CN111353119B - Biped walking stability analysis method based on track mechanical energy - Google Patents

Biped walking stability analysis method based on track mechanical energy Download PDF

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CN111353119B
CN111353119B CN202010223534.6A CN202010223534A CN111353119B CN 111353119 B CN111353119 B CN 111353119B CN 202010223534 A CN202010223534 A CN 202010223534A CN 111353119 B CN111353119 B CN 111353119B
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黄强
张润明
余张国
陈学超
李庆庆
孟立波
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Beijing Institute of Technology BIT
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Abstract

The invention discloses a biped walking stability analysis method based on mechanical energy of a track, which comprises the steps of selecting a foot-falling point and a corresponding foot-falling period of a biped robot in the current step, and calculating the mechanical energy E of the track in the current step according to an expression of the mechanical energy of the track of the biped robotn(ii) a According to the next step of the feet-falling point and the corresponding feet-falling period of the biped robot, the next step of the track mechanical energy E is calculated according to the expression of the track mechanical energy of the biped robotn+1(ii) a According to En、En+1And target mechanical energy E capable of achieving periodic stable walkingtrConstructing a stability judgment condition, and if the stability judgment condition is met, showing that the walking of the biped robot converges to the target mechanical energy, and realizing gradual stability; if the formula is not satisfied, the current position P is determinednAnd its period TnOptimizing; the invention is based on the original orbit energy and is improved, the orbit mechanical energy is provided, the direction of the mass center movement speed and the direction of the mass center position relative to the ZMP are introduced by utilizing the orbit mechanical energy, and the method can be used for representing the magnitude and the direction of the external disturbance.

Description

Biped walking stability analysis method based on track mechanical energy
Technical Field
The invention relates to the technical field of humanoid robots, in particular to a biped walking stability analysis method based on track mechanical energy.
Background
The humanoid robot is a floating-base multi-degree-of-freedom robot, and the double-foot walking function is an important component for the practicability of the humanoid robot. It is common to model the walking function of a floating base using an inverted pendulum model. However, such a model does not have progressive stability, and therefore it is necessary to design a controller to make the motion of the inverted pendulum converge with stable periodic motion. For humanoid robots modeled using Linear Inverted Pendulum (LIPM), orbital energy theory is often used to judge the machineWhether the person is subjected to additional perturbations. According to the law of conservation of orbital energy in the field of humanoid robot research: when the Zero Moment Point (ZMP) is fixed, the orbital energy of the robot is conserved without external energy input, i.e. the robot is not disturbed: oE ═ x2/2-(x-p)2w2Track energy oE constant at the initial time0Generally oE0Is set to 0. The orbital energy represents: the difference between the actual kinetic energy of the robot and the kinetic energy provided to the robot by the linear inverted pendulum.
At present, a disturbance evaluation method Based on track energy in the field of Humanoid Robots has started relevant research, for example, papers "Dynamic and Reactive Walking for human Robots Based on Foot Placement Control" and "From Non-Reactive to Reactive Walking in human Robots" use track energy to judge whether the disturbance received by the robot exceeds a threshold value when the position of a Foot-falling point is adjusted after the robot is disturbed, and calculate the distance that the swing leg needs to take off laterally according to the amount of the exceeding. Because the track energy formula does not contain a direction factor, the moving direction of the center of mass of the robot and the direction of the supporting feet relative to the center of mass are additionally considered in each step of walking.
In the paper, "walking robot balance restoration method based on orbit energy model", the author uses the orbit energy to predict whether the center of mass can cross the ZMP point, if oE >0, it indicates that the ZMP point can cross, and if oE <0, it cannot cross, so as to determine whether the robot center of mass motion diverges. Also, because oE is used, it is necessary to analyze the stability of the movement in stages, depending on the relative position of the centroid and the support feet during walking.
The disclosed data show that the disturbance evaluation method based on the track energy in the field of the humanoid robot has certain limitations, and although the disturbance magnitude of the robot can be represented, the method is not beneficial to judging the disturbance direction and predicting the motion state of the robot at the later moment.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a biped walking stability analysis method based on track mechanical energy, the invention is based on original track energy and is improved, the track mechanical energy is provided, the direction of the mass center movement speed and the direction of the mass center position relative to a ZMP are introduced by utilizing the track mechanical energy, and the method can be used for representing the magnitude and the direction of external disturbance.
The present invention achieves the above-described object by the following technical means.
A biped walking stability analysis method based on track mechanical energy comprises the following steps:
step 1, selecting a foot-setting point and a corresponding foot-setting period of the biped robot in the current step, and calculating the mechanical energy E of the track in the current step according to the expression of the mechanical energy of the track of the biped robotn；
Step 2, according to the next step of the biped robot foot-placing points and the corresponding foot-placing periods, the next step of the track mechanical energy E of the biped robot is calculated according to the expression of the track mechanical energyn+1；
Step 3, according to En、En+1And EtrConstructing a stability judgment condition, and if the stability judgment condition is met, showing that the walking of the biped robot converges to the target mechanical energy, and realizing gradual stability; if the formula is not satisfied, the current position P is determinednAnd its period TnOptimizing; etrTo achieve the target mechanical energy for periodic stability.
Further, the method for constructing the expression of the mechanical energy of the biped robot orbit comprises the following steps: improving original orbit energy and introducing a mass center state
Figure BDA0002426901260000021
And the direction of the centroid state, wherein the centroid state is determined by the current centroid position x and the centroid speed of the robot
Figure BDA0002426901260000022
A direction of the centroid state including a centroid velocity
Figure BDA0002426901260000023
Orientation and centroid position x relative to the ZMPThe direction of the solution is as follows; and further obtaining an expression of the mechanical energy of the biped robot track:
Figure BDA0002426901260000024
wherein, S () is a direction factor function;
Figure BDA0002426901260000025
external disturbance comprises the sum of kinetic energy provided by the linear inverted pendulum to the robot; p is a radical ofdIs the position of the ZMP and the position of the ZMP,
Figure BDA0002426901260000026
representing the potential energy stored by the linear inverted pendulum; w is the inverted pendulum constant.
Further, the mechanical energy E of the track at the current step is calculatednThe method comprises the following steps:
step 1.1, from the ZMP position p of the current stepnAnd its period TnThe state of the mass center at the moment is obtained
Figure BDA0002426901260000027
Step 1.2, state of mass center
Figure BDA0002426901260000028
The expression of the mechanical energy of the track of the biped robot is brought in, and the mechanical energy E of the track of the current step is calculatedn；
Further, the next orbital mechanical energy E is calculatedn+1The method comprises the following steps:
step 2.1, collecting the mass center state of the next step
Figure BDA0002426901260000029
Figure BDA00024269012600000210
Figure BDA00024269012600000211
Wherein A isnAnd BnIs the coefficient of the time function of the state of the mass center of the linear inverted pendulum, Tn、PnThe period and the ZMP position of the nth step are respectively; from this it can be deduced
Figure BDA0002426901260000031
Centroid state expression of (1):
Figure BDA0002426901260000032
step 2.2, the mass center state of the next step
Figure BDA0002426901260000033
The expression of the mechanical energy of the track of the biped robot is brought in, and the mechanical energy E of the track of the next step is obtained through calculationn+1。
Further, the stability determination condition is:
Figure BDA0002426901260000034
and n is the nth step of the robot.
Has the advantages that:
1. the mechanical energy of the biped robot track constructed by the invention is equivalent to a positive feedback spring system by using a linear inverted pendulum system, and further can describe the current energy of the robot in the form of kinetic energy and elastic potential energy. Compared with the traditional track energy concept, the method can describe the disturbance magnitude and indicate the disturbance direction, and the process of judging the direction in time division periods when the robot is controlled is omitted;
2. the invention can adjust the stability of the biped robot by using an optimization algorithm, takes the convergence of the mechanical energy of the track at the end moment of each walking cycle to a target value as the condition of stable walking of the robot, and optimizes the walking cycle and the stride length.
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Fig. 1 is a flow chart of the biped walking stability analysis method based on the mechanical energy of the track.
Detailed Description
The invention will be further described with reference to the following figures and specific examples, but the scope of the invention is not limited thereto.
In order to realize the biped walking stability analysis method based on the mechanical energy of the track, firstly, the invention provides the mechanical energy of the track, and particularly, the mass center state is introduced by improving the original track energy
Figure BDA0002426901260000035
And the direction of the centroid state; the mass center state is formed by the current mass center position x and the mass center speed of the robot
Figure BDA0002426901260000039
The direction of the centroid state includes the centroid velocity
Figure BDA0002426901260000036
The orientation and centroid position x are relative to the orientation of the ZMP. And further obtaining an expression of the mechanical energy of the biped robot track:
Figure BDA0002426901260000037
wherein, S (×) is a direction factor function, S (x) is 1 when x>0, s (x) -1 when x<0, s (x) 0 when x is 0;
Figure BDA0002426901260000038
external disturbance comprises the sum of kinetic energy provided by the linear inverted pendulum to the robot; p is a radical ofdIs the position of the ZMP and the position of the ZMP,
Figure BDA0002426901260000041
representing the potential energy stored by the linear inverted pendulum; w is an inverted pendulum constant;
the mechanical energy of the biped robot track is derived from a linear inverted pendulum formula to obtain a mass center state, and the specific process is as follows:
according to the linear inverted pendulum formula:
Figure BDA0002426901260000042
equating a linear inverted pendulum to a spring system
Figure BDA0002426901260000043
Wherein m is the equivalent mass of the spring,
Figure BDA0002426901260000044
the acceleration of the mass center is shown, w is the inherent angular velocity of the linear inverted pendulum and is highly related to the mass center, p is the ZMP position, x is the position of the mass center of the robot, K is the elastic coefficient of the spring, and deltax is the equivalent spring length variation. In contrast to spring systems, linear inverted pendulum is a positive feedback system, i.e. the further x is from P, the potential energy P-x in the P-x direction is mw2(x-p)2The larger the/2. In linear inverted pendulum motion, a force in the horizontal direction acts on the centroid, so the orbital mechanical energy is not conserved during motion. The rail mechanical energy is positive in the positive direction along the x-axis of the right hand rule.
Describing the direction and magnitude of the disturbance of the linear inverted pendulum by using the mechanical energy of the rail, and setting the ZMP speed
Figure BDA0002426901260000045
Is 0. Let the centroid initial time mechanical energy be E0,
Figure BDA0002426901260000046
and is
Figure BDA0002426901260000047
After the robot is disturbed, the following three situations occur, respectively:
in the case of (1) the case,
Figure BDA0002426901260000048
the disturbance applies negative work to the robot, so that the mass center speed is reversed:
Figure BDA0002426901260000049
the negative work produced by the disturbance is:
Figure BDA00024269012600000410
in the case of (2) the case,
Figure BDA00024269012600000411
the mechanical energy variation of the track input by disturbance is as follows:
Figure BDA00024269012600000412
in the case of (3) the case,
Figure BDA00024269012600000413
the mechanical energy variation of the track is as follows:
Figure BDA00024269012600000414
in the case of (2), the positive kinetic energy and potential energy of the robot are counteracted to generate the kinetic energy in the negative direction, and the potential energy is changed from providing the positive acceleration to providing the negative acceleration. Therefore, suppose the centroid velocity in both cases (1) and (2)
Figure BDA0002426901260000051
Similarly, the variation of the mechanical energy of the rail in the case (2) is larger than that in the case (1). If the potential energy of the (2) th case and the (3) th case are equal, the potential energy is negative, because the centroid speed of the (3) th case is the same as the direction of the initial moment, and the change amount of the track mechanical energy of the (2) th case is larger than that of the (3) th case.
Take the movement in the left and right directions during the walking process of the robot as an example. If only the mechanical energy of the track at the end time of each period is considered, the mechanical energy of the track during the period switching converges to an ideal value, and the periodic stability of the biped walking can be ensured. Therefore, the walking stability of the biped robot can be analyzed by using the mechanical energy of the biped robot track.
The invention discloses a biped walking stability analysis method based on track mechanical energy, which comprises the following specific processes:
step 1, ZMP position [ p ] from N future steps1,p2,p3...pN]And corresponding period [ T ]1,T2,T3...TN]The feet-falling point (namely ZMP position) of the biped robot of the current step and the corresponding feet-falling period are selected, and the mechanical energy E of the orbit of the current step is calculatedn(ii) a The specific process is as follows:
step 1.1, from the ZMP position P of the current stepnAnd its period TnThe state of the mass center at the moment is obtained
Figure BDA0002426901260000052
Step 1.2, state of mass center
Figure BDA0002426901260000053
The mechanical energy E of the track of the current step is obtained by calculation in the formula (1)n；
Step 2, calculating the next track mechanical energy E according to the next step of the foot-falling points and the corresponding foot-falling periods of the biped robotn+1(ii) a The specific process is as follows:
step 2.1, collecting the mass center state of the next step
Figure BDA0002426901260000054
Figure BDA0002426901260000055
Wherein A isnAnd BnIs the coefficient of the time function of the state of the mass center of the linear inverted pendulum, Tn、pnAre respectively the firstThe period of n steps and the ZMP position;
Figure BDA0002426901260000056
from this it can be deduced
Figure BDA0002426901260000057
Centroid state expression of (1):
Figure BDA0002426901260000058
step 2.2, the mass center state of the next step
Figure BDA0002426901260000059
Calculating to obtain the next track mechanical energy E by the formula (1)n+1。
Step 3, according to the stable judgment condition:
Figure BDA0002426901260000061
if En、En+1And EtrIf the above formula is satisfied, the walking of the biped robot is converged to the target mechanical energy, and gradual stabilization is realized; if the formula is not satisfied, the current position P is determinednAnd its period TnOptimization, i.e. of the current position PnAnd its period TnAdjusting to meet the stable judgment condition again; wherein E istrTo achieve the target mechanical energy for periodic stability.
The invention uses the non-linear optimization method such as particle swarm or genetic algorithm to carry out optimization on the current position PnAnd its period TnOptimizing according to the optimized position Pn' and its period Tn' recalculating orbital mechanical energy of current position En', so that it satisfies the stability determination condition.
The present invention is not limited to the above-described embodiments, and any obvious improvements, substitutions or modifications can be made by those skilled in the art without departing from the spirit of the present invention.

Claims (4)

1. A biped walking stability analysis method based on track mechanical energy is characterized by comprising the following steps:
step 1, selecting a foot-setting point and a corresponding foot-setting period of the biped robot in the current step, and calculating the mechanical energy E of the track in the current step according to the expression of the mechanical energy of the track of the biped robotn；
Step 2, according to the next step of the biped robot foot-placing points and the corresponding foot-placing periods, the next step of the track mechanical energy E of the biped robot is calculated according to the expression of the track mechanical energyn+1；
Step 3, according to En、En+1And EtrConstructing a stability judgment condition, and if the stability judgment condition is met, showing that the walking of the biped robot converges to the target mechanical energy, and realizing gradual stability; if the formula is not satisfied, the current position P is determinednAnd its period TnOptimizing; etrThe target mechanical energy for realizing periodic stable walking;
the method for constructing the expression of the mechanical energy of the biped robot orbit comprises the following steps: improving original orbit energy and introducing a mass center state
Figure FDA0003216933470000011
And the direction of the centroid state, wherein the centroid state is determined by the current centroid position x and the centroid speed of the robot
Figure FDA0003216933470000012
A direction of the centroid state including a centroid velocity
Figure FDA0003216933470000013
The direction and the direction of the centroid position x relative to the zero moment point ZMP; thereby obtaining the biped robot railExpression for mechanical energy:
Figure FDA0003216933470000014
wherein, S () is a direction factor function;
Figure FDA0003216933470000015
external disturbance comprises the sum of kinetic energy provided by the linear inverted pendulum to the robot; p is a radical ofdIs the zero moment point ZMP position and,
Figure FDA0003216933470000016
representing the potential energy stored by the linear inverted pendulum; w is the inverted pendulum constant.
2. The biped walking stability analysis method based on mechanical energy of track according to claim 1, characterized in that the mechanical energy of track E of the current step is calculatednThe method comprises the following steps:
step 1.1, from the zero moment point ZMP position p of the current stepnAnd its period TnThe state of the mass center at the moment is obtained
Figure FDA0003216933470000017
Step 1.2, state of mass center
Figure FDA0003216933470000018
The expression of the mechanical energy of the track of the biped robot is brought in, and the mechanical energy E of the track of the current step is calculatedn。
3. The biped walking stability analysis method based on mechanical energy of rail according to claim 1, wherein the mechanical energy E of rail in the next step is calculatedn+1The method comprises the following steps:
step 2.1, collecting the mass center state of the next step
Figure FDA0003216933470000019
Figure FDA00032169334700000110
Figure FDA00032169334700000111
Wherein A isnAnd BnIs the coefficient of the time function of the state of the mass center of the linear inverted pendulum, Tn、PnThe period and the ZMP position of the nth step are respectively; from this it derives
Figure FDA0003216933470000021
Centroid state expression of (1):
Figure FDA0003216933470000022
step 2.2, the mass center state of the next step
Figure FDA0003216933470000023
The expression of the mechanical energy of the track of the biped robot is brought in, and the mechanical energy E of the track of the next step is obtained through calculationn+1。
4. The biped walking stability analysis method based on mechanical energy of rail according to claim 1, 2 or 3, wherein the stability determination condition is:
Figure FDA0003216933470000024
and n is the nth step of the robot.
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