Parameter design of biped robot motion system based on multi-objective optimization

Abstract

In recent years humanoid robots have been widely used in toy, performance, education and other service industries, but most biped robots walk slowly and have poor stability. The reason is that the driver parameters of the robot cannot properly match the walking gait algorithm, and the insufficient performance of the robot driver leads to the poor motion capability of the robot. In this paper, the optimization design process of biped robot parameters is studied and expounded, and its motion capability is improved by optimizing the driving parameters of the robot. Firstly, the contradiction between walking speed, stability and driver performance of biped robot is analysed. The performance evaluation functions of the three are further established, and the optimal parameter design to a certain extent is realized based on the multi-objective optimization method. Finally, combining with the physical simulation engine, the design parameters are simulated and checked, and the robot design process is completed through the guidance of simulation results.

Keywords

Humanoid robot inverted pendulum multi objective optimization constraint

1 Introduction

Humanoid robots are designed with reference to human body structure and motion characteristics, which is an advanced platform for studying human intelligence. The research of humanoid robot brings together many disciplines such as machinery, electronics, computer, artificial intelligence, bionics, etc. Humanoid robots have shown good application prospects in service, medical treatment, education and other fields, as well as in anti-terrorism and anti-explosion and anoxic and high temperature environments that are not suitable for manual operation. In order to realize the extensive application of humanoid robots, how to optimize the performance of humanoid robots and make them more efficiently and stably in complex dynamic environment has become the key problem [1 –5].

In the walking process of biped robots, to ensure good stability, it is often necessary to limit the walking speed. If the walking speed needs to be increased, the speed and range of joint movement need to be increased, and the stability of the robot will deteriorate. When the joint drive parameters do not meet the requirements, that is, the torque and rotational speed of the drive motor are lower than expected, the robot is difficult to reach a larger walking speed and stability is not easy to be guaranteed. The driving ability of the motor is related to the weight of the motor. The larger the driving ability, the greater the weight of the motor, resulting in the greater weight of the robot, which in turn increases the demand for driving [6 –8].

There is a contradiction between the stability and speed of the robot walking and the performance of the driver, a contradiction between the safety, working efficiency and cost of the robot. At present, the research at home and abroad is mainly to ensure the speed and stability of the robot walking by improving the structure and the performance of the driver. It is often only aimed at some problems and does not pay attention to the contradictory relationship between various parameters. In the actual application of large-scale humanoid robots, due to the limitations of device performance and cost, it is necessary to select the relatively optimal parameters among the conflicting parameters under the existing conditions. This paper studies the multi-objective optimization of the conflicting objectives such as stability, speed and motor cost to realize the balance among the various performances, maximize the utilization of the various performances of the robot, and optimize the selection of the proportion of each objective according to different needs.

Scholars have also conducted some research on how to introduce multi-objective optimization methods in the field of robot control to solve the compromise solution that satisfies several constraint problems [9, 10]. Azhar et al. of Tokyo Metropolitan University proposed a three-dimensional motion control system based on biological methods for human-like bipedal walking robots. The neuromotor system was extended to establish a multi-neuronal system model in which motor neurons represent muscles. Systematic, sensory neurons represent the sensing system in the human body. To establish a motion pattern, they applied a multi-objective evolutionary algorithm to solve synaptic weights between motor neurons and validated them on a 12-DOF biped robot [11, 12].

Canadian scholar Philippe et al. proposed a multi-objective genetic algorithm based on NSGA-II to solve the contradiction between the two goals of maximizing dynamic stiffness and minimizing system noise sensitivity during the grinding process of underwater metal grinding robots. The control parameters of the robot discrete time observer are optimized and verified by the underwater grinding robot controlling the hydroelectric dam [13 –16].

In addition, Andrej Gams et al. based on the priority task control mechanism to support vector machine estimation and construct the humanoid robot centroid stability model, and achieve synchronization stability and motion tracking control on the robot COMAN [17]; Nierhoff T. et al. The -RRT algorithm incrementally samples the trajectory mimicry process in the clustering environment and uses the quadratic term distance to describe the underlying distance metric for the velocity and acceleration deviation on the reference trajectory. The nearest neighbour algorithm is used to extend the RRT* tree in the task space. The convergence speed is improved, and the motion simulation effect is verified on the humanoid robot HRP-4 [18]; Okamoto T. et al. extended the target motion abstract model in the observation learning paradigm, so that the humanoid robot self-extracts and self-adjusts the constraints. Imitate the different feature movements in the human body demonstration circle game [19]; Hamed et al. perform multi-objective optimization on the natural kinematics adjustment and kinematic redundancy solution for the periodic task execution problem of the redundant serial manipulator to output Minimum torque [20]; Miguel G. et al. to improve the robustness of the robot system and achieve the nominal design of uncertain parameters The object has the lowest sensitivity, multi-objective optimization of mechanical and control nominal design objects and verification on planar parallel robots [21], and so on.

At present, researchers at home and abroad have made many achievements in the optimization of humanoid robot balance stability, such as applying probabilistic reinforcement learning algorithm ∖cite{c4}, constructing a centroid stability model [7], and optimizing motion posture through learning algorithms [22]; A lot of researches have been done on the optimization of robot energy consumption, such as tracking the human kMPs trajectory by resonance mechanism [8], analyzing the parametric parameters of human gait [23], and some scholars applying multi-objective optimization algorithms to control humanoid robot control parameters. Optimize and improve the performance of certain aspects of the robot [9, 10]. However, how to optimize the stability, speed and motor cost of humanoid robots in a dynamic time-varying environment to achieve a balance between robot safety, work efficiency and cost, there is no general method in the existing literature; The existing dynamic multi-objective optimization algorithm [24, 25] is analysed, and it is found that there is no dynamic multi-objective optimization algorithm suitable for humanoid robots with high robustness, high real-time and high reliability [26 –30].

This article is divided into six parts. The second section analyzes the influence factors of robot gait and stability. The third section gives the objective function of robot optimization. The fourth section is the optimization method of robot parameter design. The fifth section is the simulation design verification of biped robot.

2 Robot gait and stability criterion

Robot kinematics analysis is the basis of various motion control. The main content is to study the relationship between the joint angle of the robot and the position and attitude of the connecting rod, and to express these relationships through mathematical modelling. Most humanoid robots drive the joint angle through the motor. In order to realize the control of the robot, it is necessary to determine the position of each link and joint of the robot. Therefore, the reference coordinate system should be established. The humanoid robot is divided into five parts, each part is regarded as a connecting rod, which is a structural model of two hip joints, two knee joints and two joints to form a robot; the joint of the left calf and the ground is the coordinate origin. The robot advances in the X-axis, the horizontal axis is the Y-axis perpendicular to the X-axis, and the Z-axis in the height direction establishes the coordinate system, as shown in Fig. 1, the parameter definition is shown in Table 1.

Fig. 1

Humanoid robot structure model.

Table 1

Humanoid robot model parameters

Related parameters	Structural model definition
l₁, l₂, l₃, l₄, l₅	Length of each link
m₁, m₂, m₃, m₄, m₅	Weight of each link
q₁, q₂, q₃, q₄, q₅	Angle of vertical direction of each link
θ_a1, (x_a1, y_a1, z_a1)	Left ankle joint symbol and its coordinates
θ_a2, (x_a2, y_a2, z_a2)	Right ankle joint symbol and its coordinates
θ_k1, (x_k1, y_k1, z_k1)	Left knee joint symbol and its coordinates
θ_k2, (x_k2, y_k2, z_k2)	Right knee joint symbol and its coordinates
θ_h1, θ_h2, (x_h, y_h, z_h)	Left/right hip joint symbol and its coordinates

After the coordinate system and structural model are established, the kinematics analysis of the humanoid robot can be performed. The kinematics can be divided into two parts: positive kinematics and inverse kinematics. Based on the parameters such as the length and mass of each link of the robot, positive kinematics is based on known joint angles, angles and other parameters to solve the position and attitude of the connecting rod. It can be used to describe the robot state and obstacles. The judgment of the object collision; the inverse kinematics is to solve the joint angle according to the known robot link attitude. When the robot is required to complete the specified motion, the inverse kinematics is needed to calculate the joint angle, and then the motor is driven to control the robot motion.

2.1 Robot stability criterion

The kinematic derivation can plan the motion posture of the humanoid robot in an ideal environment, but there are external force disturbances such as gravity and friction in the actual motion, which will cause the robot to move in accordance with the planned posture, even shaking and falling. Industrial robots can fix the base on the ground to maintain stability; wheeled, crawler and other robots can maintain balance by stable contact with the ground and low centre of gravity; while humanoid robots stand through the foot, the contact area with the ground is small and unstable. At the same time, its shape is like that of human beings, and the centre of gravity is higher and easy to fall. Therefore, judging the stability of the humanoid robot is a key issue for achieving normal walking and accomplishing the target operation. The zero-torque point is an important physical quantity for judging the stability of the humanoid robot.

The zero-moment point was first proposed by Vukobratovic et al. in a paper on humanoid robot control, often abbreviated as ZMP, which means: all the forces on the robot’s sole, if when replaced by a resultant force, the point of action of the foot through which the resultant force passes is called ZMP; as shown in Fig. 2. The ground force of the robot’s sole can be replaced by the resultant force f and the torque around the ZMP τ_p, as shown in the following equation: $\begin{matrix} f = {\begin{matrix} f_{x} = \int_{S} σ_{x} (m, n) dS \\ f_{y} = \int_{S} σ_{y} (m, n) dS \\ f_{z} = \int_{S} σ_{z} (m, n) dS \end{matrix} \\ τ_{p} = {\begin{matrix} τ_{px} = 0 \\ τ_{py} = 0 \\ τ_{pz} = \int_{S} {(m - p_{x}) σ_{y} (m, n) - (n - p_{y}) σ_{x} (m, n)} dS \end{matrix} \end{matrix}$ (1)

Fig. 2

ZMP of Robot.

The intersection of the resultant force F and the sole is ZMP, and the ZMP coordinates are calculated by Equation 2, the parameter definition is shown in Table 2.

Table 2

Force analysis related parameter parameter definition table

Related parameters	Corresponding structural model definition
p	Robotic foot force ZMP
p_x, p_y, p_z	ZMP coordinates on the X, Y, and Z axes
S	Plantar force area
$r = [\begin{matrix} m & n & 0 \end{matrix}]^{T}$	Position vector at a certain point in the force region
σ_x (m, n)	The ground force horizontal component force at point r (X-axis)
σ_y (m, n)	The ground force horizontal component force at point r (Y-axis)
σ_z (m, n)	Ground force vertical force per unit area at point r

$p = {\begin{matrix} p_{x} = \frac{\int_{S} m σ_{z} (m, n) dS}{\int_{S} σ_{z} (m, n) dS} \\ p_{y} = \frac{\int_{S} n σ_{z} (m, n) dS}{\int_{S} σ_{z} (m, n) dS} \\ p_{z} = 0 \end{matrix}$ (2)

In the actual situation, the specific distribution of the force of the plantar is difficult to measure, and other parameters of the robot need to be used for calculation and derivation. The commonly used physical parameters are as follows: M is the quality of the humanoid robot (kg); $c = [\begin{matrix} x & y & z \end{matrix}]^{T}$ is the humanoid robot’s centroid (m); $P = [\begin{matrix} P_{x} & P_{y} & P_{z} \end{matrix}]^{T}$ is the line momentum of the humanoid robot (N . s); $L = [\begin{matrix} L_{x} & L_{y} & L_{z} \end{matrix}]^{T}$ is the angular momentum of the humanoid robot (N . m . s); $g = [\begin{matrix} 0 & 0 & - g \end{matrix}]^{T}$ is the human body’s gravity acceleration vector (N/s²). In the dynamics of the robot, the above parameters satisfy the following formula: ${\begin{matrix} \dot{c} = P / M \\ \dot{P} = Mg + f \\ \dot{L} = c \times Mg + τ \end{matrix}$ (3)

Where $\dot{c}$ is the centroid acceleration of the humanoid robot; $\dot{P}$ is the linear momentum change rate of the humanoid robot; f is the force other than gravity that the humanoid robot is subjected to, generally the ground force; $\dot{L}$ is the angular momentum change rate of the humanoid robot; τ is the torque other than the gravitational moment of the humanoid robot.

The ground force of the humanoid robot’s sole can be replaced by the resultant force f and the torque around the ZMP τ_p, which is obtained by the formula 1. The ground force around the origin is as follows: $τ = p \times f + τ_{p}$ (4)

τ_p is the resultant moment of the ground force around point p. Substituting the formula 3 into the formula 4 solving τ_p gives: $τ = \dot{L} - c \times Mg + (\dot{P} - Mg) \times p$ (5)

Decompose the vector in the formula 5 and substitute it into τ_px = 0 and τ_py = 0 in the formula 1. The results of the first two lines are: ${\begin{matrix} τ_{px} = {\dot{L}}_{x} + {\dot{P}}_{y} P_{z} + Mgy - ({\dot{P}}_{z} - Mg) p_{y} = 0 \\ τ_{py} = {\dot{L}}_{y} - {\dot{P}}_{x} P_{z} - Mgx + ({\dot{P}}_{z} + Mg) p_{x} = 0 \end{matrix}$ (6)

Solving the formula 6 yields the Z-axis X-axis p_x and the Y-axis coordinate p_y and substitutes it into the formula 2 for p_z = 0: $p = {\begin{matrix} p_{x} = \frac{Mgx + p_{z} {\dot{P}}_{x} - {\dot{L}}_{y}}{Mg + {\dot{P}}_{z}} \\ p_{y} = \frac{Mgy + p_{z} {\dot{P}}_{y} + {\dot{L}}_{x}}{Mg + {\dot{P}}_{z}} \\ p_{z} = 0 \end{matrix}$ (7)

The ZMP is approximated by the robot linkage model. The linkage model is considered to be composed of N mass points. The inertia tensor of each link around the centroid is ignored. The angular momentum of the humanoid robot around the coordinate origin can be expressed as: $L = \sum_{i = 1}^{N} c_{i} \times P_{i}$ (8)

Where N is the number of particles that make up the humanoid robot;

$c_{i} = [\begin{matrix} x_{i} & y_{i} & z_{i} \end{matrix}] (i = 1, 2, . . ., N)$ is the coordinate of each particle (m). Substituting the formula 8 into 7 gives you: $p = {\begin{matrix} p_{x} = \frac{\sum_{i = 1}^{N} {({\ddot{z}}_{i} + g) x_{i} + (p_{z} - z_{i}) {\ddot{x}}_{i}}}{\sum_{i = 1}^{N} {\ddot{z}}_{i} + g} \\ p_{y} = \frac{\sum_{i = 1}^{N} {({\ddot{z}}_{i} + g) y_{i} + (p_{z} - z_{i}) {\ddot{y}}_{i}}}{\sum_{i = 1}^{N} {\ddot{z}}_{i} + g} \\ p_{z} = 0 \end{matrix}$ (9)

If the humanoid robot is treated as a particle, the formula 9 becomes: $p = {\begin{matrix} p_{x} = x - \frac{(z - p_{z}) \ddot{x}}{\ddot{z} + g} \\ p_{y} = y - \frac{(z - p_{z}) \ddot{y}}{\ddot{z} + g} \\ p_{z} = 0 \end{matrix}$ (10)

3 Robot optimization objective function

The gait planning of the humanoid robot is usually based on the requirements of the walking operation, and the trajectory of the hip joint and the ankle joint during the walking process is planned. When the humanoid robot is walking forward in the horizontal plane, the height of the hip joint is relatively stable, and the highest point of the hip joint starting moment is very small from the lowest point height during the movement, and no additional trajectory planning is required, so the gait planning is usually for the trajectory of the ankle joint, the commonly used planning method is the three-point planning method.

When three-point planning is performed on the ankle joint, the gait planning is usually selected as the key point by selecting the starting time of the swinging foot, the highest point of the swinging ankle joint, and the moment of swinging the foot. After setting three key points, the entire cycle trajectory curve can be derived through the cubic spline interpolation function, and then the position and attitude of the humanoid robot link during gait movement can be determined. Then, other joint angles can be calculated by inverse kinematics. Curve to determine the walking gait of the robot.

Set the humanoid robot to walk in the horizontal plane. If the obstacle is crossed and the upper and lower steps are not considered, the highest point of the swinging ankle joint should be reduced as much as possible, thereby reducing the hip and knee joint swing angle during the movement and reducing the joint. Motor torque for maximum protection of the motor. Therefore, when performing the gait planning of the humanoid robot, it is only necessary to determine the distance between the starting position of the swinging foot and the landing position of the swinging foot, that is, the step distance, and the motion posture of the robot in the walking period can be determined; in addition, a walking cycle consumption is set. At the time, you can determine the gait planning of the humanoid robot. The step and walking cycle are the variables of the gait planning, and the robot linkage model is shown in the Fig. 3.

Fig. 3

Gait planning variable model.

Set D to the step distance of the gait walking of the humanoid robot, T is the time consumed by the walking cycle. When the swinging foot is landing, the thigh and the lower leg of the swinging leg can be approximated as the same straight line, then let L be the approximation of the robot leg. The total length, θ is the approximate angle between the legs at the time of landing. According to this model, the performance function model of the gait progression speed, walking stability and motor cost of the humanoid robot is established.

3.1 Robot walking speed function

The gait forward speed of the humanoid robot is determined by the step distance and the walking cycle time. The larger the step distance and the shorter the walking cycle time, the faster the robot walks faster. The expression is as follows: $Q_{1} (D, T) = \frac{1}{j_{1}} \frac{D}{T}$ (11)

Where D is the gait walking step of the humanoid robot; T is the humanoid robot walking cycle; Q₁(D,T) is the humanoid robot walking speed; j₁ is the adjustment parameter.

3.2 Gait stability function

The stability of the humanoid robot walking is related to the centre of gravity and the position of the ZMP. When the distance between the centre of gravity of the humanoid robot and the ZMP is large or the ZMP position tends to the tip of the toe, the robot is likely to fall; if the humanoid robot is regarded as a mass point, the formula 10 is available.

The larger the centroid coordinate of the humanoid robot, the more the ZMP coordinates increase, that is, the ZMP position tends to the toes, and the stability of the robot becomes worse. When the humanoid robot reaches the limit point of the single-leg support period, the mass centre is farthest from the support foot, and the distance value can be approximated as half of the step distance D. That is, the larger the step distance D, the worse the stability of the humanoid robot. $p = {\begin{matrix} p_{x} = x - \frac{(z - p_{z}) \ddot{x}}{\ddot{z} + g} = x - \frac{z \ddot{x}}{\ddot{z} + g} \\ p_{y} = y - \frac{(z - p_{z}) \ddot{y}}{\ddot{z} + g} = y - \frac{z \ddot{y}}{\ddot{z} + g} \\ p_{z} = 0 \end{matrix}$ (12)

Adjust the formula 12, and the distance between the centre of gravity of the humanoid robot and the ZMP can be expressed as follows: ${\begin{matrix} x - p_{x} = \frac{z \ddot{x}}{\ddot{z} + g} \\ y - p_{y} = \frac{z \ddot{y}}{\ddot{z} + g} \end{matrix}$ (13)

It can be seen that the centre of gravity of the humanoid robot and the ZMP distance are related to the acceleration of the centre of gravity. The greater the acceleration of the centre of gravity of the robot, the larger the distance between the centre of gravity and the ZMP, and the worse the stability of the humanoid robot. Analyze the relationship between the acceleration of the centre of gravity of the robot and the cycle time. The formula for the reference acceleration and time is as follows: $S = \frac{1}{2} {at}^{2} \to a = \frac{2 S}{t^{2}}$ (14)

The comprehensive formula 13 and 14 show that the longer the walking cycle time of the humanoid robot, the smaller the acceleration of the center of gravity projection point, and the better the stability of the robot, the walking stability and step and walking cycle of the humanoid robot. The relationship of time can be expressed by the following formula: $Q_{2} (D, T) = j_{2} \frac{T^{2}}{D}$ (15)

Where D is the gait walking step of the humanoid robot; T is the humanoid robot walking cycle; Q₂ (D,T) is the humanoid robot walking hazard; j₂ is the adjustment parameter.

3.3 Joint performance demand function

Joint performance mainly has two parameters, namely speed and torque. During walking of biped robot, both speed and torque are required to meet the requirements. Joint speed is related to walking speed. Joint motor torque depends on robot link mass and posture. Robot link mass is constant and will not change with walking motion, so motor torque is simplified to be related to acceleration. From the angle of torque work, the power is equal to the product of force and speed, and the force and acceleration are directly proportional. Therefore, the demand function for joint performance is written as follows: $Q_{3} (D, T) = j_{3} va = j_{3} \frac{D^{2}}{T^{3}}$ (16)

Random values of step distance and period are substituted into equations 11, 15 and 16 to obtain the relationship between demand functions as shown in Figs. 4 and 5. With the increase of walking speed, the walking stability of the robot decreases and the demand for joint torque increases. For the same walking speed, the walking stability and joint performance are different for different step distances and periodic parameters, so the joint stability can be improved and the performance requirements for joints can be reduced under the condition of ensuring the walking speed through the relationship of demand functions. In Figs. 4 and 5, random point 1 is in the area between point sets, which is not the optimal choice. Random point 2 is located at the edge of the point set, but it is the worst choice. Only the edge of the point set where the random point 3 is located is the optimal choice, that is, the walking speed and stability, walking speed and performance requirements are optimized simultaneously.

Fig. 4

Simulation results with walking speed and stability.

Fig. 5

Simulation results with walking speed and performance.

3.4 Optimization objective function

In summary, there are three optimization objectives in the dynamic multi-objective optimization problem of humanoid robot gait planning: the speed of gait advancement of humanoid robot, the stability of walking and the cost of motor; two decision variables: The step of the humanoid robot’s gait walking D and the time spent in a walking cycle is T. To facilitate the optimization calculation, use the decision vector X = [x₁, x₁] ^T instead of the decision variables D and T to set x₁ has a value range of [a₁, b₁], x₂ has a range of [a₂, b₂], Combining the formulas 11, 15, and 16, the expression for this dynamic multi-objective optimization problem is as follows: $\begin{matrix} {\begin{matrix} f_{1} (X) = j_{1} \frac{x_{2}}{x_{1}} \\ f_{2} (X) = j_{2} \frac{x_{1}}{x_{2}^{2}} \\ f_{3} (X) = j_{3} \frac{x_{2}^{3}}{x_{1}^{2}} \end{matrix} \\ x_{1} \in [a_{1}, b_{1}], x_{2} \in [a_{2}, b_{2}] \end{matrix}$ (17)

Where f₁(X) is the humanoid robot walking speed objective function; f₂(X) is the stability objective function of the humanoid robot; f₃(X) is the cost objective function of the humanoid robot hip motor; X = [x₁, x₁] ^T is the system decision variable; x₁ is the gait walking step variable of the humanoid robot; x₂ is the humanoid robot walking cycle variable; L is the approximate total length of the humanoid robot legs; j₁, j₂, j₃ are adjustment parameters.

4 Target function multi-objective optimization algorithm

4.1 Multi-objective optimization algorithm

In order to optimize the performance of the humanoid robot during walking, it is necessary to analyze the relationship between the speed of the gait, the stability of the walking and the performance of the motor, and classify the performance into the objective function to determine the relevant decision vector. Then, the optimized gait is obtained through simulation experiments to verify whether the performance of the gait walking of the humanoid robot is optimized. The superiority of the improved dynamic multi-objective optimization algorithm and the feasibility of the gait optimization system are proved.

The steps of the dynamic multi-objective optimization algorithm are as follows:

Establish an initial parent population;

cloning and expanding the initial population;

Perform particle swarm variability and non-uniform variation on cloned populations;

Perform fast non-dominated sorting on all populations;

Perform individual crowding distance calculation;

Conduct elite strategy optimization to get a new parent population

If the current number of iterations reaches the set requirement, the solution set population is output, otherwise step 8 is performed;

Substitute the time variable and perform the next round of dynamic optimization.

4.2 Multi-objective optimization algorithm

The walking distance and walking period of biped robot are taken as variables, the walking speed, walking stability and motor cost of robot are taken as optimization objectives, and optimization is carried out under different population numbers and iteration times. The smaller the optimization objective value is, the better the representative performance is. The number of selected populations is 100 and the number of iterations is 100. The simulation results are shown in Figs. 6 and 7. The red dot part in the figure is on the boundary of the data point set. When the walking speed is fixed, the stability is the highest and the requirement for joint performance is the lowest.

Fig. 6

Simulation results with walking speed and stability.

Fig. 7

Simulation results with walking speed and performance.

5 Simulation design verification of biped robot

5.1 Structural strength and space check

The first consideration in the structural design of the robot is to reduce the weight. The heavier the robot is, the stronger the driving capability of the joint motor is required, and the stronger the driving capability of the joint will also lead to the increase of the joint weight. The development of material science and technology has promoted the lightweight of robots, such as lighter and higher strength materials, while multi-axis NC machining technology can realize the lightweight of hollow structures. The direct purpose of these designs is to reduce the weight, reduce the design difficulty of the driving part, reduce the moment of inertia of the structural parts, and improve the walking flexibility of the robot. As little material as possible can lead to insufficient structural strength of the structural members, and when the structural members deform, the foot end position control error increases. Therefore, after the mechanical structure design is completed, the structural strength shall be checked. As shown in Fig. 8, based on ensuring the structural strength, the weight of the structural parts shall be reduced as much as possible and the deformation shall be as small as possible. Before the simulation, check the motion space of the structural members. As shown in Fig. 9, check the motion range and interference of the components during the motion process. After the completion of this part of work, the data of structure size, weight and centre of gravity can be used by simulation software for further gait simulation.

Fig. 8

Structural strength check.

Fig. 9

Structural strength check.

5.2 Gait Simulation of robot based on physical simulation engine

V-REP is a flexible and expandable universal robot simulator, as shown in Fig. 10. The simulator supports a variety of control methods and programming methods and can easily import the robot models built by developers themselves. The biped robot model is imported into the V-REP environment to generate the robot model in the simulation environment, and the robot linkage, steering gear and other parameters are set to obtain a robot model similar to the “real object". In addition, the V-REP environment allows various sensors to be added to track the angle value of the robot so as to facilitate real-time tracking of the robot’s motion state and analysis of problems in the robot simulation environment, and facilitate analysis and improvement at the algorithm level.

Fig. 10

V-REP simulation interface.

5.3 Biped gait exercise experiment

The gait planner transmits the planned centroid trajectory and foot end trajectory to the joint angle planner, and the joint angle planner solves a total of 12 joint angle values of the left leg motion chain and the right leg motion chain through inverse kinematics and transmits the 12 joint angle values to the V-REP simulator. Finally, the V-REP simulator controls the biped robot motion in the simulation environment according to the received joint values, thus realizing real-time control of the biped robot.

The virtual prototype adopts a biped robot model built under a V-REP simulator, each leg has six degrees of freedom, the trunk is provided with an electronic gyroscope and an electronic accelerometer, and the foot end is provided with six-dimensional force, so that the robot speed and acceleration can be monitored in real time, each joint position and the centroid position of the robot can be output in real time, the running state of the robot can be judged, and the motion curves of important nodes such as the centroid and the foot end of the robot under different algorithms can be observed.

Based on the trajectory of the centre of mass and the trajectory of the foot end, the position of each joint is planned out through inverse kinematics to realize the normal walking of the robot. Given the positions and postures of the trunk and ankles of the left and right feet, the positions of 12 joints of the left and right legs are solved by analytical method, and the angles of each joint are calculated by analytical method. The simulation results are shown in the Figs. 11, 12 and 13.

Fig. 11

Simulation curves of joint angle.

Fig. 12

Simulation curves of joint speed.

Fig. 13

Simulation curve of biped robot’s joint torque.

V-rep gait simulation can be used to obtain joint speed and torque demand data. If the current drive performance does not meet the requirements, re-parameter design and repeat the above design process until the simulation verification experiments meet the requirements.

6 Conclusion

By analysing the gait planning during the robot’s walking, it was found that the speed, stability, and motor cost performance of the walking gait conflicted with each other, and there was a conflict between the path length of the path planning and the safety. To solve these problems with multiple optimization goals and mutual constraints between the goals. This paper proposes an improved dynamic multi-objective optimization algorithm to optimize the problem, summarizes the gait speed, walking stability, and motor cost performance as the objective function, performs dynamic multi-objective optimization, and finally performs simulation experiments to obtain a relatively ideal The result of performance optimization is to replace the hardware iteration by simulation iteration, and finally to achieve the performance optimization of humanoid robot walking.

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