CN112035965B - A Method for Optimizing the Dimensions of the Leg Mechanism of a Footed Robot - Google Patents

Abstract

The invention discloses a method for optimizing the size of the leg mechanism of a legged robot, which comprises the following steps: s1. Constructing the trajectory of the foot end of the robot with the support phase as a straight line and the swing phase as a corrected cycloid; s2. Using quintic polynomial interpolation to correct the pendulum The foot trajectory composed of lines and straight lines makes a smooth transition; s3. Analytical method is used to analyze the kinematics of the robot leg structure; s4. The objective function and constraint conditions are set to optimize the size of the robot leg structure.

Description

A method for optimizing the size of leg mechanism of a footed robot

Technical Field

The invention belongs to the field of footed robots, and in particular relates to a method for optimizing the size of a leg mechanism of a footed robot.

Background Art

The research field of robots today has expanded from fixed-point operations in structured environments to autonomous operations in many unstructured environments such as aerospace, land and underwater, disaster relief, services and medical care. This requires robots to have highly flexible mobility and operational performance. Although wheeled and tracked mobile robots are widely used in people's living environments, they are still very limited in meeting the requirements of future robots. Because the bionic leg robot is in point contact with the ground, it has stronger adaptability than wheeled and tracked robots in complex environments with uneven surfaces, such as mountains and ruins. Therefore, it has received widespread attention in the research field. The bionic leg robot can achieve static continuous and rapid walking, has redundancy, and static walking efficiency. This type of robot is suitable for high-risk, unstructured and on-site maintenance-incapable environments, such as rescue, exploration, space interstellar exploration and many military applications.

However, there is little mention in the research literature on the optimization of robot leg structure size, which is one of the key factors for legged robots to move from the research field to the application field. Therefore, a method for optimizing the size of leg structure of legged robots that can ensure the smooth movement of robots is needed.

Summary of the invention

In order to achieve the above technical objectives, the technical solution adopted by the present invention is as follows:

A method for optimizing the size of a leg mechanism of a footed robot comprises the following steps:

s1. Construct the robot foot trajectory with the straight line as the support phase and the modified cycloid as the swing phase;

s2. Use quintic polynomial interpolation to smoothly transition the foot end trajectory composed of the modified cycloid and the straight line;

s3. Use analytical method to perform kinematic analysis on the robot leg structure;

s4. Setting objective functions and constraints to optimize the size of the robot leg structure.

Furthermore, the robot leg structure includes a crank-rocker mechanism ABCO and a parallelogram mechanism BDEF; wherein AO is a crank, ABF is a connecting rod, BDC is a rocker, and G is a foot end.

Furthermore, in step s1, the trajectory expression of the foot end in the swing phase is:

为摆动相的初始相位角，

为相位角。Among them, β is the proportion of the swing phase to the total phase, L is the step length, H is the step height,

is the initial phase angle of the swing phase,

is the phase angle.

Furthermore, in step s2, the final foot end trajectory expression using the fifth-order polynomial transition is:

Further, in step s3, the coordinates of points B and D are:

Coordinates of point F:

Coordinates of point E:

The coordinates of point G:

Further, in step s4, the objective function expression is:

Where S _xi , S _yi are the coordinates of the i-th point given by the planning of point G on the connecting rod; G _xi , G _yi are the actual coordinates of the i-th position of point H on the connecting rod;

The optimization design variables are: x = [l ₁ ,l ₂ ,l ₃ ,l ₄ ,l ₅ ,l ₆ ,l ₇ ,θ ₁₀ ,H ₀ ,T ₀ ];

The constraints are:

At the same time, 20≤l ₃ -l ₅ .

Furthermore, in step s4, a genetic algorithm is used in combination with the fmincon interior point method to perform a global search and optimization.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention can be further illustrated by means of non-limiting examples given in the accompanying drawings;

Figure 1 is a schematic diagram of the leg mechanism of a foot-type robot;

Figure 2 is a trajectory diagram of the swing phase and the support phase;

Figure 3 shows the foot end trajectory improvement plan;

FIG4 is the final planned foot end trajectory of the present invention;

Figure 5 is a diagram of the mechanism analysis coordinate system;

Figure 6 is an optimization flow chart.

DETAILED DESCRIPTION

In order to enable those skilled in the art to better understand the present invention, the technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

A method for optimizing the size of a leg mechanism of a footed robot comprises the following steps:

s1. Construct the robot foot trajectory with the straight line as the support phase and the modified cycloid as the swing phase;

The schematic diagram of the leg mechanism of the footed robot is shown in Figure 1. The leg mechanism has only one degree of freedom, in which the ABCO quadrilateral mechanism is a crank-rocker mechanism, AO is the crank, ABF is the connecting rod, and BDC is the rocker; the quadrilateral BDEF is a parallelogram mechanism;

由修正摆线函数可得摆动相轨迹表达式为In order for a legged robot to achieve normal walking, the G-point at the foot of the leg must be able to achieve the trajectory of lifting the leg, stepping forward, and supporting on the ground. A complete robot foot trajectory can be divided into a support phase and a swing phase. When the foot is in the support phase, the foot is always in contact with the ground. In order to make the robot highly stable and simple to control, the height of the body should be kept unchanged. Therefore, from the relative motion relationship, it can be seen that the support phase trajectory is a straight line; in the swing phase, the foot takes off and steps forward. Rectangular curves, elliptical curves, parabolas, modified cycloids, etc. can be used. This patent uses energy-efficient modified cycloids to plan the swing phase trajectory. In a gait cycle, it can be seen from the robot leg structure that the total phase is 360° (that is, one crank rotation is a gait cycle). Suppose the proportion of the swing phase to the total phase is β, the step length is L, the step height is H, and the initial phase angle of the swing phase is

The expression of the swing phase trajectory can be obtained from the modified cycloid function:

为相位角，也称极角。In the formula

is the phase angle, also called the polar angle.

为例进行轨迹规划，可得整个轨迹曲线如图2所示。在足端整个运动轨迹中修正摆线与直线连接处(图中A、B点)均出现尖点，即摆动相与支撑相转换处运动轨迹出现突变，使得速度产生突变，从而对腿部机构产生冲击，对机器人运动稳定性产生重大影响。s2.采用五次多项式插值对修正摆线与直线组成的足端轨迹进行圆滑过渡Here, the step length L = 120 mm, the step height H = 70 mm, and β = 0.5.

Taking the example of trajectory planning, the entire trajectory curve is shown in Figure 2. In the entire motion trajectory of the foot end, there are sharp points at the connection between the modified cycloid and the straight line (points A and B in the figure), that is, the motion trajectory at the transition between the swing phase and the support phase has a sudden change, which causes a sudden change in speed, thereby impacting the leg mechanism and having a significant impact on the robot's motion stability. s2. Use quintic polynomial interpolation to smoothly transition the foot end trajectory composed of the modified cycloid and the straight line

The foot end trajectory composed of the modified cycloid and the straight line is smoothly transitioned by using quintic polynomial interpolation. Since the foot end trajectory is symmetrical about the center line, the right end transition function can be obtained from the left end transition function. This patent uses β = 0.5, that is, the support phase and the swing phase are equal to plan the foot end trajectory. The specific planning method is as follows:

组成；① Subtract the R length from the left end of the swing phase correction cycloid and from the left end of the support phase straight line to construct the retraction trajectory curve. As shown in Figure 3, the swing phase is composed of

composition;

② Take the coordinates of the endpoints B and C of the retraction trajectory curve as B(φ ₀ , x ₀ , y ₀ ) and C(φ ₁ , x ₁ , y ₁ ) respectively. According to the continuity of the swing phase velocity and acceleration, the corresponding velocity and acceleration coordinates of points B and C can be obtained as B ₁ (φ ₀ , x ₀ , y ₀ ) and C ₁ (φ ₁ , x ₁ , y ₁ ) respectively.

段：③ Using the coordinates of points B and C and the velocity and acceleration coordinates, construct the fifth-order polynomial function (2)

part:

段：

part:

段：

part:

The first and second order derivatives of equations (2) and (3) are respectively obtained to obtain the corresponding velocity and acceleration equations:

及纵坐标值y₀＝0，在图3中取C点对应的相位为相位

B点横坐标为

则

B₁(0，0，0)、B₂(0，0，0)，由C点相位

及式(3)、(6)可得C、C₁、C₂坐标值，由6点坐标可联立求解得式(2)、(4)各项系数为：Since point B is the starting point of the swing phase, the phase of point B can be obtained

and the ordinate value y ₀ = 0, the phase corresponding to point C in FIG3 is taken as the phase

The horizontal coordinate of point B is

but

B ₁ (0, 0, 0), B ₂ (0, 0, 0), from the phase of point C

From equations (3) and (6), we can get the coordinate values of C, C ₁ , and C _2. The six-point coordinates can be solved together to get the coefficients of equations (2) and (4):

The final foot trajectory expression using quintic polynomial transition is:

Its trajectory is shown in Figure 4;

s3. Use analytical method to perform kinematic analysis on the robot leg structure.

In order to enable the robot's leg movement to achieve the planned foot trajectory, the kinematic analysis of the foot displacement must first be performed.

在

中设

由四边形BDEF为平行四边形，有l_BD＝l_EF＝l₅、l_BF＝l_DE＝l₆。A plane rectangular coordinate system is established with point O as the origin, as shown in Figure 5. When the position of the crank is known, it can be known from the kinematic geometry of the mechanism that the coordinate position of point G at the foot end depends on the length of each rod and the position of the crank. Assume that the rod lengths of OA, AB, BC, CO, BD, DE, and FG are l ₁ , l ₂ , l ₃ , l ₄ , l ₅ , l ₆ , and l ₇ , respectively, the angle between crank OA and the positive direction of the x-axis is the crank angle θ ₁ , and the angle between rocker BC and the negative direction of the x-axis is θ ₂ . In order to facilitate the solution of θ ₂ , connect point A and point C, and assume that the angle between AC and the negative direction of the x-axis is

exist

China Construction

Since quadrilateral BDEF is a parallelogram, we have l _BD ＝l _EF ＝l ₅ , l _BF ＝l _DE ＝l ₆ .

As shown in the figure, the coordinates of points A and C can be calculated directly:

Assume that the distance between points A and C is l _AC = l ₈ , and from the coordinates of points A and C we can get:

中，由余弦定理：exist

In the formula, according to the law of cosines:

当OA处于x轴下方时，

当OA与x轴共线时，

由正弦函数为奇函数，在

范围内自带正负号。因此由几何关系可知：During the movement of the crank OA, it can be seen that when OA is above the x-axis,

When OA is below the x-axis,

When OA is collinear with the x-axis,

Since the sine function is an odd function,

The range has positive and negative signs. Therefore, from the geometric relationship, we can know that:

为负角；在A点位于x轴上方时，

为正角。因此，θ₂的求解表示式为：From the above formula, we can see that when point A is below the x-axis,

is a negative angle; when point A is above the x-axis,

is a positive angle. Therefore, the solution expression for θ ₂ is:

According to θ ₂ , the coordinates of points B and D can be calculated:

Because points A, B, and F are collinear, the coordinates of point F can be calculated using the formula for dividing points by equal proportions:

其中

可以解出E点的坐标：In parallelogram BDEF, we have

in

The coordinates of point E can be solved:

Because points E, F, and G are collinear, the coordinates of G can be known from the formula for dividing points equally:

s4. Setting objective function and constraint conditions to optimize the size of the robot leg structure

(1) Optimization objective function and design variables

During the movement of the leg mechanism, the crank rotates to drive the foot end through the planned trajectory, so the given trajectory coordinates should be linked to the crank angle. The coordinate system is established at the crank hinge point, and the height of the crank hinge point from the support point in the vertical direction (y direction) is H _0. In order to obtain the optimal solution, the trajectory moves within a certain range in the horizontal direction, and the movement amount is T _0. Then, the mathematical expression of the target trajectory planned by the robot's foot end in the global coordinate system is:

由足端运动分析可知，腿部机构足端位置由组成的各杆长度与曲柄位置决定，而曲柄位置由初始位置θ₁₀与转动增量角度确定，曲柄匀速转动时曲柄相对初始位置转过的角度为Δθ，足端依次经过规划足端轨迹离散的n个点，则

由足端轨迹的方向设定曲柄AO逆时针转动，并以逆时针转动为正，则：Discretize the foot end target trajectory into n key points, set the crank to rotate at a constant speed, and evenly select points on the planned trajectory. The phase difference of the polar angle is

From the analysis of the foot end motion, we know that the foot end position of the leg mechanism is determined by the length of each rod and the crank position, and the crank position is determined by the initial position θ ₁₀ and the rotation increment angle. When the crank rotates at a constant speed, the angle of the crank relative to the initial position is Δθ. The foot end passes through the n discrete points of the planned foot end trajectory in sequence, then

The direction of the foot end trajectory sets the crank AO to rotate counterclockwise, and counterclockwise rotation is positive, then:

θ ₁ =θ ₁₀ +Δθ (20)

According to the fact that the foot end passes through n points when the crank rotates a full circle, the objective function minimizes the root mean square error of the n coordinate values between the actual trajectory of point G on the connecting rod and the planned trajectory. The objective function expression is:

Where S _xi and S _yi are the coordinates of the i-th point given by the planning of point G on the connecting rod; G _xi and G _yi are the actual coordinates of the i-th position of point H on the connecting rod.

From the derivation of the G-point coordinates at the foot end and Equation 21, it can be seen that the objective function is a function of the rod length, crank angle and trajectory position, so the optimization design variable is taken as: x = [l ₁ ,l ₂ ,l ₃ ,l ₄ ,l ₅ ,l ₆ ,l ₇ ,θ ₁₀ ,H ₀ ,T ₀ ]

(2) Constraints

According to the overall design size limit of the leg and the leg layout ( _H0 controls the height of the robot body, T0 controls the position of the foot end trajectory relative to the crank), each rod length and the initial position of the crank have a range limit:

According to the existence of the crank rocker, the following constraints can be established:

Considering the apertures of each articulated pair and the machining dimensions of the parts, the dimensional constraint relationship between the rod lengths is established:

20≤l ₃ -l ₅

(3) Optimize calculation

Matlab software is used as an optimization analysis tool. It can be seen from the above optimization mathematical model that the optimization problem belongs to a nonlinear optimization problem with constraints. Matlab's fmincon() function is specifically used to solve constrained nonlinear problems. Its interior point method has high precision and good convergence, but the function needs to be assigned an initial value during optimization. Genetic algorithms are applicable to any optimization problem. They use global optimization, are not easily trapped in local optimal solutions, and do not rely on initial values. However, genetic algorithms also have the disadvantages of being easy to converge prematurely and having low precision. Therefore, this patent optimization method uses genetic algorithms combined with the fmincon interior point method to perform global search optimization.

The optimization process is shown in Figure 6. The optimization calculation process is divided into two steps. The first step is to use the genetic algorithm to obtain the preliminary optimization results. The second step is to use the preliminary optimization value as the initial point of the fmincon function optimization to further improve the optimization accuracy. Matlab is used to write the optimization program, and the optimization results can be calculated in the end.

The above specific embodiments are only used to help understand the method and core idea of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made to the present invention without departing from the principles of the present invention, and these improvements and modifications also fall within the scope of protection of the claims of the present invention.

Claims (2)

1. A method for optimizing the size of a leg mechanism of a foot type robot is characterized by comprising the following steps:

s1, constructing a robot foot end track by taking a straight line as a supporting phase and a corrected cycloid as a swinging phase;

s2, smooth transition is carried out on a foot end track formed by the corrected cycloid and the straight line by adopting a quintic polynomial interpolation;

s3, analyzing the leg structure of the robot by adopting an analytical method;

s4, setting an objective function and constraint conditions to optimize the size of the leg structure of the robot;

the robot leg structure comprises a crank rocker mechanism ABCO and a parallelogram mechanism BDEF; wherein AO is the crank, ABF is the tie rod, BDC is the rocker, G is the foot end;

in step s1, the trajectory expression of the foot end in the swing phase is as follows:

wherein beta is the ratio of the swing phase to the total phase, and L is the stepThe length is H, the step height is H,

is the initial phase angle of the wobble phase, is greater than or equal to>

Is a phase angle;

in step s2, the final foot end trajectory expression using quintic polynomial transition is:

in step s3, coordinates of points B and D:

coordinates of point F:

coordinates of point E:

coordinates of point G:

in step s4, the objective function expression is:

in the formula S _xi 、S _yi Planning a given ith point coordinate for a G point on the connecting rod; g _xi 、G _yi Is the actual coordinate of the ith position of the point H on the connecting rod;

the optimization design variables are: x = [ l ₁ ,l ₂ ,l ₃ ,l ₄ ,l ₅ ,l ₆ ,l ₇ ,θ ₁₀ ,H ₀ ,T ₀ ]；

The constraint conditions are as follows:

at the same time, 20 is less than or equal to l ₃ -l ₅ 。

2. The method for optimizing the size of the leg mechanism of the legged robot according to claim 1, characterized in that: in step s4, a genetic algorithm is combined with an fmincon interior point method to perform global search optimization.

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