CN104345735A - Robot walking control method based on foothold compensator - Google Patents

Abstract

The invention relates to a robot walking control method based on a foothold compensator. The robot walking control method comprises the following steps of firstly, establishing a constraint dynamic model of a robot; secondly, designing the foothold compensator based on the constraint dynamic model according to the constraint dynamic model; thirdly, establishing a heteroscedastic sparse Gauss process regression model and realizing the mapping calculation from input to output of the foothold compensator; fourthly, locally updating the heteroscedastic sparse Gauss process regression model; fifthly, establishing the foothold compensator based on the heteroscedastic sparse Gauss process regression model; sixthly, performing prediction control over the walking of the robot according to the foothold compensator based on the heteroscedastic sparse Gauss process regression model. Compared with the prior art, the robot walking control method disclosed by the invention has the advantages of accurate prediction, high learning speed and the like.

Description

A kind of robot ambulation control method based on foothold compensator

Technical field

The present invention relates to motion planning and robot control field, especially relate to a kind of robot ambulation control method based on foothold compensator.

Background technology

The foothold of dynamic adjustment anthropomorphic robot just can adjust dynamic perfromance and the controllability of robot, and then can improve the rejection ability of robot to unknown disturbance.The realization of current foothold compensator is mostly based on simple linear controller, and for anthropomorphic robot, its walking process is a complicated nonlinear system.Therefore, even if linear foothold compensator can obtain good foothold compensator gain parameter by learning method, between final foothold compensator strategy and the dynamic perfromance of robot, still there is very important error.In addition, if the foothold compensator learning process time of anthropomorphic robot is longer, is not suitable for robot foothold real-time fast in circumstances not known and compensates skill learning.Therefore, nonlinear characteristic is introduced by the present invention, devises a kind of foothold compensator based on the sparse Gaussian process of Singular variance (HspGP) model.For realizing the real-time online adjustment that foothold compensator controls, a kind of local updating method based on Singular variance Gaussian process model is proposed.This local updating method has the advantage that computation complexity is little, learning rate is fast, for the on-line study of anthropomorphic robot foothold compensator provides Fundamentals of Mathematics.

Summary of the invention

Object of the present invention be exactly in order to overcome above-mentioned prior art exist defect and a kind of robot ambulation control method based on foothold compensator is provided.

Object of the present invention can be achieved through the following technical solutions:

Based on a robot ambulation control method for foothold compensator, comprise the following steps:

1) the constrained dynamics model of robot is set up;

2) according to constrained dynamics modelling constrained dynamics model foothold compensator;

3) set up the sparse Gaussian process regression model of Singular variance, realize the mapping calculation that foothold compensator is input to output;

4) the sparse Gaussian process model of local updating Singular variance;

5) set up based on Singular variance sparse Gaussian process model foothold compensator;

6) according to carrying out PREDICTIVE CONTROL based on Singular variance sparse Gaussian process model foothold compensator to robot ambulation.

Described step 1) comprise the following steps:

11) set up the linear inverted pendulum kinetic model of robot three-dimensional, the expression formula of this kinetic model is:

${\stackrel{\·}{x}}_c={\mathrm{Ax}}_c+{\mathrm{Bu}}_x$

x _z＝Cx _c

Wherein, $A=\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ 0& 0& 0\end{array}\right],$ $B=\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right],$ $C=\left[\begin{array}{ccc}1& 0& -\frac{z_c-z_z}{g}\end{array}\right],$ $x_c={[x_c,{\stackrel{\·}{x}}_c,{\stackrel{\·\·}{x}}_c]}^T$ For robot barycenter under world coordinate system along the position of x-axis, speed and acceleration, u _xfor barycenter acceleration variable quantity and be used for controlling barycenter acceleration, p _c=[x _c, y _c, y _c] ^tfor the three-dimensional position of barycenter under world coordinate system, and p _z=[x _z, y _z, y _z] ^tfor the position of ZMP under world coordinate system, g is acceleration of gravity;

12) be positioned at the balance principle of sole support polygon according to virtual ZMP, the controlled acceleration constraint formula obtaining barycenter is:

${[{\stackrel{\·\·}{x}}_c,{\stackrel{\·\·}{y}}_c]}^T=\left\{\frac{g}{z_c-z_z}{[(x_c-x_i),(y_c-y_i)]}^T\right|{[x_i,y_i]}^T{\∈S}_c\}$

Wherein, S _cfor support polygon convex closure, x _i, y _ifor S _cthe coordinate of inner point.

Described step 2) comprise the following steps:

21) set up monopodia and support foothold compensator, the output defining this compensator is:

π＝[△t _ss，Δx _f，Δy _f] ^T

Wherein, △ t _ssfor compensating triggering from foothold, the index word of monopodia driving phase residue duration, Δ p _f=[Δ x _f, Δ y _f, 0] ^tfor next step foothold index word,

According to the output of compensator, the amendment track with reference to ZMP is:

$p_z=\left\{\begin{array}{cc}0& (0<t\&le;t_{\mathrm{ss}})\\ \mathrm{\&gamma;}(p_f+\mathrm{\&Delta;}{p}_f)& (t_{\mathrm{ss}}<t\&le;t_{\mathrm{DS}}+t_{\mathrm{ss}})\\ p_f+\mathrm{\&Delta;}{p}_f& (t_{\mathrm{DS}}+t_{\mathrm{ss}}<t<t_{\mathrm{DS}}+{2t}_{\mathrm{ss}})\end{array}\right.$

$s={[x_c,{\stackrel{\&CenterDot;}{x}}_c,y_c,{\stackrel{\&CenterDot;}{y}}_c]}^T$

Wherein, γ=(t-t _ss)/t _ds, p _ffor next step foothold position original, t _ssthe end time is supported to monopodia, t for foothold exports the decisive time _dsfor biped supporting time;

22) define monopodia and support being input as of foothold compensator:

23) performance index defining monopodia support foothold compensator are:

$J=\underset{t=t_0}{\overset{t_0+t_N}{\mathrm{\&Sigma;}}}\left(Q_z\right||p_z^{\mathrm{ref}}-{\hat{p}}_{\mathrm{vz}}|\left|\right)+\underset{k=0}{\overset{N}{\mathrm{\&Sigma;}}}\left(Q_p\right|\left|{\mathrm{\&Delta;p}}_f\left(k\right)\right||+Q_t{\mathrm{\&Delta;t}}_{\mathrm{ss}}^2\left(k\right))$

Wherein, for reference ZMP, for measuring VZMP, N for number of taking a step, t _nfor N walks the time used, Δ p _f(k) and Δ t _ssk () is kth step foothold amendment strategy, corresponding coefficient is set to Q _z=1, Q _p=100 and Q _t=1.

Described step 3) comprise the following steps:

31) set up the sparse Gaussian process model of Singular variance according to normal variance sparse Gaussian process model and sparse Gaussian process model, the prediction of output equation of the sparse Gaussian process model of Singular variance is:

${\mathrm{\&mu;}}_{\&CenterDot;}\left(x_t\right)=k_{\&CenterDot;}^T{Q}_M^{-1}{K}_{\mathrm{MN}}{(\mathrm{\&Lambda;}+\mathrm{diag}\left(r\right))}^{-1}y$

${\mathrm{\&lambda;}}_i=\mathrm{\&kappa;}(x_i,x_i)-\mathrm{\&kappa;}(x_i,\stackrel{\&OverBar;}{x})K_M^{-1}\mathrm{\&kappa;}(\stackrel{\&OverBar;}{x},x_i)$

$\mathrm{\&kappa;}(x,x^{\&prime;})={\mathrm{\&sigma;}}_f^2\exp (-\frac{1}{2}(x-x^{\&prime;})W{(x-x^{\&prime;})}^T)$

Wherein, x _tfor input state, y is that standard gaussian process model target exports, y=[y ₁, y ₂..., y _n] ^t, κ is kernel function, k _.=[κ (x _t, x ₁), κ (x _t, x ₂) ..., κ (x _t, x _n)] ^t, κ _.=κ (x ₁, x _t), K is a square formation, and each element is K (i, j)=κ (x _i, x _j), for signal variance, W is weights diagonal matrix, Λ=diag (λ), q _m=K _m+ K _mN(Λ+diag (r)) ^-1k _nM, for the uncertainty of each pseudo-input, for the pseudo-input quantity of sparse Gaussian process model;

32) do not change according to the variance at input state place, obtain final predictive equation:

${\mathrm{\&mu;}}_{\&CenterDot;}\left(x_t\right)=k_{\&CenterDot;}^{T}H$

Wherein, $H=Q_M^{-1}{K}_{\mathrm{MN}}{(\mathrm{\&Lambda;}+\mathrm{diag}\left(r\right))}^{-1}y$ And

Described step 4) comprise the following steps:

41) first off-line is built into KD tree by training the single pseudo-sample point obtained;

42) given online example, finds nearest pseudo-sample point according to KD tree;

43) the predicted vector element corresponding with nearest pseudo-sample point is upgraded;

44) method of disposable batch updating is adopted to upgrade the sparse Gaussian process model of Singular variance.

Described step 5) comprise the following steps:

51) obtaining the output of Singular variance sparse Gaussian process model foothold compensator according to the nonparametric mapping ability of Singular variance sparse Gaussian process model is:

π＝[min(Δt _ssx，△t _ssy)，Δx _f，Δy _f] ^T

Wherein, △ t _ssx=G _α(s ₁) and △ t _ssx=G _α(s ₁) for Singular variance sparse Gaussian process model foothold compensator is along the independent HSpGP model of x-axis, Δ t _ssy=G _ty(s ₂) and Δ y _f=G _y(s ₂) for Singular variance sparse Gaussian process model foothold compensator is along the independent HSpGP model of x-axis,

52) according to kinetic model foothold compensator off-line training Singular variance sparse Gaussian process model foothold compensator and the foothold compensator of the sparse Gaussian process model of online updating Singular variance;

53) utilize the renewal amount from exporting as foothold compensator to the vector measuring ZMP position with reference to ZMP position, the foothold position of calculation expectation is:

y _t=Δy _f+βΔy _z

x _t=Δx _f+βΔx _z

Wherein, x _tfor given prediction input state, Δ p _f=[Δ x _f, Δ y _f] ^tfor the foothold position index word of the current output of the foothold compensator of Singular variance sparse Gaussian process model.

Compared with prior art, the present invention has the following advantages:

One, prediction accurately, have employed nonlinear Singular variance sparse Gaussian process model foothold compensator, achieves real-time online adjustment, more accurately.

Two, pace of learning is fast, have employed a kind of local updating method based on Singular variance Gaussian process model, reduces computation complexity, improve pace of learning.

Three, model training is convenient, avoids the over-fitting problem of Partial Linear Models.

Four, model stability is high, can not destroy the forecasting accuracy of whole model because of local updating.

Accompanying drawing explanation

Fig. 1 is method flow diagram of the present invention.

Fig. 2 is constrained dynamics model following trajectory diagram.

Fig. 3 is ideal linearity inverted pendulum model pursuit path figure.

Fig. 4 is the foothold compensator design sketch based on constrained dynamics model.

Fig. 5 is the Humanoid Robot Based on Walking control block diagram adopting HSpGP foothold compensator.

Fig. 6 is for adopting HSpGP foothold compensator Y-axis track following figure.

Fig. 7 is for adopting HSpGP foothold compensator planar obit simulation tracing figure.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.

Embodiment:

As shown in Figure 1, a kind of robot ambulation control method based on foothold compensator, comprises the following steps:

1) the constrained dynamics model of robot is set up;

2) according to constrained dynamics modelling constrained dynamics model foothold compensator;

3) set up the sparse Gaussian process regression model of Singular variance, realize the mapping calculation that foothold compensator is input to output;

4) the sparse Gaussian process model of local updating Singular variance;

5) set up based on Singular variance sparse Gaussian process model foothold compensator;

6) according to carrying out PREDICTIVE CONTROL based on Singular variance sparse Gaussian process model foothold compensator to robot ambulation.

Step 1) comprise the following steps:

11) set up the linear inverted pendulum kinetic model of robot three-dimensional, the expression formula of this kinetic model is:

${\stackrel{\&CenterDot;}{x}}_c={\mathrm{Ax}}_c+{\mathrm{Bu}}_x$

x _z＝Cx _c

Wherein, $A=\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ 0& 0& 0\end{array}\right],$ $B=\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right],$ $C=\left[\begin{array}{ccc}1& 0& -\frac{z_c-z_z}{g}\end{array}\right],$ $x_c={[x_c,{\stackrel{\&CenterDot;}{x}}_c,{\stackrel{\&CenterDot;\&CenterDot;}{x}}_c]}^T$ For robot barycenter under world coordinate system along the position of x-axis, speed and acceleration, u _xfor barycenter acceleration variable quantity and be used for controlling barycenter acceleration, p _c=[x _c, y _c, y _c] ^tfor the three-dimensional position of barycenter under world coordinate system, and p _z=[x _z, y _z, y _z] ^tfor the position of ZMP under world coordinate system, g is acceleration of gravity;

12) be positioned at the balance principle of sole support polygon according to virtual ZMP, the controlled acceleration constraint formula obtaining barycenter is:

${[{\stackrel{\&CenterDot;\&CenterDot;}{x}}_c,{\stackrel{\&CenterDot;\&CenterDot;}{y}}_c]}^T=\left\{\frac{g}{z_c-z_z}{[(x_c-x_i),(y_c-y_i)]}^T\right|{[x_i,y_i]}^T{\&Element;S}_c\}$

Wherein, S _cfor support polygon convex closure, x _i, y _ifor S _cthe coordinate of inner point.

As shown in Figures 2 and 3, the effect of expression constrained dynamics model in Humanoid Robot Based on Walking controls of image, here anthropomorphic robot is carried out emulation compared based on Constrained with without track following situation when being hit under the linear inverted pendulum model of constraint respectively, as can be seen from the figure, impact occurs in about 2.5s, when not considering support polygon restraint condition, preview observing and controlling system has successfully resisted weak impact.But considering under the actual conditions supporting polygon constraint, robot cannot obtain enough barycenter and accelerate to control the barycenter departing from desired trajectory, the therefore inevitable out of trim of robot.

Step 2) comprise the following steps:

21) set up monopodia and support foothold compensator, the output defining this compensator is:

π＝[△t _ss，Δx _f，△y _f] ^T

Wherein, △ t _ssfor compensating triggering from foothold, the index word of monopodia driving phase residue duration, Δ p _f=[Δ x _f, Δ y _f, 0] ^tfor next step foothold index word,

According to the output of compensator, the amendment track with reference to ZMP is:

$p_z=\left\{\begin{array}{cc}0& (0<t\&le;t_{\mathrm{ss}})\\ \mathrm{\&gamma;}(p_f+\mathrm{\&Delta;}{p}_f)& (t_{\mathrm{ss}}<t\&le;t_{\mathrm{DS}}+t_{\mathrm{ss}})\\ p_f+\mathrm{\&Delta;}{p}_f& (t_{\mathrm{DS}}+t_{\mathrm{ss}}<t<t_{\mathrm{DS}}+{2t}_{\mathrm{ss}})\end{array}\right.$

Wherein, γ=(t-t _ss)/t _dS, p _ffor next step foothold position original, t _ssthe end time is supported to monopodia, t for foothold exports the decisive time _dSfor biped supporting time;

22) define monopodia and support being input as of foothold compensator:

$s={[x_c,{\stackrel{\&CenterDot;}{x}}_c,y_c,{\stackrel{\&CenterDot;}{y}}_c]}^T$

23) performance index defining monopodia support foothold compensator are:

$J=\underset{t=t_0}{\overset{t_0+t_N}{\mathrm{\&Sigma;}}}\left(Q_z\right||p_z^{\mathrm{ref}}-{\hat{p}}_{\mathrm{vz}}|\left|\right)+\underset{k=0}{\overset{N}{\mathrm{\&Sigma;}}}\left(Q_p\right|\left|{\mathrm{\&Delta;p}}_f\left(k\right)\right||+Q_t{\mathrm{\&Delta;t}}_{\mathrm{ss}}^2\left(k\right))$

Wherein, for reference ZMP, for measuring VZMP, N for number of taking a step, t _nfor N walks the time used, Δ p _f(k) and Δ t _ssk () is kth step foothold amendment strategy, corresponding coefficient is set to Q _z=1, Q _p=100 and Q _t=1.

As figureshown in 4, given foothold compensator input, export definition and performance index after, because constrained dynamics model can directly calculate, constraint nonlinear optimization can be adopted to calculate (CNOP) method and to export according to the foothold compensator that each foothold compensator input calculating is optimum.Can find, after employing foothold compensator, robot successfully can resist disturbance, continues stable advance.

Step 3) comprise the following steps:

31) set up the sparse Gaussian process model of Singular variance according to normal variance sparse Gaussian process model and sparse Gaussian process model, the prediction of output equation of the sparse Gaussian process model of Singular variance is:

${\mathrm{\&mu;}}_{\&CenterDot;}\left(x_t\right)=k_{\&CenterDot;}^T{Q}_M^{-1}{K}_{\mathrm{MN}}{(\mathrm{\&Lambda;}+\mathrm{diag}\left(r\right))}^{-1}y$

${\mathrm{\&lambda;}}_i=\mathrm{\&kappa;}(x_i,x_i)-\mathrm{\&kappa;}(x_i,\stackrel{\&OverBar;}{x})K_M^{-1}\mathrm{\&kappa;}(\stackrel{\&OverBar;}{x},x_i)$

$\mathrm{\&kappa;}(x,x^{\&prime;})={\mathrm{\&sigma;}}_f^2\exp (-\frac{1}{2}(x-x^{\&prime;})W{(x-x^{\&prime;})}^T)$

Wherein, x _tfor input state, y is that standard gaussian process model target exports, y=[y ₁, y ₂..., y _n] ^t, κ is kernel function, k _.=[κ (x _t, x ₁), κ (x _t, x ₂) ..., κ (x _t, x _n)] ^t, κ _.=κ (x _t, x _t), K is a square formation, and each element is K (i, j)=κ (x _i, x _j), for signal variance, W is weights diagonal matrix, Λ=diag (λ), q _m=K _m+ K _mN(Λ+diag (r)) ^-1k _nM, for the uncertainty of each pseudo-input, for the pseudo-input quantity of sparse Gaussian process model;

32) do not change according to the variance at input state place, obtain final predictive equation:

${\mathrm{\&mu;}}_{\&CenterDot;}\left(x_t\right)=k_{\&CenterDot;}^{T}H$

Wherein, $H=Q_M^{-1}{K}_{\mathrm{MN}}{(\mathrm{\&Lambda;}+\mathrm{diag}\left(r\right))}^{-1}y$ And

Step 4) comprise the following steps:

41) first off-line is built into KD tree by training the single pseudo-sample point obtained;

42) given online example, finds nearest pseudo-sample point according to KD tree;

43) the predicted vector element corresponding with nearest pseudo-sample point is upgraded;

44) method of disposable batch updating is adopted to upgrade the sparse Gaussian process model of Singular variance.

Step 5) comprise the following steps:

51) obtaining the output of Singular variance sparse Gaussian process model foothold compensator according to the nonparametric mapping ability of Singular variance sparse Gaussian process model is:

π＝[min(Δt _ssx，Δt _ssy)，Δx _f，Δy _f] ^T

Wherein, △ t _ssx=G _α(s ₁) and △ t _ssx=G _α(s ₁) for Singular variance sparse Gaussian process model foothold compensator is along the independent HSpGP model of x-axis, Δ t _ssy=G _ty(s ₂) and Δ y _f=G _y(s ₂) for Singular variance sparse Gaussian process model foothold compensator is along the independent HSpGP model of x-axis,

52) according to kinetic model foothold compensator off-line training Singular variance sparse Gaussian process model foothold compensator and the foothold compensator of the sparse Gaussian process model of online updating Singular variance;

53) utilize the renewal amount from exporting as foothold compensator to the vector measuring ZMP position with reference to ZMP position, the foothold position of calculation expectation is:

y _t＝Δy _f+βΔy _z

Wherein, x _ffor given prediction input state, Δ p _f=[Δ x _f, Δ y _f] ^tfor the foothold position index word of the current output of the foothold compensator of Singular variance sparse Gaussian process model.

Adopt HSpGP model as foothold compensator model Humanoid Robot Based on Walking control framework as shown in Figure 5, the follow-up position of stopping over of travel commands planning that first gait planning sends according to decision-making level of robot, then plan ZMP track according to position of stopping over and utilize preview to survey controller calculation expectation centroid trajectory.The walking of robot is realized by counter motion model and PD joint control.After robot completes current kinetic instruction, estimate barycenter current state by Airborne Inertial unit (IMU) metrical information and joint value of feedback.Foothold compensator according to barycenter state and HspGP prediction foothold index word and the monopodia driving phase time remodify follow-up foothold.

As shown in Figure 6 and Figure 7, upgrade the rear effect of foothold compensating controller in Disturbance Rejection for representing, the HSpGP model after allowing robot adopt final updated here in simulation software compensates to control foothold.In robot ambulation process, a quality is adopted to be the speed impacts robot shoulder of bead with 4m/s of 0.4kg.Because gravity does work to bead in bead flight course, bead acts on the actual momentum that robot produces and is greater than 2Ns.Shock occurs in about 2.5s, and very large skew occurs robot ZMP after shock.Robot huge step left under the effect of foothold compensator, and inhibit most of shock vibration.Robot adopts the adjustment of second step right crus of diaphragm to complete the suppression of residual disturbance amount then.As can be seen from the trajectory diagram of x-y plane, after robot is clashed into, the sole support polygon that its ZMP has shifted out robot is comparatively far away, out of trim is fallen down if do not taked any measure robot.

Claims (6)

1. based on a robot ambulation control method for foothold compensator, it is characterized in that, comprise the following steps:

1) the constrained dynamics model of robot is set up;

2) according to constrained dynamics modelling constrained dynamics model foothold compensator;

3) set up the sparse Gaussian process regression model of Singular variance, realize constrained dynamics model foothold compensator from the mapping calculation being input to output;

4) the sparse Gaussian process regression model of local updating Singular variance;

5) set up based on Singular variance sparse Gaussian process regression model foothold compensator;

6) according to carrying out PREDICTIVE CONTROL based on Singular variance sparse Gaussian process regression model foothold compensator to robot ambulation.

2. a kind of robot ambulation control method based on foothold compensator according to claim 1, is characterized in that, described step 1) specifically comprise the following steps:

11) set up the linear inverted pendulum kinetic model of robot three-dimensional, the expression formula of this kinetic model is:

${\stackrel{.}{x}}_c={\mathrm{Ax}}_c+{\mathrm{Bu}}_x$

x _z＝Cx _c

Wherein, $A=\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ 0& 0& 0\end{array}\right],B=\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right],C=\left[\begin{array}{ccc}1& 0& -\frac{z_c-z_z}{g}\end{array}\right],x_c={[x_c,{\stackrel{.}{x}}_c,{\stackrel{..}{x}}_c]}^T$ For robot barycenter under world coordinate system along the position of x-axis, speed and acceleration, u _xfor barycenter acceleration variable quantity and be used for controlling barycenter acceleration, p _c=[x _c, y _c, y _c] ^tfor the three-dimensional position of barycenter under world coordinate system, and p _z=[x _z, y _z, y _z] ^tfor the position of ZMP under world coordinate system, g is acceleration of gravity;

12) be positioned at the balance principle of sole support polygon according to virtual ZMP, the controlled acceleration constraint formula obtaining barycenter is:

${[{\stackrel{..}{x}}_c,{\stackrel{..}{y}}_c]}^T=\left\{\frac{g}{z_c-z_z}\right[(x_c-x_i),(y_c-y_i){]}^T|{[x_i,y_i]}^T\&Element;S_c\}$

Wherein, S _cfor support polygon convex closure, x _i, y _ifor S _cthe coordinate of inner point.

3. a kind of robot ambulation control method based on foothold compensator according to claim 1, is characterized in that, described step 2) specifically comprise the following steps:

21) set up constrained dynamics model foothold compensator, the output defining this compensator is:

π＝[Δt _ss，Δx _f，Δy _f] ^T

Wherein, Δ t _ssfor compensating triggering from foothold, the index word of monopodia driving phase residue duration, Δ p _f=[Δ x _f, Δ y _f, 0] ^tfor next step foothold index word,

According to the output of compensator, the amendment track with reference to ZMP is:

$p_z=\left\{\begin{array}{cc}0& (0<t\&le;t_{\mathrm{SS}})\\ \mathrm{\&gamma;}(p_f+\mathrm{\&Delta;}{p}_f)& (t_{\mathrm{SS}}<t\&le;t_{\mathrm{DS}}+t_{\mathrm{SS}})\\ p_f+\mathrm{\&Delta;}{p}_f& (t_{\mathrm{DS}}+t_{\mathrm{SS}}<t<t_{\mathrm{DS}}+2t_{\mathrm{SS}})\end{array}\right.$

Wherein, γ=(t-t _sS)/t _dS, p _ffor next step foothold position original, t _sSthe end time is supported to monopodia, t for foothold exports the decisive time _dSfor biped supporting time;

22) being input as of constrained dynamics model foothold compensator is defined:

$s={[x_c,{\stackrel{.}{x}}_c,y_c,{\stackrel{.}{y}}_c]}^T;$

23) performance index defining constrained dynamics model foothold compensator are:

$J=\underset{t=t_0}{\overset{t_0+t_N}{\mathrm{\&Sigma;}}}\left(Q_z\right||p_z^{\mathrm{ref}}-{\hat{p}}_{\mathrm{vz}}|\left|\right)+\underset{k=0}{\overset{N}{\mathrm{\&Sigma;}}}\left(Q_p\right|\left|\mathrm{\&Delta;}{p}_f\left(k\right)\right||+Q_1\mathrm{\&Delta;}{t}_{\mathrm{ss}}^2\left(k\right))$

Wherein, for reference ZMP, for measuring VZMP, N for number of taking a step, t _nfor N walks the time used, Δ p _f(k) and Δ t _ssk () is kth step foothold amendment strategy, corresponding coefficient is set to Q _z=1, Q _p=100 and Q _t=1.

4. a kind of robot ambulation control method based on foothold compensator according to claim 1, is characterized in that, described step 3) specifically comprise the following steps:

31) set up the sparse Gaussian process model of Singular variance according to normal variance sparse Gaussian process model and sparse Gaussian process model, the prediction of output equation of the sparse Gaussian process model of Singular variance is:

${\mathrm{\&mu;}}_{*}\left(x_t\right)=k_{*}^T{Q}_M^{-1}{K}_{\mathrm{MN}}{(\mathrm{\&Lambda;}+\mathrm{diag}\left(r\right))}^{-1}y$

${\mathrm{\&lambda;}}_i=\mathrm{\&kappa;}(x_i,x_j)-\mathrm{\&kappa;}(x_i,\stackrel{\&OverBar;}{x})K_M^{-1}\mathrm{\&kappa;}(\stackrel{\&OverBar;}{x},x_i)$

$\mathrm{\&kappa;}(x,x^{\&prime;})={\mathrm{\&sigma;}}_f^2\exp (-\frac{1}{2}(x-x^{\&prime;})W{(x-x^{\&prime;})}^T)$

Wherein, x _tfor input state, y is that standard gaussian process model target exports, y=[y ₁, y ₂..., y _n] ^t, κ is kernel function, k _*=[κ (x _t, x ₁), κ (x _t, x ₂) ..., κ (x _t, x _n)] ^t, κ _*=κ (x _t, x _t), K is a square formation, and each element is K (i, j)=κ (x _i, x _j), for signal variance, W is weights diagonal matrix, Λ=diag (λ), q _m=K _m+ K _mN(Λ+diag (r)) ^-1k _nM, for the uncertainty of each pseudo-input, for the pseudo-input quantity of sparse Gaussian process model;

32) do not change according to the variance at input state place, obtain final predictive equation:

${\mathrm{\&mu;}}_{*}\left(x_r\right)=k_{*}^{T}H$

Wherein, $H=Q_M^{-1}{K}_{\mathrm{MN}}{(\mathrm{\&Lambda;}+\mathrm{diag}\left(r\right))}^{-1}y$ And

5. a kind of robot ambulation control method based on foothold compensator according to claim 1, is characterized in that, described step 4) specifically comprise the following steps:

41) first off-line is built into KD tree by training the single pseudo-sample point obtained;

42) given online example, finds nearest pseudo-sample point according to KD tree;

43) the predicted vector element corresponding with nearest pseudo-sample point is upgraded;

44) method of disposable batch updating is adopted to upgrade the sparse Gaussian process model of Singular variance.

6. a kind of robot ambulation control method based on foothold compensator according to claim 1, is characterized in that, described step 5) specifically comprise the following steps:

51) obtaining the output of Singular variance sparse Gaussian process model foothold compensator according to the nonparametric mapping ability of Singular variance sparse Gaussian process model is:

π＝[min(Δt _ssx，Δt _ssy)，Δx _f，Δy _f] ^T

Wherein, Δ t _ssx=G _ts(s _t) and Δ t _ssx=G _tx(s ₁) for Singular variance sparse Gaussian process model foothold compensator is along the independent HSpGP model of x-axis, Δ t _ssy=G _ty(s ₂) and Δ y _f=G _y(s ₂) for Singular variance sparse Gaussian process model foothold compensator is along the independent HSpGP model of x-axis,

52) according to kinetic model foothold compensator off-line training Singular variance sparse Gaussian process model foothold compensator and the foothold compensator of the sparse Gaussian process model of online updating Singular variance;

53) utilize the renewal amount from exporting as foothold compensator to the vector measuring ZMP position with reference to ZMP position, the foothold position of calculation expectation is:

y _t＝Δy _f+βΔy _z

x _t＝Δx _f+βΔx _z

Wherein, x _tfor given prediction input state, Δ p _f=[Δ x _f, Δ y _f] ^tfor the foothold position index word of the current output of the foothold compensator of Singular variance sparse Gaussian process model.