CN108345211A - Biped anthropomorphic robot and its non-linear gait planning method and control method - Google Patents

Biped anthropomorphic robot and its non-linear gait planning method and control method Download PDF

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CN108345211A
CN108345211A CN201710058545.1A CN201710058545A CN108345211A CN 108345211 A CN108345211 A CN 108345211A CN 201710058545 A CN201710058545 A CN 201710058545A CN 108345211 A CN108345211 A CN 108345211A
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zmp
gait
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foot
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阮仕涛
姜东晓
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Shenzhen Prafly Technology Co Ltd
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    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
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Abstract

A kind of biped anthropomorphic robot and its non-linear gait planning method and control method, planing method include：S1, gait parameter input by user is obtained；S2, ZMP reference locus is generated based on gait parameter input by user；S3, using the Preview Control algorithms for incorporating nonlinear factor, obtain centroid trajectory according to reference to the tracks ZMP；Wherein, the nonlinear factor is related to the kinematic parameter along acceleration of gravity direction.Gait planning performance can be improved in the present invention, saves the kinergety consumption of system entirety, optimizes the linear walking posture of existing biped robot；User is only needed to input the parameter of five " What You See Is What You Get ", not needing user has the professional knowledge of robot gait planning, has good user experience.

Description

Biped anthropomorphic robot and its non-linear gait planning method and control method
Technical field
The present invention relates to artificial intelligence field more particularly to a kind of biped anthropomorphic robot and its non-linear gait planning sides Method and control method.
Background technology
The primary and foremost purpose of mankind manufacture machine people is to produce the class people's system that can replace the mankind, helps oneself to go to complete to be difficult very To impossible task.Complete anthropomorphic robot is mainly made of vision system+both arms/wrist/hand system+biped system.Depending on Brain centres are taken in feel, formulate global action plan using the information that visual sensor is fed back to, both arms/wrist/hand utilizes power Feel that the sensors such as tactile go to realize these operations, and biped system expands the working space of robot, ensure that robot exists Can be with continue working in complicated or hazard region, while large-scale redevelopment need not be carried out to environment exclusively for it, it can be direct In the living and working environment of the mankind with mankind's work compound.Just because of this, both feet humanoid robot is with its unique advantage The extensive concern for receiving each side becomes the hot spot of robot research field.Compared with wheeled robot, both feet humanoid robot Running gear floor space is small, and scope of activities is big, requires low to pedestrian environment and has certain ability for going beyond obstacle, mobile " blind area " is small, thus has broader practice field, it may have very high productive value and commercial value.Such as in extreme environment Lower to replace manual work, sea floor exploration, Underwater resources exploitation, earthquake searches and rescues, monitoring and maintenance in nuclear power station etc..In addition, double Foot is the introduction of mobile-robot system in itself, and Soccer robot, machine spider, robot dog etc. can also be made by improvement.
Wherein, trajectory planning and gait equilibrium problem are the focuses of biped robot's research field.In mechanical structure, biped The generally single leg of walking robot has 6 degree of freedom, is distributed in ankle-joint (2 degree of freedom), and knee joint (1 degree of freedom) and hip close On section (3 degree of freedom).12 degree of freedom of both legs may be implemented to walk, and run, and jump is squatted down, up/down stair, transverse shifting Deng action.Trajectory planning is exactly that foot and barycenter (waist) should be with what kind of movement roads when realizing these actions to robot The research of diameter, the track that good planning algorithm obtains can keep the stability that robot system is lasting in movement.It is with walking Example, the process are defined as biped or so alternately as support leg, and the holding state stablized between holding and ground is simultaneously, mobile Foot alternately moves forward.Whether this process is in stable state, and academic and industrial quarters is all made of ZMP (point of zero moment) reasons at present By as basis for estimation, i.e.,：Robot in walking, there is the inertia brought when gravity and barycenter acceleration and deceleration for centroid position Power, the resultant force (or resultant force extended line) of the two power and the intersection point on ground are point of zero moment (ZMP), the power of the horizontal direction and Torque is zero, i.e., robot does not have the trend that horizontal direction is toppled at this point.If in walking process, ZMP points are in always In monopodia foot face or in the polygon that biped track is constituted, then it is assumed that gait is stable.
However, due to whether considering that barycenter longitudinal movement (being moved along Z-direction) determines the track rule of robot ambulation Whether the problem of drawing is non-linear, and biped run trace planning problem is reduced to not consider barycenter longitudinal movement (along Z mostly at present Axis direction move) linear problem go to consider.The algorithm for solving this kind of linear problem includes linear interpolation, and linear Fourier becomes It changes, linear Preview Control etc..Wherein linear Preview Control algorithms can be according to following ZMP reference locus Current centroid trajectory is adjusted, but, in order to meet ZMP stability criterions, barycenter is constituted in x-y axis for the linear walking of this simplification Plane on need to swing by a relatively large margin so that leg joint prevents Singularity, and knee joint must be kept persistently to be bent Notable feature.The former causes robot ambulation pattern to deviate mankind's walking mode, and the latter needs to apply at knee joint lasting Torque increases the energy expenditure of robot.On the other hand, nonlinear Walking Gait Planning Algorithm mostly uses diagonal based on three at present The Thomas algorithms of matrix, influence of the ZMP trace informations to current centroid trajectory however it does not look to the future.
Invention content
The technical problem to be solved in the present invention is, for the drawbacks described above of the prior art, provides a kind of biped apery machine Device people and its non-linear gait planning method and control method.
The technical solution adopted by the present invention to solve the technical problems is：Construct a kind of non-linear step of biped anthropomorphic robot State planing method, method include：
S1, gait parameter input by user is obtained；
S2, ZMP reference locus is generated based on gait parameter input by user；
S3, using the Preview Control algorithms for incorporating nonlinear factor, obtain barycenter according to reference to the tracks ZMP Track；Wherein, the nonlinear factor is related to the kinematic parameter along acceleration of gravity direction.
In the non-linear gait planning method of biped anthropomorphic robot of the present invention, the use described in step S3 is whole The Preview Control algorithms for having closed nonlinear factor, obtaining centroid trajectory according to the tracks reference ZMP includes：Linear Nonlinear factor is integrated in the combination of the state transition equation and output equation of Preview Control algorithms, structure is non-linear Trajectory planning mathematical model, and current centroid trajectory is adjusted according to following ZMP reference locus,
The state transition equation is：X (k+1)=AX (k)+Bu (k),
The output equation is：xzmp(k)=C** X (k),
Wherein：
Wherein, parameter A, B is the preset parameter determined by frequency Δ t；Parameter C*To incorporate nonlinear factorVariable, g indicate acceleration of gravity, zcomIndicate that barycenter is along the position in acceleration of gravity direction when movement It moves,Indicate that barycenter is along the acceleration in acceleration of gravity direction when movement；X (k) be state transition equation output, x (k),Displacement, speed and the acceleration of k moment barycenter are indicated respectively；U (k) represents optimal input controller, is state The input of transport equation indicates k moment accelerationDifferential；xzmp(k) it is the output of output equation, indicates k moment ZMP One point of reference locus, the output X (k) of state transition equation is the input of output equation, and the output equation establishes matter Non-linear relation between heart point and ZMP reference locus；For the error of ZMP actual paths and ZMP reference locus With GxX (k) is the feedback of centroid trajectory,For N after the k momentpReference in a sampling time The tracks ZMP；Wherein, Gi,Gx,GpRespectively gain parameter, and by by parameter A, B and C*Discrete multitude as input blocks the side of carrying Journey is calculated.
In the non-linear gait planning method of biped anthropomorphic robot of the present invention, the gait inputted in step S1 is joined Number is：Step-length x, step width y, time t used is often walkedf, it is static when height of center of mass zheightWith step number Num.
In the non-linear gait planning method of biped anthropomorphic robot of the present invention, the step S2 includes：
S21, the front for defining robot initial standing place are X-axis positive direction, right-hand side is Y-axis positive direction, bipod Between central point be set as origin, in foot support phase, the foot contacted with ground be known as support leg, another be swing foot；
S22, reference locus vector of the support leg in X-Y plane is generated based on gait parameter input by user Reference locus vector torsoX, the torsoY of supportX, supportY and body in X-Y plane, wherein SupportX indicates that support leg track along the x-axis direction, supportY indicate that, along Y direction support leg track, torsoX is indicated along X The body track of axis direction, torsoY are indicated along the body track of Y direction；
Wherein, supportX=[0, x, 2x, 3x ..., Numx], in the ban using left foot as support leg, right crus of diaphragm is to swing foot When, supportY=[- y, y ,-y, y ..., (- 1)NumY], in the ban using right crus of diaphragm as support leg, when left foot is swing foot, supportY=[y,-y,y,-y,…,(-1)(Num-1)·y]；TorsoX=[0, x/2,3x/2,5x/2 ..., (2Num-1) x/ 2], [0,0,0,0 ... 0] torsoY=；
S23, it is obtained with reference to the tracks ZMP based on the reference locus vector of support leg and body.
In the non-linear gait planning method of biped anthropomorphic robot of the present invention, the step S23 includes：
S230, t is defined0、t1、t2Respectively initial time, close to t0Fixed point and time used close to step S1 input tfFixed point, torsoXiFor along the body position of the i-th step of x-axis；
If S231, t >=t0And t ＜ t1
If S232, t >=t1And t ＜ t2
xzmp(t)=supportX (t)
yzmp(t)=supportY (t)
If S233, t >=t2And t ＜ tf,
The invention also discloses a kind of non-linear gait control methods of biped anthropomorphic robot, including：
S100, perform claim require 1-5 any one of them gait planning methods to obtain centroid trajectory；
S200, swing foot track is calculated；
S300, it is based on centroid trajectory and swings foot track, the time sequence in each joint in leg is acquired using inverse kinematics model Row angle, steering engine according to this time sequence angle control articulation so that robot walk out the gait parameter in step S1 institute it is right The expectation gait answered.
The invention also discloses a kind of biped anthropomorphic robots based on the non-linear gait control method, including：
Man-machine interaction unit, for obtaining gait parameter input by user；
ZMP reference locus generation units, for generating ZMP reference locus based on gait parameter input by user；
Centroid trajectory generation unit, for using the Preview Control algorithms for incorporating nonlinear factor, according to ginseng It examines the tracks ZMP and obtains centroid trajectory；Wherein, the nonlinear factor is related to the kinematic parameter along acceleration of gravity direction；
Gait execution unit swings foot track for calculating, and based on centroid trajectory and swings foot track, utilizes inverse kinematics Model acquires the time series angle in each joint in leg, and steering engine controls articulation so that robot according to this time sequence angle Walk out the expectation gait corresponding to gait parameter input by user.
Implement biped anthropomorphic robot of the invention and its non-linear gait planning method and control method, has following Advantageous effect：The present invention optimizes linear Preview Control algorithms, integrates and the movement along acceleration of gravity direction The relevant nonlinear factor of parameter had not only considered influence of the following ZMP trace informations to current centroid trajectory, but also can improve step The performance of state planning saves the kinergety consumption of system entirety, optimizes the linear walking posture of existing biped robot；Into one Step ground, height of center of mass and this five " institutes of step number when the present invention only needs user input step-length, step width, often walk used time, is static See i.e. gained " parameter, do not need user have robot gait planning professional knowledge, have good user experience；And And when generating with reference to the tracks ZMP, there is an alternating in view of bipedal prop-up stage and foot support phase, generate it is more smooth more The tracks reference ZMP of the nearly full curve of adjunction.
Description of the drawings
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below There is attached drawing needed in technology description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this The embodiment of invention for those of ordinary skill in the art without creative efforts, can also basis The attached drawing of offer obtains other attached drawings：
Fig. 1 is the flow chart of the preferred embodiment of the non-linear gait planning method of biped anthropomorphic robot of the present invention；
Fig. 2 is the center of mass motion track contrast schematic diagram of linear and nonlinear gait；
Fig. 3 is linear and nonlinear inverted pendulum model contrast schematic diagram；
Fig. 4 is desk trolley model simplification figure；
Fig. 5 is multiple walking cycle inner support feet and the tracks reference ZMP；
Fig. 6 is 2.2 unit of height of center of mass, non-linear when along acceleration of gravity direction mechanical periodicity using 2 units as amplitude The 3D for the foot and centroid trajectory that Preview Control algorithms obtain schemes and vertical view；
Fig. 7 is 2.2 unit of height of center of mass, using 2 units as amplitude, when along acceleration of gravity direction mechanical periodicity, linearly The 3D for the foot and centroid trajectory that Preview Control algorithms obtain schemes and vertical view；
Fig. 8 is 2.2 unit of height of center of mass, non-linear when along acceleration of gravity direction mechanical periodicity using 2 units as amplitude The 3D for the foot and centroid trajectory that Thomas algorithms obtain schemes and vertical view；
Fig. 9 is 2.2 unit of height of center of mass, using 2 units as amplitude, when along acceleration of gravity direction mechanical periodicity, and three kinds of calculations The barycenter that method obtains is along Y-axis track comparison diagram；
Figure 10 is non-linear and linear Preview Control algorithms obtain in Fig. 6 and Fig. 7 barycenter along Y-axis track pair Compare enlarged drawing；
Figure 11 is 2.2 unit of height of center of mass, non-when along acceleration of gravity direction mechanical periodicity using 0.05 unit as amplitude The 3D figures and vertical view for the foot and centroid trajectory that linear Preview Control algorithms obtain；
Figure 12 is 2.2 unit of height of center of mass, using 0.05 unit as amplitude, when along acceleration of gravity direction mechanical periodicity, and line Property the obtained foot and centroid trajectory of Preview Control algorithms 3D figures and vertical view；
Figure 13 is 2.2 unit of height of center of mass, non-when along acceleration of gravity direction mechanical periodicity using 0.05 unit as amplitude The 3D figures and vertical view for the foot and centroid trajectory that linear Thomas algorithms obtain；
Figure 14 is 2.2 unit of height of center of mass, using 0.05 unit as amplitude, when along acceleration of gravity direction mechanical periodicity, and three The barycenter that kind algorithm obtains is along Y-axis track comparison diagram.
Specific implementation mode
In order to better understand the above technical scheme, in conjunction with appended figures and specific embodiments to upper It states technical solution to be described in detail, it should be understood that the specific features in the embodiment of the present invention and embodiment are to the application The detailed description of technical solution, rather than to the restriction of technical scheme, in the absence of conflict, the present invention is implemented Technical characteristic in example and embodiment can be combined with each other.
It is the flow chart of the preferred embodiment of the non-linear gait planning method of biped anthropomorphic robot of the present invention with reference to figure 1. The present invention the non-linear gait planning method of biped anthropomorphic robot include：
S1, gait parameter input by user is obtained；
S2, ZMP reference locus is generated based on gait parameter input by user；
S3, using the Preview Control algorithms for incorporating nonlinear factor, obtain barycenter according to reference to the tracks ZMP Track；Wherein, the nonlinear factor is related to the kinematic parameter along acceleration of gravity direction；
The present invention control method include；
Gait planning method described in S100, execution is to obtain centroid trajectory；
S200, swing foot track, the rail are calculated using Polynomial Trajectory Algorithm (PTA) algorithm Mark is also considered as the track of leg link ending coordinates system；
S300, it is based on centroid trajectory and swings foot track, the time sequence in each joint in leg is acquired using inverse kinematics model Row angle, steering engine according to this time sequence angle control articulation so that robot walk out the gait parameter in step S1 institute it is right The expectation gait answered, this partly belongs to the prior art, and details are not described herein again.
Step S1-S3 is described in detail below.
About step S1：
Parameter specifically includes in the step：Step-length x, step width y, time t used is often walkedf, it is static when height of center of mass zheightWith Step number Num.The parameter of this 5 " What You See Is What You Get ", not needing user has the professional knowledge of robot gait planning.In addition, The parameter that the present invention subsequently uses also is summarized in table 1 together, in addition to 5 above-mentioned parameters, remaining parameter do not need user to Go out, increases the facility in user's use.
Table 1：The main gait parameter list used in the present invention
About step S2：
Specifically, the step S2 of the present invention includes：
S21, acceleration of gravity direction is defined as Z axis, the front of robot initial standing place is X-axis positive direction, the right side Hand side is Y-axis positive direction, and central point is set as origin between bipod, and in foot support phase, foot contact with ground is known as support Foot, another are to swing foot；
S22, reference locus vector of the support leg in X-Y plane is generated based on gait parameter input by user Reference locus vector torsoX, the torsoY of supportX, supportY and body in X-Y plane.Wherein, SupportX indicates that support leg track along the x-axis direction, supportY indicate that, along Y direction support leg track, torsoX is indicated along X The body track of axis direction, torsoY are indicated along the body track of Y direction.It should be noted that although track itself is to connect It is continuous, but discrete vector can only be first obtained from five parameters of step S1, when generating with reference to the tracks ZMP, the present invention can to from Scattered data do smoothing processing, to wait for close to full curve.The rectangular path of Fig. 5 illustrate support leg within the multistep period from Scattered exchange and movement.
In the ban using left foot as support leg, right crus of diaphragm is that the track definition of support leg when swinging foot is：
SupportX=[0, x, 2x, 3x ..., Numx]
SupportY=[- y, y ,-y, y ..., (- 1)Num·y]
If it is elder generation using right crus of diaphragm as support leg, left foot be swing foot support leg track becomes in the Y direction：
SupportY=[y ,-y, y ,-y ..., (- 1)(Num-1)·y]
Definition always lags behind support leg half along the body track torsoX of X-direction and walks the i.e. distance of x/2, i.e.,：
TorsoX=[0, x/2,3x/2,5x/2 ..., (2Num-1) x/2]
It keeps small as possible along the body track of Y direction to rock, perfect condition is：
TorsoY=[0,0,0,0 ... 0]
S23, it is obtained with reference to the tracks ZMP based on the reference locus vector of support leg and body.
It, as shown in Figure 5, should be as possible close to support with reference to the tracks ZMP in order to keep the stabilization of gait based on ZMP theories The center line of foot track designs.Can directly it simplify xzmp=supprotX,yzmp=supprotY, support leg track as With reference to the tracks ZMP, but because exchanging the support leg moment does not account for the case where of short duration both feet support, cause the mutation of curve. For the present invention using the linear Bezier (B é zier Curve) for being equivalent to linear interpolation, generation includes bipedal prop-up stage, It is more smoothly more nearly the reference ZMP of full curve, it is specific as follows：
First, t is defined0、t1、t2Respectively initial time, close to t0Fixed point and time used close to step S1 input tfFixed point, it is so-called close to t0Refer to compared with t0Big default value, close to tfRefer to compared with tfSmall default value, such as t0=0.0, tf=1.0, t1=0.1, t2=0.9.From t0To t1With from t2To tfIt is equivalent to bipedal prop-up stage, from t1To t2It is equivalent to single foot Driving phase.T is in end of time tfIt is interior using Δ t as the sampling time at interval, torsoXiFor along the body position of the i-th step of x-axis；
If t >=t0And t ＜ t1
If t >=t1And t ＜ t2
xzmp(t)=supportX(t)
yzmp(t)=supportY (t)
If t >=t2And t ＜ tf,
About step S3：
In Fig. 2, the left side is the center of mass motion track of non-linear gait, and the right is the center of mass motion track of linear gait.It can To find out, there are the longitudinal movements of barycenter to make knee that need not continue to keep flexuosity, also closer to people in posture Class is walked.Fig. 3 shows a kind of matter of the inverted pendulum model (being counted as robot model of simplification) moved there is no z-axis direction Heart space is the plane that x-y axis is constituted.It is proved from the moving equilibrium power system model of biped robot's system below this Non-linear nature.
According to dAlembert principle (D'Alambert principle), in any moment of particle movement, active force, about Beam force constitutes balanced system of force with inertia force, i.e. power not additional at the particle or torque applies.Such as formula (1) description The small vehicle model of desk (being considered as simplified robot multi-body system model) reaches bright Bell's balanced system of force in ZMP points in Fig. 4.It is small Vehicle center is equivalent to robot barycenter, is that there is no the balanced system of force models of z-axis direction movement.Formula (1) first part is small Vehicle barycenter arrives the torque of ZMP points along the z-axis direction, and g is acceleration of gravity, and second part is the torque of trolley along the x-axis direction, constant zheightHeight of center of mass when being static, Part III are the moment of inertia of trolley.If it is considered that the movement in z-axis direction, such as formula (2), the acceleration plus barycenter in the z-direction is needed at first part gThe z of second partheightReplace with variation Height of center of mass zcom.Formula (3) and (4) respectively describe extensive to being derived according to balanced system of force formula (2) when multi-body system The relationship of ZMP point and particle trajectory.If ignoring moment of inertia termWithAnd think ∑imixi/∑imi=xcom(similarly ycom), formula (3) and (4) can be reduced to formula (5) and (6) respectively.Trajectory planning linear at present is calculated Method is all to define zcom=zheight,Linear formula (7) and (8) are reduced to, with known with reference to ZMP track xzmp, yzmpWith constant zheight, g generates centroid trajectory xcom,ycom.In formula (5) and (6)It is referred to as non- Linear factor.
The present invention proposes that the Preview Control that centroid trajectory is generated based on the non-linear relation for remaining the factor are excellent Change algorithm, the performance of gait planning can be improved, saves the kinergety consumption of system entirety, optimize walking posture.Specifically, Step S3 of the present invention includes：It is whole in the combination of the state transition equation and output equation of linear Preview Control algorithms Nonlinear factor is closed, builds nonlinear trajectory planning mathematical model, and current matter is adjusted according to following ZMP reference locus Heart track.
State transition equation is：
X (k+1)=AX (k)+Bu (k),
Linear convergent rate equation is：
xzmp(k)=C*X (k) (9A)
Nonlinear object equation is：
xzmp(k)=C**X(k) (9B)
Wherein：
C≡[1 0 -zheight/g] (11)
Wherein, X (k) be state transition equation output, x (k),The position of k moment barycenter is indicated respectively Shifting, speed and acceleration；U (k) represents optimal input controller, indicates k moment accelerationDifferential；xzmp(k) k is indicated One point of moment ZMP reference locus.The input of state transition equation is u (k), output is X (k), state transition equation it is defeated Go out the input that X (k) is output equation, output equation is the matrix form of formula (5) (6) (7) and (8), and parameter selection C is (corresponding 8) or C* (corresponding formula 5 and 6) determines that output equation is linear or non-linear formula 7 and, the output of output equation is xzmp(k), the output equation establishes the non-linear relation between center of mass point and ZMP reference locus.
As can be seen that once it is determined that frequency Δ t and height of center of mass zheight, A, B and C are during state transition Fixed parameter.However, parameter C known to the above-mentioned discussion to nonlinear factor is not immobilizing as described in formula (11) , but have nonlinear change in Z-direction as described in formula (12).This variation can be to optimal input controller model u (k) parameter has an impact, to have an impact to the result of performance indicator and the centroid trajectory of generation.Formula (10) describes linearly Preview Control methods minimize the optimal input controller model u (k) needed when performance indicator, whereinFor ZMP actual paths and ZMP reference locus error and, GxX (k) is the feedback of centroid trajectory, For N after the k momentpThe tracks reference ZMP in a sampling time.Gi,Gx,GpRespectively gain Parameter.These parameter values are by A, B and C as described in the pseudocode of table 2*Discrete Riccati equation as input (Discrete-time Algebraic Riccati Equations) is calculated.The C it can be seen from the process*Middle variation Nonlinear factorSo that the parameter of optimal input controller model is also with dynamic change, and it is existing Due to the linear factor z of C in technologyheight/ g is constant so three parameters of optimal controller model are also constant in linear problem.
Table 2：The pseudocode of controller parameter is sought by state transition equation and output equation parameter
With reference to Fig. 6-14, by two groups of description of test present invention and linear Preview Control algorithms and non-thread The performance comparison of property Thomas algorithms.The difference of two groups of experiments is that barycenter is different in the amplitude of the periodic motion in Z-direction.If Step-length x=1, step width y=0.45 are set, time t used is often walkedf=0.2, height of center of mass z when staticheight=2.2 and step number Num =30.With zheight=2.2 units be standard, take along Z axis motion amplitude Vz be respectively 2 and 0.05 unit periodic motion WithReference value：
1), barycenter CoM along the z-axis direction motion amplitude Vz=2 when, illustrate barycenter along Z axis motion amplitude with reference to figure 6-10 For 2 experimental result.Fig. 6 is the ZMP and barycenter rail that non-linear Preview Control optimization algorithms proposed by the present invention obtain The 3D and vertical view of mark, Fig. 7 are linear Previ ew Control algorithms, and Fig. 8 is the corresponding result of non-linear Thomas algorithms.
First, find out from Fig. 6,7 and 8, the centroid trajectory that non-linear Thomas algorithms obtain the amplitude moved along Y-axis more Greatly, exceeding the tracks ZMP close to 7 times, it is meant that tangible machine people's waist swings and swings relatively with foot more acutely, Robot balance is easily caused to be difficult to maintain.And the performance of non-linear and linear Preview Control algorithms is relatively good, along Y-axis The amplitude of direction movement very little for the tracks ZMP only accounts for ZMP along about the 22% of Y-axis motion amplitude, that is, shaking reduces Nearly 80%, the stability of tangible machine people is more preferable.The barycenter CoM that three kinds of algorithms obtain is figure along the track that Y-direction moves comparison 9。
Figure 10 is exaggerated the disparity map of linear and nonlinear Preview Control methods, it can be seen that this patent proposes The non-linear Preview Control algorithms of optimization the vibration amplitude of track is still reduced into 1 times of left side compared to linear method It is right.
2), barycenter along the z-axis direction motion amplitude Vz=0.05 when：Figure 11-14 illustrates barycenter 0.05 experimental result.Figure 11 is the ZMP and barycenter that non-linear Preview Control optimization algorithms proposed by the present invention obtain The 3D and vertical view of the tracks CoM, Figure 12 are linear Preview Control algorithms, and Figure 13 is that non-linear Thomas algorithms correspond to Result.
It is compared with Fig. 6-8, barycenter is obviously mitigated along the movement of Z-direction in Figure 11-13.And the barycenter of Figure 11-13 is in Y The difference that axis direction is rocked is not very big.Also find out that barycenter CoM that three kinds of algorithms obtain is moved along Y-direction from Figure 14 detail views Track difference is little, and wherein linear and nonlinear Preview Control algorithms obtain the same relatively stable track, rather than Linear Thomas algorithms are slightly poorer to them.
When barycenter CoM is smaller along z-axis vibrations, as can be seen from Figure 14 Thomas algorithms compare linear and nonlinear in the starting stage More stablize the tracks CoM of Preview Control algorithmic rules.
Correspondingly, the invention also discloses a kind of biped anthropomorphic robot based on above-mentioned non-linear gait planning method, Including：
Man-machine interaction unit, for obtaining gait parameter input by user；
ZMP reference locus generation units, for generating ZMP reference locus based on gait parameter input by user；
Centroid trajectory generation unit, for using the Preview Control algorithms for incorporating nonlinear factor, according to ginseng It examines the tracks ZMP and obtains centroid trajectory；Wherein, the nonlinear factor is related to the kinematic parameter along acceleration of gravity direction；
Gait execution unit swings foot track for calculating, and based on centroid trajectory and swings foot track, utilizes inverse kinematics Model acquires the time series angle in each joint in leg, and steering engine controls articulation so that robot according to this time sequence angle Walk out the expectation gait corresponding to gait parameter input by user.
In conclusion implementing biped anthropomorphic robot of the invention and its non-linear gait planning method and controlling party Method has the advantages that：The present invention optimizes linear Preview Control algorithms, and integration adds with along gravity The relevant nonlinear factor of kinematic parameter of directional velocity had both considered shadow of the following ZMP trace informations to current centroid trajectory It rings, and the performance of gait planning can be improved, save the kinergety consumption of system entirety, optimize existing biped robot's line Property walking posture；Further, the height of center of mass when present invention only needs user input step-length, step width, often walk used time, is static With the parameter of step number this five " What You See Is What You Get ", not needing user has the professional knowledge of robot gait planning, has good Good user experience；And when generating with reference to the tracks ZMP, there is the friendship in view of bipedal prop-up stage and foot support phase It replaces, generates the tracks reference ZMP for being more smoothly more nearly full curve.
It should be clear that word " equal ", " identical " " simultaneously " or other similar terms in the present invention, are not limited to It is absolute equal or identical in mathematical term, when implementing right described in this patent, can be close on engineering significance or In acceptable error range.
The embodiment of the present invention is described with above attached drawing, but the invention is not limited in above-mentioned specific Embodiment, the above mentioned embodiment is only schematical, rather than restrictive, those skilled in the art Under the inspiration of the present invention, without breaking away from the scope protected by the purposes and claims of the present invention, it can also make very much Form, all of these belong to the protection of the present invention.

Claims (7)

1. a kind of non-linear gait planning method of biped anthropomorphic robot, which is characterized in that method includes：
S1, gait parameter input by user is obtained；
S2, ZMP reference locus is generated based on gait parameter input by user；
S3, using the Preview Control algorithms for incorporating nonlinear factor, obtain centroid trajectory according to reference to the tracks ZMP； Wherein, the nonlinear factor is related to the kinematic parameter along acceleration of gravity direction.
2. the non-linear gait planning method of biped anthropomorphic robot according to claim 1, which is characterized in that in step S3 The use incorporates the Preview Control algorithms of nonlinear factor, and centroid trajectory packet is obtained according to reference to the tracks ZMP It includes：Nonlinear factor, structure are integrated in the combination of the state transition equation and output equation of linear Preview Control algorithms Nonlinear trajectory planning mathematical model is built, and current centroid trajectory is adjusted according to following ZMP reference locus,
The state transition equation is：X (k+1)=AX (k)+Bu (k),
The output equation is：xzmp(k)=C** X (k),
Wherein：
Wherein, parameter A, B is the preset parameter determined by frequency Δ t；Parameter C*To incorporate nonlinear factorVariable, g indicate acceleration of gravity, zcomIndicate that barycenter is along the position in acceleration of gravity direction when movement It moves,Indicate that barycenter is along the acceleration in acceleration of gravity direction when movement；X (k) be state transition equation output, x (k),Displacement, speed and the acceleration of k moment barycenter are indicated respectively；U (k) represents optimal input controller, is shape The input of state transport equation indicates k moment accelerationDifferential；xzmp(k) it is the output of output equation, indicates the k moment One point of ZMP reference locus, the output X (k) of state transition equation is the input of output equation, and the output equation establishes Non-linear relation between center of mass point and ZMP reference locus；For the mistake of ZMP actual paths and ZMP reference locus Difference and GxX (k) is the feedback of centroid trajectory,For N after the k momentpGinseng in a sampling time Examine the tracks ZMP；Wherein, Gi,Gx,GpRespectively gain parameter, and by by parameter A, B and C*Discrete multitude's card as input carries Equation calculation obtains.
3. the non-linear gait planning method of biped anthropomorphic robot according to claim 1, which is characterized in that in step S1 The gait parameter of input is：Step-length x, step width y, time t used is often walkedf, it is static when height of center of mass zheightWith step number Num.
4. the non-linear gait planning method of biped anthropomorphic robot according to claim 3, which is characterized in that the step S2 includes：
S21, the front for defining robot initial standing place are X-axis positive direction, right-hand side is Y-axis positive direction, between bipod Central point is set as origin, and in foot support phase, the foot contacted with ground is known as support leg, another is to swing foot；
S22, generated based on gait parameter input by user reference locus vector supportX of the support leg in X-Y plane, Reference locus vector torsoX, the torsoY of supportY and body in X-Y plane, wherein supportX is indicated along x Axis direction support leg track, supportY indicate that, along Y direction support leg track, torsoX indicates the body rail along X-direction Mark, torsoY are indicated along the body track of Y direction；
Wherein, supportX=[0, x, 2x, 3x ..., Numx], in the ban using left foot as support leg, when right crus of diaphragm is swing foot, SupportY=[- y, y ,-y, y ..., (- 1)NumY], in the ban using right crus of diaphragm as support leg, left foot is supportY when swinging foot =[y,-y,y,-y,…,(-1)(Num-1)·y]；TorsoX=[0, x/2,3x/2,5x/2 ..., (2Num-1) x/2], torsoY =[0,0,0,0 ... 0]；
S23, it is obtained with reference to the tracks ZMP based on the reference locus vector of support leg and body.
5. the non-linear gait planning method of biped anthropomorphic robot according to claim 4, which is characterized in that the step S23 includes：
S230, t is defined0、t1、t2Respectively initial time, close to t0Fixed point and time t used close to step S1 inputf's Fixed point, torsoXiFor along the body position of the i-th step of x-axis；
If S231, t >=t0And t ＜ t1
If S232, t >=t1And t ＜ t2
xzmp(t)=supportX (t)
yzmp(t)=supportY (t)
If S233, t >=t2And t ＜ tf,
6. a kind of non-linear gait control method of biped anthropomorphic robot, which is characterized in that including：
S100, enforcement power require 1-5 any one of them gait planning methods to obtain centroid trajectory；
S200, swing foot track is calculated；
S300, it is based on centroid trajectory and swings foot track, the time series angle in each joint in leg is acquired using inverse kinematics model Degree, steering engine control articulation so that robot walks out corresponding to the gait parameter in step S1 according to this time sequence angle Expect gait.
7. a kind of biped anthropomorphic robot based on the non-linear gait control method described in claim 6, which is characterized in that packet It includes：
Man-machine interaction unit, for obtaining gait parameter input by user；
ZMP reference locus generation units, for generating ZMP reference locus based on gait parameter input by user；
Centroid trajectory generation unit, for using the Preview Control algorithms for incorporating nonlinear factor, according to reference The tracks ZMP obtain centroid trajectory；Wherein, the nonlinear factor is related to the kinematic parameter along acceleration of gravity direction；
Gait execution unit swings foot track for calculating, and based on centroid trajectory and swings foot track, utilizes inverse kinematics model The time series angle in each joint in leg is acquired, steering engine controls articulation so that robot walks out according to this time sequence angle Expectation gait corresponding to gait parameter input by user.
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