CN106547206A - A kind of multi-foot robot dynamic stability based on strength of one's legs algorithm for estimating quantitatively judges method - Google Patents
A kind of multi-foot robot dynamic stability based on strength of one's legs algorithm for estimating quantitatively judges method Download PDFInfo
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Abstract
The invention provides a kind of multi-foot robot dynamic stability based on strength of one's legs algorithm for estimating quantitatively judges method, it is adaptable to stability real-time detection of robot ambulation when unstructured moving grids.The present invention is obtained behind joint and fuselage motion state by sensor, tries to achieve the variate-value calculated needed for stability margin by forward and inverse kinematics.Then the strength of one's legs of supporting leg is estimated by strength of one's legs algorithm for estimating, the support shaft most easily tumbled and the foot point that falls is obtained by strength of one's legs size.By strength of one's legs calculating and effectively make a concerted effort to support shaft and tumbling for the foot point that falls with resultant moment with joint efforts in barycenter, and then the angle of stability of can be supported by formula axle and the foot point that falls, choose the normalized power angle stability margin value that the reckling in angle of stability is calculated robot by formula.It is an advantage of the current invention that：This method directly judges the stability margin to support shaft and the foot point that falls；The stability change that the height of barycenter brings can be characterized；The multi-dimension force sensor measurement strength of one's legs of rapid wear need not be adopted.
Description
Technical field
The invention belongs to robot control field, specifically a kind of Robotic Dynamic stability based on strength of one's legs algorithm for estimating
Quantitative judgement method, the stability margin in real-time detection multi-foot robot motion process.
Background technology
Multi-foot robot is a kind of complex machines people with highly branched chain, redundancy and time-varying topology structure, with than wheeled
The higher landform adaptability of robot, has huge application potential in military and civilian field and is widely applied prospect,
By extensive concern and the attention of domestic and international robot research person.
Multi-foot robot typically can be divided into four-footed, six foots and eight biped robots by the number of foot.Due to multi-foot robot row
The environment walked is often complex, can be potentially encountered rugged topography, stair, barrier, or even Rolling Stone etc., these complicated landform and
Environmental disturbances bring very big challenge to the stability of robot.Using accurate stability criteria monitor in real time robot
Stability for keep robot balance, it is ensured that robot does not tumble, complete disaster relief task it is critical that.Robot it is steady
Qualitative judgement is primarily referred to as judging that falling down can or can not occur tumbling in robot by certain stability margin value that stability margin is more than zero
When robot be in stable state, when stability margin is less than zero, robot will occur and tumble, i.e. robot unstability.
At present, the determination of stability method of robot is divided into steady stability criterion and dynamic stability criterion.Steady stability
Property criterion does not account for the impact of inertia force and external force to stability, and static stability criterion mainly has two classes, and a class is to be based on
The method of center of gravity projection and support polygon relation, they have center of gravity projection method, Small-signal stability method, longitudinal stability boundary method
With deflection longitudinal stability boundary method.Another kind of is the steady stability criterion based on energy, and they have energy stabilization boundary method, topple
Energy stabilization boundary method and normalized energy stability boundary method.Dynamic stability criterion is referred to and considers inertia force and external force
The stability criteria of impact, is broadly divided into two classes.The first kind is based on point of zero moment（ZMP, Zero Moment Point）'s
Dynamic stability criterion.Yugoslavia scholar Miomir Vukobratovic proposed ZMP stability criterias in 1970, should
Method becomes the classical way for being applied to biped robot determination of stability, and hereafter numerous scholars are carried on the basis of this concept
The decision method of oneself, such as Center of Pressure method, effective mass center method etc. are gone out, it is theoretical that its essence belongs to ZMP.But have
Person points out that ZMP methods are not used to walk in the determination of stability of the multi-foot robot in on-plane surface landform, because determining by ZMP
Justice understands that ZMP points are the intersection points made a concerted effort with sole supporting plane of inertia force and gravity, when the number of robot supporting leg is more than
During equal to four, when ground surface or terrain is on-plane surface landform, robot foot will not be coplanar with the contact point on ground, now ZMP points
Will be unable to try to achieve.Other class dynamic stability decision method is the stability criteria based on momentum, mainly has dynamic stability side
Boundary's method, topples over Criterion on stability and supports torque diagnostic method.This kind of method for outer force-disturbance, the not gentle inertia in ground
The situation that power is present be also it is feasible, but this kind of criterion does not account for centroid position and changes impact to stability, because
It is that, for the object on a ground, its centroid position is poorer apart from ground more high stability.The present invention utilizes polypody machine
Device people posture information and sufficient end strength of one's legs information carry out dynamic stability judgement to robot, do not utilize supporting plane to judge stable
Property, directly judge around tumbling for support shaft and tumbling around the foot point that falls, enable the method to the situation suitable for uneven road surface, and
And consider impact of the centroid position variation to robot stabilization.
The either determination of stability method based on ZMP, or determination of stability method proposed by the present invention, is required for adopting
Calculated with ground contact force with vola, therefore correct detection vola contact force becomes crucial and prerequisite.At present all using
FSR is installed in vola（Pressure sensor）Or the method for multi-dimension force sensor realizes the detection to vola power.But FSR can only be examined
Survey normal pressure, it is impossible to detect the power in remaining direction；Multi-dimension force sensor is expensive, and fragile.The present invention proposes a kind of base
In the strength of one's legs algorithm for estimating of kinetic model, extraneous contact force is estimated by the motion state and Motor torque of robot, can be with
The size and Orientation of effective detection vola power, and without the need for force snesor.
The content of the invention
It is an object of the invention to propose a kind of multi-foot robot dynamic stability quantitative judgement side estimated based on strength of one's legs
Method, the method consider inertia force, External force interference, and consider barycenter and change impact to stability, with amount of calculation it is few,
The features such as reliability is high, and the multi-dimension force sensor of rapid wear is substituted using strength of one's legs method of estimation, robot building cost is reduced, is carried
High detection reliability.
A kind of multi-foot robot dynamic stability based on strength of one's legs algorithm for estimating that the present invention is provided quantitatively judges method, its
It is characterised by, the method comprises the steps：
Step 1：Joint angles, fuselage posture information are obtained in real time, and positive kinematics meter is carried out to robot using these information
Calculate, obtain coordinate of the barycenter of each component of robot in reference frame, and the coordinate of each supporting leg foot end points；
Step 2：Using centroid calculation formula calculator device people totality coordinate of the barycenter in reference frame；
Step 3：The strength of one's legs information of supporting leg, and equivalent each pin at robot barycenter are obtained in real time using strength of one's legs algorithm for estimating
Power, obtains making a concerted effort and resultant moment to robot barycenter；
Step 4：The vector of two support shafts most easily tumbled is calculated, two axis that the pin maximum with strength of one's legs is connected are for most
Two axis easily tumbled；
Step 5：Calculate respectively with joint efforts and resultant moment is to the maximum pin of strength of one's legs in two axis most easily tumbled and step 4
Tumble；
Step 6：Three for obtaining in calculation procedure 5 respectively tumble effectively make a concerted effort with tipping pitman cross barycenter vertical line angle and matter
The heart and strength of one's legs maximum fall foot point line angle, three angles are respectively respective axis and the angle of stability of the foot point that falls；
Step 7：In three angles obtained in selecting step 6, reckling stablizes abundant angle as robot, stable Yu Jiao with close
Power obtains stability margin value as normalized after being multiplied.
The present invention is a kind of multi-foot robot dynamic stability detection method based on strength of one's legs algorithm for estimating, for polypody machine
Determination of stability when device people is moved under unstructured moving grids, decision method are succinctly clear and definite.The core of the present invention is estimated by strength of one's legs
Calculating method estimates vola ground contact force, and all strength of one's legs synthesize at barycenter and make a concerted effort and resultant moment, then calculate most easy to two
The support shaft tumbled and the stability margin angle of the foot point that falls.In the case where strength of one's legs size and Orientation is all constant, if machine
People's height of center of mass increases, and the angle for effectively making a concerted effort to cross with tipping line between the vertical line of barycenter is bound to reduce, therefore the method
Can reflect that barycenter changes the impact brought to stability.
Description of the drawings
Fig. 1 is multi-foot robot dynamic stability quantitative detecting method flow chart.
Fig. 2 is Hexapod Robot structure and coordinate system schematic diagram.
Fig. 3 is to stablize abundant angle around tipping pitman to calculate schematic diagram.
Fig. 4 is to stablize abundant angle around the foot point that falls to calculate schematic diagram.
Fig. 5 is strength of one's legs algorithm for estimating computing block diagram.
Specific embodiment
With reference to embodiments and accompanying drawing the present invention is further detailed explanation, but embodiment of the present invention is not limited to
This.The specific embodiment chooses six sufficient serial manipulators in multi-foot robot（As shown in Figure 2）As effective object, but implement right
As not limited to this, four-footed, eight foots or parallel robot etc. it is equally applicable.
As shown in figure 1, a kind of multi-foot robot dynamic stability based on strength of one's legs algorithm for estimating that present example is provided
Quantitative judgement method is comprised the following steps.
Step 1：Joint angles, fuselage posture information are obtained in real time, and positive motion is carried out to robot using these information
Learn and calculate, obtain coordinate of the barycenter of each component of robot in reference frame, and the coordinate of each supporting leg foot end points.
In Fig. 2OxyzFor reference frame, machine can be carried out by motor absolute value encoder and fuselage Position and attitude sensor
The positive the computation of inverse- kinematics of people, falls foot point in reference frame such that it is able to obtain each supporting leg shown in Fig. 2OxyzIn seat
Markp i （i =1,2,…,n）, while the coordinate of each component can also be obtained.
Step 2：Using centroid calculation formula calculator device people totality coordinate of the barycenter in reference frame.
Wherein, r and s represent the number that the number and every leg of multi-foot robot leg contain individual member, m respectivelybRepresent fuselage
Quality, mijRepresent the quality of i-th leg, j-th component.
Step 3：The strength of one's legs information of supporting leg is obtained in real time using strength of one's legs algorithm for estimating, and it is equivalent each at robot barycenter
Individual strength of one's legs, obtains making a concerted effort and resultant moment to robot barycenter.
Supporting leg strength of one's legs information is estimated to obtain by strength of one's legs algorithm for estimating, concrete as shown in Figure 5.Firstly the need of pre-building machine
Device people's leg mechanism kinetics equation and joint-friction model, and parameter identification is carried out to unknown parameter, obtain accurate machine
People's leg power model.In the process of walking, current of electric information and encoder can be obtained by servomotor in real time for robot
To angular velocity information be uploaded to controller.
Need to use angle, angular speed and the angular acceleration in joint in kinetic model, and motor encoder can only obtain
Angular speed, it is therefore desirable to which state observer estimates angle and angular acceleration, and the angular speed that encoder is directly exported is to carry
The signal of noise, state observer can also filter noise.The state observer adopted in the present invention is Kalman filter.If, then by Kalman filter, you can obtain the optimal estimation value of state、With。
As motor is not direct drive connecting rod, it is connected with connecting rod often by decelerator or other kinematic pairs,
And these intermediate links often have larger inertia and friction, need to solve joint moment τ by disturbance observero。
For joint i has following equilibrium equation：
K in formulaiFor motor torque coefficient, IiFor current of electric, JiIt is to convert to the articulation inertia on motor shaft,
τdisiIt is extraneous all disturbance sums.τdisiIt is defined as follows,
In formulaThe joint moment of torsion asked for is needed as,Tried to achieve by the friction model set up.It should be noted that will herein
Other disturbances are all merged in frictional force, therefore friction model typically can not add viscous friction to retouch with simple static friction
State, needs rationally set up new friction model according to actual conditions.Simultaneous (2) and (3) formula are obtained joint moment and are
The kinetic model of the leg mechanism for pre-building is
Wherein M for 3 × 3 inertial matrix, C is coriolis force and centripetal force item, and G is gravity item, TfIt is to rub except driving joint
Other joint-frictions outside wiping.The state estimation that state observer is obtainedWithIn (5) formula of substitution, you can obtain
τdyna。
Joint drive power includes two parts, and a part is driving force needed for drive mechanism motion when acting on without external force, another
Part is impact of the external force effect to joint drive power, that is, have following formula
τo=τdyna+τreact (6)
Then
τreact=τo-τdyna (7)
Torque in the joint space that formula (7) is obtained, may map in cartesian coordinate system by Jacobian matrix,
If the strength of one's legs of i-th supporting leg isOrder
bi=pi-pc (9)
B in formulaiAs shown in Figure 2.Then strength of one's legs can be obtained by following formula to make a concerted effort and resultant moment the equivalent of barycenter
Step 4：The vector of two support shafts most easily tumbled is calculated, two axis that the pin maximum with strength of one's legs is connected are for most
Two axis easily tumbled.
Robot may tumble around a support shaft when tumbling, it is also possible to tumble around the foot point that falls, occur tumbling
When two pin stress that tipping line is located can be caused maximum, if tumbling around the foot point that falls, then the sufficient stress is maximum.Therefore can
The stability margin of two axis that the fall foot point maximum with strength of one's legs is connected to reduce amount of calculation accordingly, need to be only calculated, and is calculated
Around the stability margin of the maximum foot point that falls of strength of one's legs, without the stability margin for calculating other support shafts again with the foot point that falls.If
The strength of one's legs of m article of supporting leg is maximum, then have
The vector of two support shafts then most easily tumbled is αmAnd am+1。
Step 5：Calculate respectively with joint efforts and resultant moment is to the maximum pin of strength of one's legs in two axis most easily tumbled and step 4
Tumble.
F with joint effortsrIn do not result in tumbling for robot parallel to the component of axis of support, as shown in figure 3, without loss of generality, close
Power frTo aiThe effective force of tumbling of axle is
Wherein E3Represent that 3 × 3 unit is put to the proof,Represent aiUnit vector.
Equally, resultant moment nrIn also only perpendicular to aiThe component of axle is produced around a to robotiThe roll-over action of axle, this effectively inclines
Turning over moment components is
As shown in Figure 3, by niIt is decomposed into a pair of couples fni, then the roll-over action of torque can be incorporated to fiIn, formed final
Tumble.
Wherein IiRepresented the axle a of barycenteriVertical line, For IiUnit vector.Then make a concerted effort
With resultant moment to aiTumble and be
Similarly, can equally calculate and be tumbled for foot point i that falls effectively make a concerted effort with resultant moment with joint efforts.Now make a concerted effort frAll can be right
The foot point that falls is produced and is tumbled, therefore is set to fbiFor frTo the power of effectively tumbling of foot point i that falls it is
fbi=fr (16)
But resultant moment nrIn only perpendicular to biComponent be only the effective tilting moment component to foot point i that falls, by following formula meter
Obtain
WhereinFor biUnit vector.Equally by effective tilting moment component nbiA pair of couples are decomposed into,
Can then obtain, make a concerted effort and resultant moment tumbling and be to foot point i that falls
I is replaced with into m and m+1, the two axis a for most easily tumbling can be corresponded tomAnd am+1And three of foot point m that falls tumble
Effectively make a concerted effort With
Step 6：Three for obtaining in calculation procedure 5 respectively are tumbled the folder of the vertical line for effectively making a concerted effort barycenter is crossed with corresponding tipping pitman
Angle and the angle with the barycenter-foot point that falls line.
To support shaft aiAngle of stability refer to that corresponding being tumbled effectively make a concerted effortWith the vertical line I of tipping pitmaniAngle, obtained by following formula
Arrive
WhereinRepresentUnit vector, ξiCan be obtained by following formula
Similarly, constitute angle of stability around fall foot point with the barycenter-foot point that falls line with joint efforts to effectively tumbling for the foot point that falls, by
Following formula is calculated
For two support shafts most easily tumbled and the foot point that falls that have determined, i.e., with falling with maximum strength of one's legs
Three related angle of stabilities of foot point m are θm, θm+1WithThe wherein positive and negative state for illustrating robot of angle of stability, if stable
Angle is in rollover conditions less than zero robot, is in stable state if greater than zero robot, if equal to zero machine
People is in critical stable state.
Step 7：Angle of stability of the reckling as robot in three angles obtained in selecting step 6, stablizes abundant angle and makes a concerted effort
Stability margin value is obtained as normalized after multiplication.
Once there is an angle of stability to occur in that minus situation in step 6, robot is at rollover conditions, therefore chooses three
In person, minimum angle is the angle of stability of robot.It should be noted that in the case of angle of stability identical, f with joint effortsrSize
Also the degree of stability of robot is characterized, such as in the case where robot stabilized angle is more than zero, frIt is bigger, need the bigger external world
Perturbed force Cai Nengshi robot tumbles, therefore the power angle stability margin of definition robot is robot stabilized angle and frMould take advantage of
Product.For convenience, it is normalized, the power angle stability margin computing formula of normalised robot is as follows
Wherein θnomAnd fnomIt is defined as robot and angle of stability when not being subject to external interference power is not moved in level ground
Make a concerted effort with strength of one's legs at barycenter, now the stability margin of robot is maximum.
Therefore the present invention can be expressed as based on the Robotic Dynamic determination of stability method of power angle stability margin：Stablize abundant in power angle
When degree α is more than zero, robot is in stable state, and α is bigger, i.e., closer to 1, robot stabilization is higher；α was less than for zero opportunity
Device people play pendulum, i.e., in rollover conditions, and the unstable degree of α more small machine people is bigger；α is machine equal to zero
People is in critical stable state.
It is the height of center of mass in the case where other conditions are constant that the present invention can embody impact of the height of center of mass to stability
Increase can bring angle of stability θiWithReduction, as shown in figure 4, the reduction so as to cause α in formula (24), i.e. power angle stability margin
Reduction.
Claims (7)
1. a kind of multi-foot robot dynamic stability based on strength of one's legs algorithm for estimating quantitatively judges method, it is characterised in that the party
Method comprises the steps：
(1) joint angles, fuselage posture information are obtained in real time, and positive kinematics calculating is carried out to robot using these information,
Obtain coordinate of the barycenter of each component of robot in reference frame, and the coordinate of each supporting leg foot end points；
(2) using centroid calculation formula calculator device people totality coordinate of the barycenter in reference frame；
(3) using the strength of one's legs information of strength of one's legs algorithm for estimating real-time estimation supporting leg, and equivalent each strength of one's legs at robot barycenter,
Obtain making a concerted effort and resultant moment to robot barycenter；
(4) vector of two support shafts most easily tumbled is calculated, two axis that the pin maximum with strength of one's legs is connected are most easy
Two axis tumbled；
(5) calculate respectively and make a concerted effort and resultant moment is inclined to the pin of strength of one's legs maximum in two axis most easily tumbled and step 4
Turn over and effectively make a concerted effort；
(6) three for obtaining in calculation procedure 5 respectively tumble effectively make a concerted effort with tipping pitman cross barycenter vertical line angle and barycenter
Fallen the angle of the line of foot point with strength of one's legs maximum, and three angles are respectively respective axis and the angle of stability of the foot point that falls；
(7) in three angles for obtaining in selecting step 6, reckling stablizes abundant angle as robot, stablizes abundant angle with phase with joint efforts
Stability margin value is obtained as normalized after taking advantage of.
2. the dynamic stability of multi-foot robot according to claim 1 quantitatively judges method, it is characterised in that step
(3), in, strength of one's legs size and Orientation is estimated by strength of one's legs algorithm for estimating.Initially with the motor speed that state estimator is obtained by encoder
Degree estimates angular displacement and angular acceleration, obtains the optimal estimation value of stateWithMust have to joint further according to disturbance observer
Effect torque
The joint moment of torsion according to needed for kinetic model calculates drive mechanism motion
Joint drive power includes two parts, and a part is driving force, another part needed for drive mechanism motion when acting on without external force
It is impact of the external force effect to joint drive power, then can obtains the part of joint moment shared by external force effect,
τreact=τo-τdyna (3)
Then mapped in cartesian coordinate system by Jacobian matrix
。
3. multi-foot robot dynamic stability according to claim 1 quantitatively judges method, it is characterised in that step (4)
In, the support shaft most easily tumbled is judged by strength of one's legs information and the foot point that falls, so as to without the need for entering to other support shafts and the foot point that falls
Row is calculated, and simplifies calculating process.
4. multi-foot robot dynamic stability according to claim 1 quantitatively judges method, it is characterised in that step (5)
In, calculate respectively according to the following equation and support shaft and being tumbled for the foot point that falls effectively make a concerted effort：
Wherein frAnd nrRespectively strength of one's legs at barycenter make a concerted effort and resultant moment, E3For 3 × 3 unit matrix,For support shaft
Unit vector, IiFor the barycenter-foot point that falls line vector,For IiUnit vector.
5. multi-foot robot dynamic stability according to claim 1 quantitatively judges method, it is characterised in that step (6)
In, the angle of stability of the angle of stability and the foot point that falls of support shaft is calculated according to below equation：
。
6. multi-foot robot dynamic stability according to claim 1 quantitatively judges method, it is characterised in that step (7)
In, according to the power angle stability margin of below equation calculating robot
Wherein θm, θm+1WithThe corresponding angle of stability of two support shafts respectively most easily tumbled and most easy tumble
The corresponding angle of stability of the foot point that falls, θnomAnd fnomRobot is defined as in level ground, without moving, not by external interference
At angle of stability and barycenter during power, strength of one's legs makes a concerted effort.
7. multi-foot robot dynamic stability according to claim 1 quantitatively judges method, it is characterised in that without utilization
The relation made a concerted effort between support polygon or supporting plane of strength of one's legs carries out determination of stability, but calculates and tumble effectively with joint efforts
To support shaft (side of support polygon) and the angle of stability of the foot point that falls, the stability status of robot are characterized with angle.
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