CN108345211A  Biped anthropomorphic robot and its nonlinear gait planning method and control method  Google Patents
Biped anthropomorphic robot and its nonlinear gait planning method and control method Download PDFInfo
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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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 G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
 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
 G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
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Abstract
A kind of biped anthropomorphic robot and its nonlinear 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
Technical field
The present invention relates to artificial intelligence field more particularly to a kind of biped anthropomorphic robot and its nonlinear 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 largescale 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 mobilerobot 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 anklejoint (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 Zdirection) determines the track rule of robot ambulation
Whether the problem of drawing is nonlinear, 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 xy 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 nonlinear gait planning method and control method.
The technical solution adopted by the present invention to solve the technical problems is：Construct a kind of nonlinear 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 nonlinear 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 nonlinear
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：x_{zmp}(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, z_{com}Indicate 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；x_{zmp}(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
Nonlinear relation between heart point and ZMP reference locus；For the error of ZMP actual paths and ZMP reference locus
With G_{x}X (k) is the feedback of centroid trajectory,For N after the k moment_{p}Reference in a sampling time
The tracks ZMP；Wherein, G_{i},G_{x},G_{p}Respectively gain parameter, and by by parameter A, B and C^{*}Discrete multitude as input blocks the side of carrying
Journey is calculated.
In the nonlinear gait planning method of biped anthropomorphic robot of the present invention, the gait inputted in step S1 is joined
Number is：Steplength x, step width y, time t used is often walked_{f}, it is static when height of center of mass z_{height}With step number Num.
In the nonlinear 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 Xaxis positive direction, righthand side is Yaxis 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 XY plane is generated based on gait parameter input by user
Reference locus vector torsoX, the torsoY of supportX, supportY and body in XY plane, wherein
SupportX indicates that support leg track along the xaxis 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)^{Num}Y], in the ban using right crus of diaphragm as support leg, when left foot is swing foot,
supportY=[y,y,y,y,…,(1)^{(Num1)}·y]；TorsoX=[0, x/2,3x/2,5x/2 ..., (2Num1) 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 nonlinear gait planning method of biped anthropomorphic robot of the present invention, the step S23 includes：
S230, t is defined_{0}、t_{1}、t_{2}Respectively initial time, close to t_{0}Fixed point and time used close to step S1 input
t_{f}Fixed point, torsoX_{i}For along the body position of the ith step of xaxis；
If S231, t >=t_{0}And t ＜ t_{1}
If S232, t >=t_{1}And t ＜ t_{2}
x_{zmp}(t)=supportX (t)
y_{zmp}(t)=supportY (t)
If S233, t >=t_{2}And t ＜ t_{f},
The invention also discloses a kind of nonlinear gait control methods of biped anthropomorphic robot, including：
S100, perform claim require 15 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 nonlinear gait control method, including：
Manmachine 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 nonlinear 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 steplength, 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 propup 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 nonlinear 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, nonlinear 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, nonlinear 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 Yaxis track comparison diagram；
Figure 10 is nonlinear and linear Preview Control algorithms obtain in Fig. 6 and Fig. 7 barycenter along Yaxis track pair
Compare enlarged drawing；
Figure 11 is 2.2 unit of height of center of mass, nonwhen 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, nonwhen 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 Yaxis 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 nonlinear gait planning method of biped anthropomorphic robot of the present invention with reference to figure 1.
The present invention the nonlinear 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 S1S3 is described in detail below.
About step S1：
Parameter specifically includes in the step：Steplength x, step width y, time t used is often walked_{f}, it is static when height of center of mass z_{height}With
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 abovementioned 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 Xaxis positive direction, the right side
Hand side is Yaxis 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 XY plane is generated based on gait parameter input by user
Reference locus vector torsoX, the torsoY of supportX, supportY and body in XY plane.Wherein,
SupportX indicates that support leg track along the xaxis 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)^{(Num1)}·y]
Definition always lags behind support leg half along the body track torsoX of Xdirection and walks the i.e. distance of x/2, i.e.,：
TorsoX=[0, x/2,3x/2,5x/2 ..., (2Num1) 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 x_{zmp}=supprotX,y_{zmp}=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 propup stage,
It is more smoothly more nearly the reference ZMP of full curve, it is specific as follows：
First, t is defined_{0}、t_{1}、t_{2}Respectively initial time, close to t_{0}Fixed point and time used close to step S1 input
t_{f}Fixed point, it is socalled close to t_{0}Refer to compared with t_{0}Big default value, close to t_{f}Refer to compared with t_{f}Small default value, such as t_{0}=0.0,
t_{f}=1.0, t_{1}=0.1, t_{2}=0.9.From t_{0}To t_{1}With from t_{2}To t_{f}It is equivalent to bipedal propup stage, from t_{1}To t_{2}It is equivalent to single foot
Driving phase.T is in end of time t_{f}It is interior using Δ t as the sampling time at interval, torsoX_{i}For along the body position of the ith step of xaxis；
If t >=t_{0}And t ＜ t_{1}
If t >=t_{1}And t ＜ t_{2}
x_{zmp}(t)=supportX(t)
y_{zmp}(t)=supportY (t)
If t >=t_{2}And t ＜ t_{f},
About step S3：
In Fig. 2, the left side is the center of mass motion track of nonlinear 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 zaxis direction
Heart space is the plane that xy axis is constituted.It is proved from the moving equilibrium power system model of biped robot's system below this
Nonlinear 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 multibody 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 zaxis direction movement.Formula (1) first part is small
Vehicle barycenter arrives the torque of ZMP points along the zaxis direction, and g is acceleration of gravity, and second part is the torque of trolley along the xaxis direction, constant
z_{height}Height of center of mass when being static, Part III are the moment of inertia of trolley.If it is considered that the movement in zaxis direction, such as formula
(2), the acceleration plus barycenter in the zdirection is needed at first part gThe z of second part_{height}Replace with variation
Height of center of mass z_{com}.Formula (3) and (4) respectively describe extensive to being derived according to balanced system of force formula (2) when multibody system
The relationship of ZMP point and particle trajectory.If ignoring moment of inertia termWithAnd think ∑_{i}m_{i}x_{i}/∑_{i}m_{i}=x_{com}(similarly y_{com}), 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 z_{com}=z_{height},Linear formula (7) and (8) are reduced to, with known with reference to ZMP track x_{zmp},
y_{zmp}With constant z_{height}, g generates centroid trajectory x_{com},y_{com}.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 nonlinear 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：
x_{zmp}(k)=C*X (k) (9A)
Nonlinear object equation is：
x_{zmp}(k)=C^{*}*X(k) (9B)
Wherein：
C≡[1 0 z_{height}/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；x_{zmp}(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 nonlinear formula 7 and, the output of output equation is
x_{zmp}(k), the output equation establishes the nonlinear 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 z_{height}, A, B and C are during state transition
Fixed parameter.However, parameter C known to the abovementioned discussion to nonlinear factor is not immobilizing as described in formula (11)
, but have nonlinear change in Zdirection 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, G_{x}X (k) is the feedback of centroid trajectory, For N after the k moment_{p}The tracks reference ZMP in a sampling time.G_{i},G_{x},G_{p}Respectively gain
Parameter.These parameter values are by A, B and C as described in the pseudocode of table 2^{*}Discrete Riccati equation as input
(Discretetime 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 technology_{height}/ 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. 614, by two groups of description of test present invention and linear Preview Control algorithms and nonthread
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 Zdirection.If
Steplength x=1, step width y=0.45 are set, time t used is often walked_{f}=0.2, height of center of mass z when static_{height}=2.2 and step number Num
=30.With z_{height}=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 zaxis direction motion amplitude Vz=2 when, illustrate barycenter along Z axis motion amplitude with reference to figure 610
For 2 experimental result.Fig. 6 is the ZMP and barycenter rail that nonlinear 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 nonlinear Thomas algorithms.
First, find out from Fig. 6,7 and 8, the centroid trajectory that nonlinear Thomas algorithms obtain the amplitude moved along Yaxis 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 nonlinear and linear Preview Control algorithms is relatively good, along Yaxis
The amplitude of direction movement very little for the tracks ZMP only accounts for ZMP along about the 22% of Yaxis 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 Ydirection 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 nonlinear 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 zaxis direction motion amplitude Vz=0.05 when：Figure 1114 illustrates barycenter
0.05 experimental result.Figure 11 is the ZMP and barycenter that nonlinear 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 nonlinear Thomas algorithms correspond to
Result.
It is compared with Fig. 68, barycenter is obviously mitigated along the movement of Zdirection in Figure 1113.And the barycenter of Figure 1113 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 Ydirection 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 zaxis 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 abovementioned nonlinear gait planning method,
Including：
Manmachine 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 nonlinear 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 steplength, 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 propup 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 abovementioned 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 nonlinear 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 nonlinear 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：x_{zmp}(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, z_{com}Indicate 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；x_{zmp}(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
Nonlinear relation between center of mass point and ZMP reference locus；For the mistake of ZMP actual paths and ZMP reference locus
Difference and G_{x}X (k) is the feedback of centroid trajectory,For N after the k moment_{p}Ginseng in a sampling time
Examine the tracks ZMP；Wherein, G_{i},G_{x},G_{p}Respectively gain parameter, and by by parameter A, B and C^{*}Discrete multitude's card as input carries
Equation calculation obtains.
3. the nonlinear 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：Steplength x, step width y, time t used is often walked_{f}, it is static when height of center of mass z_{height}With step number Num.
4. the nonlinear 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 Xaxis positive direction, righthand side is Yaxis 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 XY plane,
Reference locus vector torsoX, the torsoY of supportY and body in XY 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 Xdirection
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)^{Num}Y], in the ban using right crus of diaphragm as support leg, left foot is supportY when swinging foot
=[y,y,y,y,…,(1)^{(Num1)}·y]；TorsoX=[0, x/2,3x/2,5x/2 ..., (2Num1) 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 nonlinear gait planning method of biped anthropomorphic robot according to claim 4, which is characterized in that the step
S23 includes：
S230, t is defined_{0}、t_{1}、t_{2}Respectively initial time, close to t_{0}Fixed point and time t used close to step S1 input_{f}'s
Fixed point, torsoX_{i}For along the body position of the ith step of xaxis；
If S231, t >=t_{0}And t ＜ t_{1}
If S232, t >=t_{1}And t ＜ t_{2}
x_{zmp}(t)=supportX (t)
y_{zmp}(t)=supportY (t)
If S233, t >=t_{2}And t ＜ t_{f},
6. a kind of nonlinear gait control method of biped anthropomorphic robot, which is characterized in that including：
S100, enforcement power require 15 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 nonlinear gait control method described in claim 6, which is characterized in that packet
It includes：
Manmachine 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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CN108958261A (en) *  20180802  20181207  中山赛伯坦智能科技有限公司  A method of the steady carrying target object based on 2D wheeled robot 
CN110209183A (en) *  20190604  20190906  吉林大学  A kind of hexapod robot unstability adjusting algorithm based on dualthreshold voltage ZMP 
CN111198581A (en) *  20200117  20200526  同济大学  Speed adjusting method and device for virtual passive walking robot and storage medium terminal 
CN111240339A (en) *  20200211  20200605  之江实验室  Humanoid gait planning method of biped robot 

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Cited By (5)
Publication number  Priority date  Publication date  Assignee  Title 

CN108958261A (en) *  20180802  20181207  中山赛伯坦智能科技有限公司  A method of the steady carrying target object based on 2D wheeled robot 
CN110209183A (en) *  20190604  20190906  吉林大学  A kind of hexapod robot unstability adjusting algorithm based on dualthreshold voltage ZMP 
CN111198581A (en) *  20200117  20200526  同济大学  Speed adjusting method and device for virtual passive walking robot and storage medium terminal 
CN111198581B (en) *  20200117  20210212  同济大学  Speed adjusting method and device for virtual passive walking robot and storage medium terminal 
CN111240339A (en) *  20200211  20200605  之江实验室  Humanoid gait planning method of biped robot 
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