CN114137998B - Biped robot balance controller based on quick ankle adjustment - Google Patents

Biped robot balance controller based on quick ankle adjustment Download PDF

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CN114137998B
CN114137998B CN202111461183.3A CN202111461183A CN114137998B CN 114137998 B CN114137998 B CN 114137998B CN 202111461183 A CN202111461183 A CN 202111461183A CN 114137998 B CN114137998 B CN 114137998B
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CN114137998A (en
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黄强
董宸呈
余张国
陈学超
石青
陈焕钟
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Beijing Institute of Technology BIT
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Abstract

The invention provides a balance controller of a biped robot based on rapid ankle adjustment, which comprises a mass center controller, a state discriminator, a zero moment point tracker, a temporary stable state controller and a force/moment tracker, wherein the mass center controller is connected with the state discriminator; the centroid controller calculates the position of an expected zero moment point according to the position and speed feedback of the robot centroid; the state discriminator judges the state of the expected zero moment point: when the expected zero moment point position is in the stable domain, the zero moment point tracker calculates the expected contact force/moment of the feet according to the actual zero moment point position and the expected zero moment point position, and then the expected contact force/moment is tracked by using the force/moment tracker; when the position of the expected zero moment point is in a critical stable region, the temporary stable state controller pulls the expected zero moment point back to the stable region; and triggering the foot-falling point control when the position of the expected zero moment point is in the divergent domain. The invention can make the robot realize rapid balance response and realize stable motion.

Description

Biped robot balance controller based on quick ankle adjustment
Technical Field
The invention belongs to the technical field, and particularly relates to a balance controller of a biped robot based on rapid ankle adjustment.
Background
When the robot performs regular walking, running and other movements, the contact force and the contact moment of the feet and the ground determine the motion state of the robot. Therefore, the balance control of the robot can be realized by the control of the foot contact force and the contact moment, and the balance control can be divided into upper-layer control and lower-layer control; according to the attitude deviation of the robot, the upper layer controls to output expected contact force and contact torque, and the lower layer controls to realize the following of the expected force and the expected torque.
The upper-layer control of the existing method belongs to feedback control of a linear system, the output quantity is a continuous value, the method is effective in dealing with general disturbance, but the regulation capability is limited in dealing with sudden large disturbance such as large external thrust or unknown ground protrusion.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a biped robot balance controller based on rapid ankle adjustment, so that the robot can realize rapid balance response and realize stable motion.
The present invention achieves the above-described object by the following technical means.
Biped robot balance controller based on quick ankle regulation includes:
the mass center controller is used for calculating the position of the expected zero moment point according to the position and the speed feedback of the mass center of the robot;
the state discriminator is used for judging the state of the expected zero moment point, triggering the zero moment point tracker when the position of the expected zero moment point is in a stable domain, triggering the temporary stable state controller when the position of the expected zero moment point is in a critical stable domain, and triggering the foot-falling point control when the position of the expected zero moment point is in a divergent domain;
the zero moment point tracker calculates the expected contact force/moment of the feet according to the actual zero moment point position and the expected zero moment point position;
the temporary stable state controller controls the expected zero moment point at the edge of the support domain, so that the foot tilting action is generated through the force/moment tracker, and the state is quickly pulled back to the stable domain;
the control rate of the temporary stability state controller is as follows:
Figure BDA0003388781030000011
wherein:
Figure BDA0003388781030000012
the position of a zero moment point is expected in the x direction of the humanoid robot,
Figure BDA0003388781030000013
to imitate a humanThe robot plans the zero moment point position in the y direction, geo x For a humanoid robot, the geometrical parameters of the x-direction support domain, geo y For the geometrical parameters of the y-direction support domain of the humanoid robot,
Figure BDA0003388781030000021
is the actual mass center position of the humanoid robot in the x direction,
Figure BDA0003388781030000022
for the actual barycenter position of humanoid robot y direction, x direction and y direction belong to humanoid robot horizontal plane coordinate system, and:
Figure BDA0003388781030000023
Figure BDA0003388781030000024
wherein: parameter(s)
Figure BDA0003388781030000025
g is gravitational acceleration, z c Is the height of the centroid of the robot, geo is the geometrical parameter of the supporting domain of the robot, x is the centroid position of the robot,
Figure BDA0003388781030000026
is the robot centroid velocity.
In the above technical solution, the temporary stable state controller considers time optimal control:
Figure BDA0003388781030000027
Figure BDA0003388781030000028
u(t)∈U＝[-geo,geo]
Figure BDA0003388781030000029
t 0 ＝0
wherein: matrix array
Figure BDA00033887810300000210
Matrix array
Figure BDA00033887810300000211
geo is a geometric parameter of a robot support domain, t is control time, u (t) is a control quantity, and t 0 To control the starting time, t f To control the termination time, x (t) is the state quantity, U is the support domain, x 0 Is in an initial state.
In the above technical solution, the temporary stable state controller introduces a co-modal variable
Figure BDA00033887810300000212
Defining a Hamiltonian:
Figure BDA00033887810300000213
according to the coordination state condition:
Figure BDA00033887810300000214
obtaining by solution:
Figure BDA00033887810300000215
wherein: c. C 1 、c 2 Is a constant.
In the above technical solution, c 1 、c 2 The following conditions are satisfied:
①c 1 > 0 and c 2 ＞0：u＝geo
②c 1 < 0 and c 2 ＜0：u＝-geo
③c 1 > 0 and c 2 ＜0：
Figure BDA0003388781030000031
④c 1 < 0 and c 2 ＞0：
Figure BDA0003388781030000032
Wherein λ is 2 (t) time to traverse the horizontal axis
Figure BDA0003388781030000033
In the above technical solution, the expected zero moment point position is based on
Figure BDA0003388781030000034
And calculating to obtain the result, wherein,
Figure BDA0003388781030000035
is the desired position of the ZMP in the mold,
Figure BDA0003388781030000036
it is the planned position of the ZMP,
Figure BDA0003388781030000037
is the position of the actual center of mass,
Figure BDA0003388781030000038
is the position of the planned center of mass,
Figure BDA0003388781030000039
is the actual center of mass velocity and,
Figure BDA00033887810300000310
is the projected centroid velocity, k c And k v Respectively, position term and speed term feedback coefficients.
In the above technical solution, the stable region is: along a polygon formed by the two-foot supporting domain, straight lines which are parallel to all side lines of the supporting domain and have a distance delta are formed towards the inner side, and a region enclosed by the left straight line and the right straight line is a stable domain; the region outside the stable region and inside the two-foot support region is a critical stable region; the area outside the double-foot supporting area is a divergent area; where δ is the stability margin.
In the above technical solution, the force/moment tracker tracks an expected contact force/moment, specifically:
according to the distribution coefficient alpha of the two feet, the expected force and moment of the left foot and the right foot are obtained:
Figure BDA00033887810300000311
wherein:
Figure BDA00033887810300000312
in order to be the total desired force,
Figure BDA00033887810300000313
in order to be able to sum up the desired torque,
Figure BDA00033887810300000314
in order to expect the force for the right foot,
Figure BDA00033887810300000315
in order to expect the force for the left foot,
Figure BDA00033887810300000316
the moment is expected for the right foot,
Figure BDA00033887810300000317
the desired moment for the left foot;
the admittance controller is designed such that the robot bipedal force/moment tracks the desired contact force/moment.
The beneficial effects of the invention are as follows: the near steady state controller considers time optimal control, introduces a covariate, and the control rate output by the near steady state controller is used for calculating total expected torque, when the expected zero torque point position is in a critical stable domain, the near steady state controller is triggered, the near steady state controller controls the expected zero torque point at the edge of a support domain, so that the foot tilting action is generated through the force/torque tracker, and the state is quickly pulled back to the stable domain.
Drawings
FIG. 1 is a block diagram of a balancing controller for a rapid ankle adjustment-based biped robot according to the present invention;
FIG. 2 (a) is a schematic illustration of the present invention at a desired zero moment point at steady state;
FIG. 2 (b) is a schematic diagram of the desired zero moment point of the present invention in a critical steady state;
FIG. 2 (c) is a schematic view of the desired zero moment point of the present invention in a divergent state;
FIG. 3 (a) is a schematic representation of a desired ZMP of the present invention directly below the centroid position;
FIG. 3 (b) is a schematic representation of the expected ZMP within the support zone with less disturbance according to the present invention;
FIG. 3 (c) is a schematic representation of the expected ZMP at the edge of the support zone with a large perturbation according to the present invention;
FIG. 4 is a controlled state diagram of the robot under the control of the temporary steady state controller according to the present invention;
fig. 5 is a schematic diagram of calculation of left and right foot force/moment distribution of the humanoid robot.
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.
As shown in figure 1, the balance controller of the biped robot based on rapid ankle adjustment comprises a mass center controller, a state discriminator, a zero moment point tracker, a temporary stability state controller and a force/moment tracker.
(1) And (3) calculating to obtain the position of an expected Zero Moment Point (ZMP) by the mass center controller according to the position and speed feedback of the mass center of the robot:
Figure BDA0003388781030000041
wherein the content of the first and second substances,
Figure BDA0003388781030000042
is the desired position of the ZMP in the desired position,
Figure BDA0003388781030000043
it is the planned position of the ZMP,
Figure BDA0003388781030000044
is the position of the actual center of mass,
Figure BDA0003388781030000045
is the position of the planned center of mass,
Figure BDA0003388781030000046
is the actual center of mass velocity and,
Figure BDA0003388781030000047
is the projected centroid velocity, k c And k v Respectively a position term and a speed term feedback coefficient;
(2) The state discriminator judges the state of the expected zero moment point to determine the control mode of the trigger; the types of states are shown in fig. 2 (a), (b), and (c):
the stability domain is defined as: along a polygon formed by the two-foot supporting domain, a straight line which is parallel to each side line of the supporting domain and has a distance delta (stability margin) is made inwards, and finally, a region enclosed by the left straight line and the right straight line is a stable domain; the region outside the stable region and inside the two-foot support region is a critical stable region; the area outside the two-foot support area is a divergent area. As shown in fig. 2 (a), when the desired ZMP position is within the stable region (which is now a stable state), the zero-moment point tracker is triggered and the robot can easily remain stable; as shown in fig. 2 (b), when the desired ZMP position is in the critical stability domain (in this case, the critical stability state), the critical stability state controller is triggered to quickly pull the desired ZMP back into the stability domain; as shown in fig. 2 (c), when the desired ZMP position is in the divergent domain (now divergent state), the foot-drop control should be triggered, otherwise the robot will fall, where the foot-drop control is prior art and the present invention does not take into account.
When the robot is standing stably, the ZMP is expected to be directly below the centroid position, as shown in fig. 3 (a); when the robot is disturbed, the actual center of mass position of the robot deviates from the expected center of mass position, the desired ZMP is subjected to feedback adjustment, if the disturbance is small, the desired ZMP is in the support domain, and the foot of the robot can still well fit the ground, as shown in fig. 3 (b); if the perturbation is large, the ZMP is expected to be at the edge of the support field, and the robot foot will naturally generate a foot tilting motion under the control of the foot force/moment tracker, as shown in fig. 3 (c).
(3) The principle of the zero moment point tracker is as follows: the desired contact force/moment magnitude for the feet is calculated from the actual ZMP position and the desired ZMP position, and then the desired contact force/moment is tracked using a force/moment tracker. Wherein the actual ZMP position is measured and calculated by a six-dimensional force sensor mounted on the ankle of both feet and the desired ZMP position is calculated by a centroid controller.
(4) Controller for temporary stable state
Given a quantity of state of
Figure BDA0003388781030000051
Where x (t) is a function of the robot centroid position over time,
Figure BDA0003388781030000052
as a function of robot centroid velocity over time. The clinical steady state controller pulls the desired ZMP back into the steady domain quickly, so time-optimal control is considered:
Figure BDA0003388781030000053
wherein: matrix array
Figure BDA0003388781030000054
Matrix of
Figure BDA0003388781030000055
Parameter(s)
Figure BDA0003388781030000056
g is gravitational acceleration, z c Is the height of the centroid of the robot, geo is the geometrical parameter of the support domain of the robot, t is the control time, u (t) is the control quantity, t 0 To control the starting time, t f For control of the termination time, U is the support field, x 0 Is in an initial state;
introduction of covariates into a transient state controller
Figure BDA0003388781030000057
Defining a Hamiltonian:
Figure BDA0003388781030000058
according to the maximum value principle, obtaining the control rate of the temporary stability state controller:
Figure BDA0003388781030000061
according to the coordination state condition:
Figure BDA0003388781030000062
obtaining by solution:
Figure BDA0003388781030000063
according to constant c 1 、c 2 The positive or negative of (undetermined from the initial state) is known as λ 2 (t) there are four cases; the corresponding control law can be expressed as:
①c 1 > 0 and c 2 ＞0：u＝geo
②c 1 < 0 and c 2 ＜0：u＝-geo
③c 1 > 0 and c 2 ＜0：
Figure BDA0003388781030000064
④c 1 < 0 and c 2 ＞0：
Figure BDA0003388781030000065
Wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003388781030000066
T s is in the case of (3), (4), lambda 2 (t) time to cross the horizontal axis.
According to the four conditions, the control is switched once at most, and the controller is a typical bang-bang controller; under the control of the bang-bang controller, the controlled state of the robot is shown in fig. 4.
In fig. 4:
Figure BDA0003388781030000067
Figure BDA0003388781030000068
wherein: r is - 、r + Dividing the state plane into two parts, using R respectively - 、R + Is shown, wherein:
Figure BDA0003388781030000069
Figure BDA0003388781030000071
the control quantity u is the position of the zero moment point expected by the robot, and thus the control rate of the temporary stability state controller can be expressed as:
Figure BDA0003388781030000072
wherein:
Figure BDA0003388781030000073
the ZMP position is desired for the x-direction of the humanoid robot,
Figure BDA0003388781030000074
expected ZMP position, geo, for the y-direction of the humanoid robot x For a humanoid robot, the geometrical parameters of the x-direction support domain, geo y For the geometrical parameters of the y-direction support domain of the humanoid robot,
Figure BDA0003388781030000075
is the actual mass center position of the humanoid robot in the x direction,
Figure BDA0003388781030000076
the position of the actual mass center of the humanoid robot in the y direction is shown; wherein the x direction and the y direction belong to a horizontal plane coordinate system of the humanoid robot.
(5) Force/moment tracker
As shown in FIG. 5, the actual ZMP position is (x) z ,y z ) The position of the left ankle is (x) L ,y L ) The right ankle position is (x) R ,y R ) From the positions of these three points, two straight lines L are calculated 1 、L 2 Wherein L is 1 Two points of the left ankle and the right ankle, L 2 Past the actual ZMP and perpendicular to L 1 Is merged with (x) 0 ,y 0 )。
L 1 The equation of (a) is:
y＝ax+b
and:
Figure BDA0003388781030000077
L 2 the equation of (a) is:
Figure BDA0003388781030000078
and:
Figure BDA0003388781030000079
according to a straight line L 1 、L 2 Equation (c), calculating (x) 0 ,y 0 )：
Figure BDA00033887810300000710
Figure BDA00033887810300000711
Calculating the two-pin distribution coefficient alpha:
Figure BDA0003388781030000081
calculating the total expected force
Figure BDA0003388781030000082
Figure BDA0003388781030000083
Wherein M is the total mass of the robot, a z Acceleration of the robot centroid along the vertical direction;
calculating a total desired torque
Figure BDA0003388781030000084
Figure BDA0003388781030000085
Wherein:
Figure BDA0003388781030000086
to the desired ZMP positionVector and
Figure BDA0003388781030000087
Figure BDA0003388781030000088
is the actual ZMP position vector;
according to the distribution coefficients of the two feet, the expected force and moment of the left foot and the right foot are obtained:
Figure BDA0003388781030000089
in order for the robot's bipedal forces and moments to follow the desired forces and moments, the admittance controller is designed, denoted as:
Figure BDA00033887810300000810
wherein, the delta P is the ankle position regulating quantity,
Figure BDA00033887810300000811
adjustment of ankle posture, F rel For the actual force on the foot, τ rel Is the actual moment, k, experienced by the foot p,f 、k d,f 、k p,τ 、k d,τ Are feedback coefficient matrices.
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 (7)

1. Biped robot balance control ware based on quick ankle is adjusted, its characterized in that includes:
the mass center controller is used for calculating the position of the expected zero moment point according to the position and the speed feedback of the mass center of the robot;
the state discriminator judges the state of the expected zero moment point, triggers the zero moment point tracker when the position of the expected zero moment point is in a stable domain, triggers the temporary stable state controller when the position of the expected zero moment point is in a critical stable domain, and triggers the control of the foot falling point when the position of the expected zero moment point is in a divergent domain;
the zero moment point tracker calculates the expected contact force/moment of the double feet according to the position of the actual zero moment point and the position of the expected zero moment point;
the temporary stable state controller controls the expected zero moment point at the edge of the support domain, so that the force/moment tracker generates a foot raising action to quickly pull the state back into the stable domain;
the control rate of the temporary stability state controller is as follows:
Figure FDA0003388781020000011
wherein:
Figure FDA0003388781020000012
the position of a zero moment point is expected in the x direction of the humanoid robot,
Figure FDA0003388781020000013
planning the position of the zero moment point, geo, for the y-direction of the humanoid robot x For a humanoid robot, the geometrical parameters of the x-direction support domain, geo y For the geometrical parameters of the y-direction support domain of the humanoid robot,
Figure FDA0003388781020000014
is the actual mass center position of the humanoid robot in the x direction,
Figure FDA0003388781020000015
for the actual barycenter position of humanoid robot y direction, x direction and y direction belong to humanoid robot horizontal plane coordinate system, and:
Figure FDA0003388781020000016
Figure FDA0003388781020000017
wherein: parameter(s)
Figure FDA0003388781020000018
g is gravitational acceleration, z c Is the height of the centroid of the robot, geo is the geometrical parameter of the supporting domain of the robot, x is the centroid position of the robot,
Figure FDA0003388781020000019
is the robot centroid velocity.
2. The rapid ankle adjustment based biped robot balancing controller of claim 1, wherein the critical stability state controller considers time optimal control:
Figure FDA0003388781020000021
Figure FDA0003388781020000022
u(t)∈U＝[-geo,geo]
Figure FDA0003388781020000023
t 0 ＝0
wherein: matrix array
Figure FDA0003388781020000024
Matrix array
Figure FDA0003388781020000025
geo is a geometric parameter of a robot support domain, t is control time, u (t) is a control quantity, and t 0 To control the starting time, t f To control the termination time, x (t) is the state quantity, U is the support field, x 0 Is in an initial state.
3. The rapid ankle adjustment based biped robot balance controller of claim 2 wherein the critical steady state controller introduces a covariate variable
Figure FDA0003388781020000026
Defining a Hamiltonian:
Figure FDA0003388781020000027
according to the coordination state condition:
Figure FDA0003388781020000028
obtaining by solution:
Figure FDA0003388781020000029
wherein: c. C 1 、c 2 Is a constant.
4. The rapid ankle adjustment based biped robot balance controller of claim 3 wherein c is 1 、c 2 The following conditions are satisfied:
①c 1 > 0 and c 2 ＞0：u＝geo
②c 1 < 0 and c 2 ＜0：u＝-geo
③c 1 > 0 and c 2 ＜0：
Figure FDA00033887810200000210
④c 1 < 0 and c 2 ＞0：
Figure FDA00033887810200000211
Wherein λ is 2 (t) time to traverse the horizontal axis
Figure FDA0003388781020000031
5. The rapid ankle adjustment based biped robot balance controller of claim 1 wherein the desired zero moment point position is based on
Figure FDA0003388781020000032
And calculating to obtain the result, wherein,
Figure FDA0003388781020000033
is the desired position of the ZMP in the desired position,
Figure FDA0003388781020000034
it is the planned position of the ZMP,
Figure FDA0003388781020000035
is the position of the actual center of mass,
Figure FDA0003388781020000036
is the position of the planned center of mass,
Figure FDA0003388781020000037
is the actual center of mass velocity and,
Figure FDA0003388781020000038
is the projected centroid velocity, k c And k v Respectively a position term and a speed term feedback coefficient.
6. The rapid ankle adjustment based biped robot balance controller according to claim 1 wherein the stability domain is: along a polygon formed by the two-foot supporting domain, straight lines which are parallel to all side lines of the supporting domain and have a distance delta are formed towards the inner side, and a region enclosed by the left straight line and the right straight line is a stable domain; the region outside the stable region and inside the two-foot support region is a critical stable region; the area outside the double-foot supporting area is a divergent area; where δ is the stability margin.
7. The rapid ankle adjustment based biped robot balance controller according to claim 1, wherein the force/torque tracker tracks a desired contact force/torque, in particular:
according to the distribution coefficient alpha of the two feet, the expected force and moment of the left foot and the right foot are obtained:
Figure FDA0003388781020000039
wherein:
Figure FDA00033887810200000310
in order to be the total desired force,
Figure FDA00033887810200000311
in order to obtain the total desired torque,
Figure FDA00033887810200000312
in order to expect the force for the right foot,
Figure FDA00033887810200000313
in order to expect the force for the left foot,
Figure FDA00033887810200000314
the moment is expected for the right foot,
Figure FDA00033887810200000315
the desired moment for the left foot;
the admittance controller is designed such that the robot bipedal force/moment tracks the desired contact force/moment.
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