CN104252173A - Walking control method of biped walking robot - Google Patents

Abstract

The invention discloses a walking control method of a biped walking robot, which comprises the following steps: step 1 setting the walking parameters of the biped walking robot; step 2 calculating the center of mass of the biped walking robot and the trajectory of the reference ZMP; Learn to calculate the walking pattern of the biped walking robot; Step 4 calculates the ground friction coefficient required for the biped walking robot to walk without slipping, and judge whether the biped walking robot is slipping; Step 5 If the biped walking robot slips, adjust the Step 2, Step 3 and Step 4 above are repeated for the walking parameters of the walking robot. The walking control method of the biped walking robot of the present invention can judge whether the biped walking robot will slip on the ground with low friction coefficient, and at the same time, by adjusting the walking parameters of the walking mode of the biped walking robot, the minimum ground friction coefficient required for the walking mode can be reduced , to improve the walking ability of the biped walking robot on the ground with low friction coefficient.

Description

Walking Control Method of Biped Walking Robot

technical field

The invention relates to a control method of a robot, in particular to a walking control method of a robot.

Background technique

At present, the stability control methods of biped walking robots all use the ZMP stability criterion. ZMP refers to the action point where the horizontal component of the torque of the ground force is zero. The condition is that the ZMP is always located in the supporting polygon, which refers to the convex set of the contact area between the foot of the biped robot and the ground. The intuitive physical meaning of bipedal walking that satisfies the ZMP stability criterion means that the bipedal robot will not fall over during walking. The walking control of the existing biped robot is based on the ZMP stability criterion to plan the motion of each joint of the biped walking robot, so that the ZMP of the biped walking robot is always located within the supporting polygon during the walking process.

However, the existing ZMP stability criterion has certain limitations. Kajita, a well-known biped walking robot expert from AIST in Japan, once pointed out that there are three situations where ZMP cannot be applied, one of which is the slippage between the soles of the robot's feet and the ground. In fact, the ZMP stability criterion is based on the premise of ignoring the ground friction, that is, it is considered that the friction between the feet of the biped robot and the ground is large enough, and there is no possibility of slipping between the feet of the biped walking robot and the ground. . This premise is feasible in an ideal environment. Of course, the walking motion of the biped walking robot based on the ZMP stability criterion planning meets the stability requirements of walking. However, for the case where the friction between the feet of the biped walking robot and the ground is small, the walking motion of the biped walking robot based on the ZMP stability criterion planning can only ensure that the robot will not fall during the walking process, but cannot Make sure the robot does not slip.

Contents of the invention

The purpose of the present invention is to provide a walking control method for a biped walking robot, which can determine whether the biped walking robot will slip on the ground with a low friction coefficient, and at the same time, by adjusting the walking parameters of the walking mode of the biped walking robot, reduce the time required for the walking mode. The required minimum ground friction coefficient can improve the walking ability of the biped walking robot on the ground with low friction coefficient.

In order to achieve the above object, the technical scheme adopted in the present invention is as follows:

A walking control method of a biped walking robot, comprising the following steps: Step 1: setting the walking parameters of the biped walking robot; Step 2: calculating the center of mass of the biped walking robot and the trajectory of the reference ZMP; Step 3: Calculate the walking pattern of the biped walking robot by inverse kinematics; step 4: calculate the ground friction coefficient required for the biped walking robot to walk without slipping, and judge whether the biped walking robot is slipping; step 5: If the biped walking robot slips while walking, adjust the walking parameters of the biped walking robot, and repeat the above steps 2, 3 and 4.

Further, in step 4, the ground friction coefficient required for the biped walking robot to walk without slipping is calculated according to the horizontal force component and the vertical force component of the force between the supporting foot of the biped walking robot and the ground.

Further, the ground friction coefficient required for the biped walking robot to walk without slipping calculated in step 4 is compared with the actual ground friction coefficient, and if the required ground friction coefficient is less than the actual ground friction coefficient, Then described biped walking robot does not skid while walking, otherwise then skids.

Further, in step 4, if the biped walking robot walks without slipping, the planned walking pattern of the biped walking robot meets the ZMP stability requirement.

Further, the generation of the walking pattern of the biped walking robot in step 3 is based on the table-cart as the walking model of the biped walking robot.

Further, the generation of the walking pattern of the biped walking robot in step 3 takes the differential of the acceleration of the center of mass as the system input.

Further, the generation of the walking pattern of the biped walking robot in step three is to track and control the reference ZMP trajectory through the method of minimizing the evaluation function, and the parameters in the evaluation function are used to set the walking parameters.

Further, the parameters in the evaluation function are used to set the walking speed and step length of the walking parameters.

Further, the walking pattern of the biped walking robot generated in step 3 satisfies the ZMP stability criterion of biped walking, and is combined with the slipping stability criterion.

Compared with the prior art, the walking control method of the biped walking robot of the present invention can judge whether the biped walking robot will slip on the ground with low friction coefficient, and at the same time reduce the walking mode by adjusting the walking parameters of the walking mode of the biped walking robot. The required minimum ground friction coefficient improves the walking ability of the biped walking robot on the ground with low friction coefficient.

Description of drawings

Fig. 1 is the schematic diagram of the biped walking robot of the walking control method of the biped walking robot of the present invention;

Fig. 2 is the schematic diagram of the table-car model of the walking control method of biped walking robot of the present invention;

FIG. 3 is a schematic flowchart of the walking control method of the biped walking robot of the present invention.

Detailed ways

The walking control method of the biped walking robot of the present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

The present invention provides a method for a bipedal walking robot 1 to walk on the ground with low friction coefficient. By designing a walking pattern generation method with adjustable walking speed and step length, and in combination with the stability criterion considering the sliding friction constraint, the adjustment The parameter of the walking mode is to set the walking mode suitable for the friction coefficient of the ground, and improve the walking control method of the biped walking robot 1 .

Please refer to Fig. 1, the determination method of the walking stability of the biped walking robot 1 when considering the sliding friction constraint, as follows:

When the bipedal walking robot 1 walks on the ground, the force between the right foot 11R (a supporting foot) and the ground is f, its horizontal component is f _t , its vertical component is f _z , and the friction coefficient of the ground is μ , no sliding between the right foot 11R and the ground needs to meet the following conditions

f _t <μf _z (1)

For a known walking pattern, the momentum of the biped walking robot 1 can be expressed as

$\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; c</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Among them, m _i and c _i are the mass and centroid position of each connecting rod respectively.

The horizontal component f _t and the vertical component f _z of the ground force f can be obtained by differentiating the formula (2) as

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span>\sqrt{{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}}_{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

(3)

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; =</span>{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; Mg</span>}$

Where M is the overall weight of the biped walking robot 1, and g is the acceleration due to gravity.

According to formula (3), it can be obtained that the ground friction coefficient for the biped walking robot 1 to walk without sliding is

${\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; nec</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

When μ _nec ≤ μ, the biped walking robot 1 will not slide on the ground when walking, and the ZMP stability criterion is met, that is, when the biped walking robot 1 is walking, the ground force f The point where the horizontal component of the moment is zero is within the supporting polygon formed by the supporting feet of the biped walking robot 1 and the ground, and the biped walking robot 1 will not topple over, and the strict sense of the biped walking robot 1 can be realized. Walking on is stable. This method can be used as an extension of the existing ZMP stability criterion to make a more stringent judgment on the stability of the biped walking robot 1 , so that the application range of the biped walking robot 1 is wider.

The present invention proposes a walking pattern generation method that can adjust walking speed and step length based on the above-mentioned new stability criterion, so as to adapt to the walking situation of the biped walking robot 1 when the ground friction coefficient is small, as follows:

Please refer to Fig. 1 and Fig. 2, when described biped walking robot 1 walks on the ground of low friction coefficient, can adopt classical table-cart model representation:

${\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}{\mathrm{<span\; class="notranslate">\; g</span>}}\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}$

(5)

${\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}{\mathrm{<span\; class="notranslate">\; g</span>}}\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}$

Where x and y represent the projection of the center of mass of the biped walking robot 1 on the horizontal ground, and p _x and p _y represent the position of the ZMP.

Assume that the differential of the acceleration of the center of mass of the biped walking robot 1 is the input variable of the system, namely

${\mathrm{<span\; class="notranslate">\; in</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\stackrel{<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}$

(6)

${\mathrm{<span\; class="notranslate">\; in</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\stackrel{<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}$

but

$\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; x</span>}\\ \stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}\\ \stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; x</span>}\\ \stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}\\ \stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}\end{array}\right]<span\; class="notranslate">\; +</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}$

$\frac{\mathrm{<span\; class="notranslate">\; d</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; the\; y</span>}\\ \stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}\\ \stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; the\; y</span>}\\ \stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}\\ \stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}\end{array}\right]<span\; class="notranslate">\; +</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

Meanwhile, formula (5) can be expressed as

${\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}{\mathrm{<span\; class="notranslate">\; g</span>}}\end{array}\right]\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; x</span>}\\ \stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}\\ \stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}\end{array}\right]$

(8)

${\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}{\mathrm{<span\; class="notranslate">\; g</span>}}\end{array}\right]\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; the\; y</span>}\\ \stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}\\ \stackrel{<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}\end{array}\right]$

Combining formula (7) and formula (8), it can be discretized to get

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; Ax</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; bu</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}\\ {\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; Ay</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; bu</span>}}_{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}\\ {\mathrm{<span\; class="notranslate">\; p</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; cx</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}\\ {\mathrm{<span\; class="notranslate">\; p</span>}}_{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; cy</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

in

${\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>{\left[\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k\&Delta;t</span>}<span\; class="notranslate">\; )</span>& \stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k\&Delta;t</span>}<span\; class="notranslate">\; )</span>& \stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k\&Delta;t</span>}<span\; class="notranslate">\; )</span>\end{array}\right]}^{\mathrm{<span\; class="notranslate">\; T</span>}}$

${\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>{\left[\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k\&Delta;t</span>}<span\; class="notranslate">\; )</span>& \stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k\&Delta;t</span>}<span\; class="notranslate">\; )</span>& \stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k\&Delta;t</span>}<span\; class="notranslate">\; )</span>\end{array}\right]}^{\mathrm{<span\; class="notranslate">\; T</span>}}$

u _xk =u _x (kΔt)

u _yk =u _y (kΔt)

p _xk =p _x (kΔt)

p _yk =p _y (kΔt)

$\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; \&Delta;t</span>}& {\mathrm{<span\; class="notranslate">\; \&Delta;t</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; \&Delta;t</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]$

$\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&Delta;t</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 6</span>}\\ {\mathrm{<span\; class="notranslate">\; \&Delta;t</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; g</span>}\end{array}\right]$

In order to make the planned p _xk and p _yk track the reference ZMP as much as possible and Here, the tracking control is realized by minimizing the evaluation function, and the evaluation function is as follows

$\mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{<span\; class="notranslate">\; \&infin;</span>}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}^{\mathrm{<span\; class="notranslate">\; ref</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{<span\; class="notranslate">\; \&infin;</span>}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}^{\mathrm{<span\; class="notranslate">\; ref</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$

In the formula, Q _x , Q _y , R _x , R _y are positive weighting coefficients, where

${\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}{\mathrm{<span\; class="notranslate">\; Q</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; Q</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; Q</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}\end{array}\right]<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}{\mathrm{<span\; class="notranslate">\; Q</span>}}_{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; Q</span>}}_{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; Q</span>}}_{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span>$

in and is a coefficient related to walking speed and step length, that is, by setting different and The value can adjust the walking speed and step length. At this time, the input of the system can be obtained according to the preview control theory

${\mathrm{<span\; class="notranslate">\; u</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; +</span>\left[\begin{array}{cccc}{\mathrm{<span\; class="notranslate">\; f</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}& {\mathrm{<span\; class="notranslate">\; f</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}& <span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span>& {\mathrm{<span\; class="notranslate">\; f</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}}}\end{array}\right]\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; p</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; ref</span>}}\\ {\mathrm{<span\; class="notranslate">\; p</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; ref</span>}}\\ <span\; class="notranslate">\; \&CenterDot;</span>\\ <span\; class="notranslate">\; \&CenterDot;</span>\\ <span\; class="notranslate">\; \&CenterDot;</span>\\ {\mathrm{<span\; class="notranslate">\; p</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; N</span>}}}^{\mathrm{<span\; class="notranslate">\; ref</span>}}\end{array}\right]$

(13)

${\mathrm{<span\; class="notranslate">\; u</span>}}_{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Ky</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; +</span>\left[\begin{array}{cccc}{\mathrm{<span\; class="notranslate">\; f</span>}}_{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}& {\mathrm{<span\; class="notranslate">\; f</span>}}_{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}& <span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span>& {\mathrm{<span\; class="notranslate">\; f</span>}}_{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}}}\end{array}\right]\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; p</span>}}_{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; ref</span>}}\\ {\mathrm{<span\; class="notranslate">\; p</span>}}_{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; ref</span>}}\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ <span\; class="notranslate">\; \&Center\; Dot;</span>\\ {\mathrm{<span\; class="notranslate">\; p</span>}}_{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; N</span>}}}^{\mathrm{<span\; class="notranslate">\; ref</span>}}\end{array}\right]$

In the formula

K=(R+b ^T Pb) ^-1 b ^T P A (14)

f _i =(R+b ^T Pb) ^-1 b ^T (A-bK) ^T×(i-1) c ^T Q

where the matrix P is the solution of the following equation

P=A ^T PA+c ^T Qc-A ^T Pb(R+b ^T Pb) ^-1 b ^T PA (15)

So far, the walking mode of the biped walking robot 1 can be calculated, that is, the trajectory of the center of mass of the biped walking robot 1 and the trajectory of the reference ZMP, so that the coordinate system Σ0 established on the waist of the biped walking robot 1 is The base coordinate system takes ∑w as the world coordinate system, as shown in Figure 1. The walking mode (p ₀ , R ₀ , θ) of the biped walking robot 1 can be calculated through inverse kinematics, where (p ₀ , R ₀ ) is the position of the base frame Σ0 in the world coordinate system Σw position and posture, θ is the angle of each joint of the biped walking robot 1 .

In summary, please refer to Fig. 1 and Fig. 3, the walking control method of the biped walking robot 1 disclosed by the present invention includes the following steps:

Step 1 S1: Set the correlation coefficient of the walking parameters of the biped walking robot 1 described in formula (11) and formula (12).

Step 2 S3: Calculate the center of mass of the biped walking robot 1 and the trajectory of the reference ZMP according to formula (13).

Step 3 S5: Taking Σ0 as the base coordinate system and Σw as the world coordinate system, calculate the walking pattern (p ₀ , R ₀ , θ) of the biped walking robot 1 through inverse kinematics.

The generation of described walking pattern is to be the walking model of described biped walking robot 1 with desk-cart, take the differential of the acceleration of center of mass as system input, track and control the reference ZMP track by the method for minimizing the evaluation function, in the evaluation function Parameters are used to set walking parameters such as walking speed and step length. The generated walking pattern of the biped walking robot 1 satisfies the ZMP stability criterion of biped walking, and is combined with the slipping stability criterion to form a stricter walking stability of the biped walking robot 1 The criterion broadens the walking motion of the biped walking robot 1 in a non-ideal environment.

Step 4 S7: Calculate the ground friction coefficient μ _nec required for the biped walking robot 1 to walk without slipping according to formula (2), formula (4) and formula (7), and judge whether the biped walking robot 1 is walking slippery .

Whether the biped walking robot 1 is slipping on the ground is calculated according to the horizontal force component f _t and the vertical force component f _z of the force f between the supporting feet of the biped walking machine 1 and the ground. The minimum ground friction coefficient μ _nec required for the robot 1 to walk without slipping is compared with the actual ground friction coefficient μ. If the required minimum ground friction coefficient μ _nec is smaller than the ground friction coefficient μ, the bipedal walking robot 1 does not Skid, and vice versa. If the biped walking robot 1 walks without slipping, the planned walking pattern of the biped walking robot 1 meets the ZMP stability requirement.

Step 5 S9: If the biped walking robot 1 slips while walking, adjust the walking parameters of the biped walking robot 1, and repeat the above steps 2, 3 and 4.

The walking control method of the biped walking robot 1 of the present invention can judge whether the biped walking robot 1 will slip on the ground with low friction coefficient, and at the same time, by adjusting the walking parameters of the biped walking robot 1 walking mode, reduce The minimum ground friction coefficient required by the walking mode improves the walking ability of the biped walking robot 1 on ground with a low friction coefficient.

The preferred specific embodiments of the present invention have been described in detail above, and it should be understood that those skilled in the art can make many modifications and changes according to the concept of the present invention without creative work. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning or limited experiments on the basis of the prior art should be within the scope of protection defined by the claims.

Claims (9)

1. a walking control method of a biped walking robot, is characterized in that, comprises the following steps: Step 1: setting the walking parameters of the biped walking robot; Step 2: Calculate the center of mass of the biped walking robot and the trajectory of the reference ZMP; Step 3: Calculate the walking pattern of the biped walking robot through inverse kinematics; Step 4: Calculate the ground friction coefficient required for the biped walking robot to walk without slipping, and judge whether the biped walking robot is slipping; Step 5: If the biped walking robot slips while walking, adjust the walking parameters of the biped walking robot, and repeat the above steps 2, 3 and 4. 2. the walking control method of biped walking robot as claimed in claim 1, is characterized in that: in step 4, according to the horizontal force component and the vertical force component of force between described biped walking robot support pin and ground, calculate The ground friction coefficient required for the biped walking robot to walk without slipping. 3. the walking control method of biped walking robot as claimed in claim 2, is characterized in that: described biped walking robot that calculates in step 4 does not slip required described ground friction coefficient and actual ground friction coefficient In comparison, if the required ground friction coefficient is smaller than the actual ground friction coefficient, the biped walking robot will not slip while walking, otherwise it will slip. 4. the walking control method of biped walking robot as claimed in claim 1, is characterized in that: if described biped walking robot walks without skidding in step 4, then the described walking of described biped walking robot of planning Mode meets ZMP stability requirements. 5. the walking control method of biped walking robot as claimed in claim 1, is characterized in that: the generation of described walking pattern of described biped walking robot in step 3 is that the walking of biped walking robot is that table-dolly is Model. 6. The walking control method of the biped walking robot according to claim 5, characterized in that: the generation of the walking pattern of the biped walking robot in step 3 takes the differential of the acceleration of the center of mass as the system input. 7. the walking control method of biped walking robot as claimed in claim 6, is characterized in that: the generation of the described walking pattern of described biped walking robot in step 3 is the method tracking control reference ZMP by evaluation function minimization Trajectories, parameters in the evaluation function are used to set the walking parameters. 8. The walking control method of the biped walking robot according to claim 7, characterized in that: the parameters in the evaluation function are used to set the walking speed and step length of the walking parameters. 9. the walking control method of biped walking robot as claimed in claim 8, is characterized in that: the described walking mode of described biped walking robot generated in step 3 meets the ZMP stability criterion of biped walking, Combined with the slipping stability criterion.