting S_iFor mono- dynamic subset of V, S_iGather for continually adding such some summits in traversal loop：With certain V_i(i=1,2, 3, when 8) being initial vertex, the current V-S of its arrival is searched for using traversal method_iIn set, the weights sum on each summit is Minimum approach, and with variable Best [V_j] (j=1,2,3, what 8) special record currently can search for are pushed up from starting Point V_iTransform to any one summit V_jOptimum posture convert approach weights sum；Variable R OAD [V is used simultaneously_j] special record Summit V_jThe corresponding previous summit in its current optimum posture conversion approach, is designated as ROAD [V_j]=", is front apicad ", will be each Individual Best [V_j] (j=1,2,3, after 8) being compared to each other, select that summit V with minimum weights sum_a, every time, By such a V_aIt is put into S_iIn set；

With initial vertex V₄To representative points V₂Conversion approach determination process as a example by, illustrate to determine the minimum conversion way of weights The algorithmic procedure in footpath and its corresponding step, the program flow diagram for finding optimal path are as shown in Figure 4：

Step 1：Initialization：Determine that initial vertex is V₄, representative points are V₂, now have V={ V_i(i=1,2,3,4,5, 6,7,8)},S₄={ V₄, meanwhile, Best [V₄]=W₄₄=0, Best [V₁]=W₄₁=21, Best [V₃]=W₄₃=26, Best [V₅]=W₄₅=55, for not with V₄Directly there are Best [V on other summits of connection_j]=∞ (j=2,6,7,8), while which is each Initial vertex, i.e. ROAD [V are set to apicad before self-corresponding_j]=V₄(j=1,2,3,4,5,6,7,8).

Step 2：The current S of comparison₄Initial vertex V in set₄With current V-S₄Conversion way in set between all summits Footpath, it is seen then that Best [V₁]=21 are minimum, now, V₁≠V₂, then by summit V₁It is added to S₄In set, currently, S₄={ V₄, V₁}。

Step 3：Calculate current S₄Initial vertex V in set₄By way of summit V₁When, to V-S₄Each summit V in set_jPower Value sum：Best[V₁]+W_1j(j=2,3,5,6,7,8), by its with originally without summit V₁Each weights sum Best [V_j] (j=2,3,5,6,7,8) compare, it is possible to find, by way of summit V₁To V₆When have Best [V₁]+W₁₆=21+47=68 is little In past Best [V₆]=∞, therefore take Best [V₆]=Best [V₁]+W₁₆=68, at the same record its it is corresponding before be apicad ROAD[V₆]=V₁.And by way of summit V₁Weights to other summits are all infinities, therefore other Best [V_j] (j=2,3,5, 7,8) and its apicad no longer update before corresponding.

Step 4：Return to step 2, the current S of comparison₄Initial vertex V in set₄With current V-S₄In set between all summits Conversion approach, it is seen then that Best [V₃]=26 are minimum, now, V₃≠V₂, then by summit V₃It is added to set S₄In, currently, S₄={ V₄,V₁,V₃}。

Step 5：Return to step 3, calculates current S₄Initial vertex V in set₄By way of summit V₃When, to V-S₄It is each in set Individual summit V_jWeights sum：Best[V₃]+W_3j(j=2,5,6,7,8), by its with originally without summit V₃Each weights Sum Best [V_j] (j=2,5,6,7,8) compare, it is possible to find, by way of summit V₃Weights to other summits are all infinities, Therefore all of Best [V_j] (j=2,5,6,7,8) and its it is corresponding before apicad do not update.

Step 6：Return to step 2, compares S₄Initial vertex V in set₄With current collection V-S₄In all summits weights it With, it is seen then that Best [V₅]=55 are minimum, now, V₅≠V₂, then by summit V₅It is added to set S₄In, currently, S₄={ V₄, V₁,V₃,V₅}。

Step 7：Return to step 3：Calculate current S₄Initial vertex V in set₄By way of summit V₅When, to V-S₄It is each in set Individual summit V_jWeights sum：Best[V₅]+W_5j(j=2,6,7,8), by its with originally without summit V₅Each weights it With Best [V_j] (j=2,6,7,8) compare, it is possible to find：

By way of summit V₅To V₂When have Best [V₅]+W₅₂=55+89=144, less than past Best [V₂]=∞, therefore take Best[V₂]=Best [V₅]+W₅₂=144, at the same record its it is corresponding before apicad be ROAD [V₆]=V₅；

By way of summit V₅To V₇When have Best [V₅]+W₅₇=55+43=98, less than past Best [V₇]=∞, therefore take Best[V₇]=Best [V₅]+W₅₇=98, at the same record its it is corresponding before apicad be ROAD [V₇]=V₅；

By way of summit V₅To V₈When have Best [V₅]+W₅₈=55+42=97, less than past Best [V₈]=∞, therefore take Best[V₈]=Best [V₅]+W₅₈=97, at the same record its it is corresponding before apicad be ROAD [V₈]=V₅。

And by way of summit V₅To summit V₆Weights be infinitely great, therefore Best [V₆] and its it is corresponding before apicad no longer more Newly.

Step 8：Return to step 2, compares S₄Initial vertex V in set₄With current collection V-S₄In all summits complexity Weights sum, it is seen then that Best [V₆]=68 are minimum, now, V₆≠V₂, then by summit V₆It is added to set S₄In, currently, S₄ ={ V₄,V₁,V₃,V₅,V₆}。

Step 9：Return to step 3, calculates current S₄Initial vertex V in set₄By way of summit V₆When, to V-S₄It is each in set Individual summit V_jWeights sum：Best[V₆]+W_6j(j=2,7,8), by its with originally without summit V₆Each weights sum Best[V_j] (j=2,7,8) compare, it is possible to find, by way of summit V₆Weights sum to other summits is all infinity, therefore institute Some Best [V_j] (j=2,7,8) and its it is corresponding before apicad do not update.

Step 10：Return to step 2, compares S₄Initial vertex V in set₄With current collection V-S₄In all summits weights Sum, it is seen then that Best [V₈]=97 are minimum, now, V₈≠V₂, then by summit V₈It is added to set S₄In, currently, S₄={ V₄, V₁,V₃,V₅,V₆,V₈}。

Step 11：Return to step 3, calculates current S₄Initial vertex V in set₄By way of summit V₈When, to V-S₄It is each in set Individual summit V_jWeights sum：Best[V₈]+W_8j(j=2,7), by its with originally without summit V₈Each weights sum Best[V_j] (j=2,7) compares, it is possible to find, by way of summit V₈To V₂When have Best [V₈]+W₈₂=97+56=153, was more than Best [the V for going₂]=144, therefore Best [V₂] and ROAD [V₂] do not update.

And by way of summit V₈To summit V₇Weights sum be infinitely great, therefore Best [V₇] and ROAD [V₇] do not update.

Step 12：Return to step 2, compares S₄Initial vertex V in set₄With current collection V-S₄In all summits weights Sum, it is seen then that Best [V₇]=98 are minimum, now, V₇≠V₂, then by summit V₇It is added to set S₄In, currently, S₄={ V₄, V₁,V₃,V₅,V₆,V₇,V₈}。

Step 13：Return to step 3, calculates current S₄Initial vertex V in set₄By way of summit V₇When, to V-S₄It is each in set Individual summit V_jWeights sum：Best[V₇]+W_7j(j=2), by its with originally without summit V₇Each weights sum Best [V_j] (j=2) compare, it is possible to find, by way of summit V₇To summit V₂Weights sum be infinitely great, therefore Best [V₂] and ROAD [V₂] do not update.

Step 14：Return to step 2, compares S₄Initial vertex V in set₄With current collection V-S₄In all summits complexity Degree weights sum, it is seen then that Best [V₂]=144 are minimum, now, V₂=V₂.Execution step 4.

Step 15：I.e. the content of the invention the step of 4, successively record representative points V₂, and by ROAD [V₂] start reverse backtracking Before each apicad, until tracing back to initial vertex V₄Till (have：ROAD[V₂]=V₅→ROAD[V₅]=V₄)。

Then, institute's record approach will be followed successively by V₂→V₅→V₄, its reverse process：V₄→V₅→V₂It is by V₄Transform to V₂'s Optimal mapping approach, algorithm terminate.

Graph theory knowledge involved in the present invention and programmed method are the known sex knowledge of this area, repeat no more.

Claims (1)

1. a kind of determination method of fighter toy posture changing optimal path, it is characterised in that take following steps：

The first step, establishes the various possible deformation attitudes of fighter toy, and takes the title generation on a corresponding diagram opinion summit for which Number (i=1,2,3, n), while, it is established that show the summit connected graph whether various attitudes mutually directly can convert；

Second step, determines each summit V_i(i=1,2,3, n) between posture changing complexity weights computational methods：

For the summit that can directly convert or directly connect, between each summit motion angle of the complexity weights of posture changing by joint Two factors of side-play amount of degree and center of gravity are determining；

If fighter toy is from certain attitude to another kind of posture changing, relative to current pose, its 4 thigh articulations Angle be respectively defined as θ_b1, θ_b2, θ_b3, θ_b4, corresponding 4 calf joint movement angles are respectively defined as θ_s1, θ_s2, θ_s3, θ_s4, the horizontal-shift component of robot body's center of gravity is X_d, the vertical shift component of center of gravity is Y_d, and take X_dMaxIt is level side The maximum offset of center of gravity upwards, Y_dMaxFor the maximum offset of center of gravity in vertical direction, then big leg joint mean motion angle For:

${\mathrm{\&theta;}}_b=\frac{{\mathrm{\&theta;}}_{b1}+{\mathrm{\&theta;}}_{b2}+{\mathrm{\&theta;}}_{b3}+{\mathrm{\&theta;}}_{b4}}{4}---\left(1\right)$

In the same manner, calf joint mean motion angle is:

${\mathrm{\&theta;}}_s=\frac{{\mathrm{\&theta;}}_{s1}+{\mathrm{\&theta;}}_{s2}+{\mathrm{\&theta;}}_{s3}+{\mathrm{\&theta;}}_{s4}}{4}---\left(2\right)$

By variable θ_bAnd θ_sIt is normalized, even if obtain data being between 0 to 1；The method of normalized is：By institute The θ for obtaining_bAnd θ_sNumerical value is divided by 360 degree；Center of gravity horizontal and vertical offset component is respectively divided by into the peak excursion in all directions again Amount, while, it is considered in vertical direction, center of gravity rises or falls the load difference to motor, Y when setting center of gravity rises_dFor just, weighing The Y when heart falls_dIt is negative, then, the complexity weights of center of gravity horizontal-shift pass throughFormula represents, the complexity of center of gravity vertical shift Degree weights pass throughFormula represents that λ is between 0 and Y in formula_dMaxCertain test bit between/3；When again rise fuselage Complexity weights are somewhat tuned up, and complexity weights when declining somewhat are turned down, center of gravity component is synthesized vector p then, then p The mould of vector can be write as：

$\left|p\right|=\sqrt{{\left(\frac{\left|\mathrm{\&lambda;}+Y_d\right|}{Y_{dMax}}\right)}^2+{\left(\frac{X_d}{X_{dMax}}\right)}^2}---\left(3\right)$

Then, according to θ during deformation_b、θ_sImpact to deformation complexity and experience, determine that each of which is multiple in posture changing with p In miscellaneous degree weights, shared proportion, uses constant w respectively₁、w₂、w₃Represent, wherein w₁、w₂、w₃Meet w₃>w₁>w₂Rule, finally In order that computer can quickly and accurately processing data, the complexity weights of the posture changing for calculating are amplified into 100 times simultaneously Round so as in rational integer range；

So, it is written as by the complexity weight computing formula for converting between various attitudes:

$W=(w_1\&times;\frac{{\mathrm{\&theta;}}_b}{360}+w_2\&times;\frac{{\mathrm{\&theta;}}_s}{360}+w_3\&times;|p\left|\right)\&times;100---\left(4\right)$

When one timing of body parameters, so that it may be derived from posture changing complexity weights different between each summit；Above-mentioned attitude A kind of complexity when conversion complexity weights represent robot from posture changing to another kind of attitude, weights are lower, appearance Conversion between state is easier, conversely, being then more difficult to；

Represented with infinitely great symbol ∞ for the weights between summit are not directly connected；

3rd step, sets up each summit V_i(i=1,2,3, n) between weight matrix

Second step computational methods are drawn the weights between each summit, W is used_ijRepresented by summit V respectively_iConvert directly to summit V_jWhen Weights, now, have the weights W of i=j on diagonal_ij=0；One is set up accordingly, and there is i × j (herein, i=j) individual element Weight matrix W:

$W=\left[\begin{array}{cccc}{W}_{11}& W_{12}& \mathrm{...}& W_{1j}\\ W_{21}& W_{22}& \mathrm{...}& W_{2j}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ W_{i1}& W_{i2}& \mathrm{...}& W_{ij}\end{array}\right]---\left(5\right)$

4th step, determines the minimum conversion approach of weights

First, V is set as all summit V in posture changing figure can be connected_i(i=1,2,3, set n)；Setting S_iFor V One dynamic subset, S_iGather for continually adding such some summits in traversal loop：With certain V_i(i=1,2, 3, when n) being initial vertex, the current V-S of its arrival is searched for using traversal method_iIn set, the weights sum on each summit is Minimum approach, and with variable Best [V_j] (j=1,2,3, what n) special record currently can search for are pushed up from starting Point V_iTransform to any one summit V_jOptimum posture convert approach weights sum；Variable R OAD [V is used simultaneously_j] special record Summit V_jThe corresponding previous summit in its current optimum posture conversion approach, is designated as ROAD [V_j]=", is front apicad ", will be each Individual Best [V_j] (j=1,2,3, after n) being compared to each other, select that summit V with minimum weights sum_a, every time, By such a V_aIt is put into S_iIn set；

Then, the minimum conversion approach of weights is calculated, calculating process is as follows：

Step 1, initialization：Determine initial vertex V_i(i=1,2,3, n), and representative points V_end(end=1, 2, n), by initial vertex V_iIt is put into S_iIn set, now, S_i={ V_i, and by summit V_iWith each top in V set Weights between point are each placed in Best [V_j] (j=1,2,3, n) among, as initial vertex currently with each summit it Between minimum weights sum, now have, Best [V_j]=W_ij, while its each self-corresponding forward direction summit is set to into initial vertex, That is ROAD [V_j]=V_i(j=1,2,3, n)；

Step 2, the current S of comparison_iInitial vertex V in set_iWith current V-S_iConversion approach in set between all summits, choosing It is the V-S corresponding to minimum conversion approach to go out each weights sum_iSummit V in set_a, V_aThe power of corresponding conversion approach Value sum should be Best [V_a]；

If V_a≠V_end, then by summit V_aIt is added to current S_iIn set, S is expressed as_i=S_i∪{V_a}；

If V_a=V_end, execution step 4；

Step 3, the current S of calculating_iInitial vertex V in set_iBy way of summit V_aWhen, to V-S_iEach summit V in set_j(j=1,2, 3, approach weights sum n)：Best[V_a]+W_aj, by its with originally without summit V_aEach weights sum Best [V_j] compare, if to some summits V therein_jExist：(Best[V_a]+W_aj)<Best[V_j], then update its corresponding minimum Weights are Best [V_j]=Best [V_a]+W_aj, accordingly update V_jIt is apicad ROAD [V before corresponding_j]=V_a, otherwise not more Newly；

Return to step 2, continues executing with；

Step 4, successively record representative points V_end, and by ROAD [V_end] start reverse backtracking each before apicad, up to ROAD[V_j] it is initial vertex V_iTill, the reverse process of recorded approach is to transform to representative points most by initial vertex Good conversion approach, algorithm terminate.