Biped robot robust constraint tracking control method based on parameter optimization

Abstract

The invention relates to the technical field of biped robot control, in particular to a biped robot robust constraint tracking control method based on parameter optimization. According to the method, the improved inverted pendulum model is adopted, the important characteristics of the biped robot can still be reflected while the advantages of a single mass model are fully utilized, and a series of errors and interference problems generated due to the fact that the model is too simplified are avoided. Key parameters of the improved inverted pendulum model are set to be variable, and the dynamic characteristics of the improved inverted pendulum model are convenient to adjust. The robust constraint control method is designed, motion equations of a limited mechanical system of equality constraint and inequality constraint are considered at the same time, control input meets the Gaussian principle and the Alembert principle, and therefore moderate control force is generated in the real world to meet the system performance.

Description

Technical Field

[0001] The invention relates to the technical field of biped robot control, and in particular to a robust constraint tracking control method of a biped robot based on parameter optimization. Background Art

[0002] Bipedal robots are robots that imitate the way humans walk and stand. With their humanoid design, flexible movement ability and high autonomy, they have shown unique advantages in many fields. In order to maintain the stability of bipedal robots during walking and simplify gait planning and balance control, the inverted pendulum model is used in the gait design of bipedal robots. It regards the robot as a structure consisting of a center of mass and massless legs, thus simplifying the complex bipedal robot model into a relatively simple inverted pendulum model for various operations. This model has been widely used in the research of bipedal robots and has achieved good control effects.

[0003] However, the traditional inverted model still has some shortcomings. First, the center of mass motion trajectory obtained by the traditional inverted pendulum model is not smooth enough, which causes the robot's gait to be too stiff and the impact force between the robot and the ground to be large in actual movement, which does not meet the requirements of a smooth gait. Secondly, the traditional inverted pendulum model simplifies the complex bipedal robot into a mass point and a massless linkage system. This oversimplification ignores the interference caused by the unmodeled parts such as arms and legs, as well as the interaction between the joints of the robot, which may lead to the robot's gait in actual applications being inaccurate or inapplicable, causing the final movement to deviate from the reference movement and affecting the robot's stability.

[0004] In addition, the robot system is not a simple unconstrained system. In the actual motion process, it will be subject to a series of constraints, such as structural constraints brought by its own structure, or functional constraints introduced to meet certain expected functions. These constraints can be further divided into equality constraints and inequality constraints. The additional control force introduced by inequality constraints will hinder the equality constraint compliance performance, increase the complexity of the control problem, and bring additional challenges to the control design. Existing robust control research mainly focuses on trajectory tracking problems, namely equality constraints, while the research on inequality constraints is not in-depth. There has been no effective solution to derive and analyze the motion problem of mechanical systems under two constraints at the same time. Summary of the invention

[0005] The present invention discloses a robust constraint tracking control method for a biped robot based on parameter optimization, and the specific method is as follows:

[0006] Simplify the structure of bipedal robots;

[0007] Construct dynamic models for simplified structures;

[0008] Plan the trajectory of the center of mass of a bipedal robot;

[0009] Optimize the trajectory of the center of mass of a bipedal robot;

[0010] According to the biped robot's motion trajectory along the optimized center of mass, the zero moment point of the biped robot's motion process is calculated;

[0011] Construct the fitness function of the optimization algorithm based on the zero moment point;

[0012] According to the fitness function, the parameters of the biped robot are optimized and calculated.

[0013] Furthermore, the specific method is as follows:

[0014] According to the optimized parameters of the bipedal robot, a servo controller is designed to control the bipedal robot.

[0015] Furthermore, the optimized biped robot parameters include: a virtual damper damping coefficient and a virtual spring stiffness.

[0016] Further, the structure of the bipedal robot is simplified as follows:

[0017] Based on the inverted pendulum, a virtual spring and a virtual damper are added at the mass center of the biped robot inverted pendulum.

[0018] Furthermore, the dynamic model constructed has the following specific formula:

[0019]

[0020] Where θ is the swing angle of the inverted pendulum, is the angular velocity of the inverted pendulum, is the angular acceleration of the inverted pendulum, l is the pendulum length, k is the stiffness of the virtual spring, B is the damping coefficient of the virtual damper, and m is the mass.

[0021] Furthermore, the planned trajectory of the center of mass of the bipedal robot is given by the following formula:

[0022]

[0023]

[0024] In the formula, x(t) and z(t) are the trajectories of the center of mass in the x and z directions, α and β are the coefficients of the differential equation, and θ(0) and They are the initial conditions of the swing angle and the swing angular velocity, that is, their sizes at time 0.

[0025] Furthermore, the trajectory of the center of mass of the bipedal robot is optimized by using a high-order spline interpolation polynomial. The optimized specific formula is as follows:

[0026] x h (t) = a6t 6 +a5t 5 +a4t 4 +a3t 3 +a2t 2 +a1t+a0

[0027] z h (t) = z(t)

[0028] In the formula, x h (t) and z h (t) are the motion trajectories of the hip joint in the x and z directions, respectively. a0, a1, a2, a3, a4, a5, and a6 are polynomial coefficients, which are determined by the spring coefficient k, the damping coefficient B, the horizontal distance S1 between the hip joint and the ankle joint at the initial moment, the half-step length S, and the period T.

[0029] Furthermore, the zero moment point of the biped robot's motion process is calculated, and the specific formula is as follows:

[0030]

[0031] In the formula, zmp x is the position of the zero moment point in the x direction, and are the accelerations of the hip joint in the x and z directions respectively, and g is the acceleration due to gravity.

[0032] Furthermore, the fitness function, the specific formula is as follows:

[0033]

[0034] Where P is the fitness function, P1, P2, and P3 are the stability margin, motion speed, and energy consumption parts of the fitness function, respectively, D is the distance from the robot's ankle joint to the center of the sole, and τ is the ankle joint torque.

[0035] Furthermore, the servo controller is designed, and the specific formula is as follows:

[0036]

[0037] In the formula, F e and F i are the equality constraint force and inequality constraint force respectively, M is the inertia matrix, A is the constraint matrix, b is the equality constraint vector, F is the force in the unconstrained case, and r is the adjustable vector.

[0038] Due to the adoption of the above technical solution, the present invention has the following beneficial effects:

[0039] 1. An improved inverted pendulum model is adopted, which can fully utilize the advantages of the single-mass model while still reflecting the important characteristics of the bipedal robot and avoiding a series of errors and interference problems caused by oversimplification of the model.

[0040] 2. The present invention sets the key parameters of the improved inverted pendulum model to be variable, which is convenient for adjusting its dynamic characteristics. The improved particle swarm optimization algorithm is used to enable the bipedal robot to achieve a gait trajectory with the maximum stability margin, thereby ensuring the stability of its movement to the greatest extent.

[0041] 3. In order to achieve stable control of the bipedal robot under constraints, the present invention designs a robust constraint control method, which gives the motion equations of the constrained mechanical system that simultaneously considers equality constraints and inequality constraints, and makes the control input satisfy the Gaussian principle and the D'Alembert principle, thereby generating a moderate control force in the real world to meet the system performance.

[0042] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be achieved and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] The accompanying drawings of the present invention are as follows.

[0044] Figure 1 It is a schematic diagram of the overall process of the present invention.

[0045] Figure 2 A simplified schematic diagram of the bipedal robot structure.

[0046] Figure 3 Schematic diagram of the actual movement of the bipedal robot during a cycle.

[0047] Figure 4 To improve the particle swarm algorithm flow chart.

[0048] Figure 5 Schematic diagram of the servo controller algorithm flow chart. DETAILED DESCRIPTION

[0049] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0050] A robust constraint tracking control method for a biped robot based on parameter optimization, such as Figure 1 As shown, the specific steps are as follows:

[0051] S1. Simplify the structure of the bipedal robot.

[0052] In step S1, the left-right movement of the biped robot is not considered, but only its forward-backward movement is considered, that is, the center of mass of the robot only moves in the XOY plane. An improved inverted pendulum model is proposed based on the traditional linear inverted pendulum: a virtual spring and a virtual damper are added at the center of mass of the linear inverted pendulum, such as Figure 2 As shown in the figure. The robot center of mass motion based on the linear inverted pendulum model is relatively stiff, its motion trajectory is not smooth enough and will produce a large impact force, affecting the stability of the motion. The virtual spring of the improved inverted pendulum model can be used to simulate the compliant gait of the bipedal robot. The center of mass motion trajectory curve of the bipedal robot based on this model is smoother, with less rigid impact, which is more in line with the actual motion trajectory of the robot. The friction between the joints of the bipedal robot will also affect the center of mass motion trajectory. The virtual damper in the improved inverted pendulum model can offset this effect to a certain extent. By modifying the key parameters of the model, the dynamic characteristics of the inverted pendulum can be easily adjusted to minimize the interference caused by unmodeled dynamics, such as swinging legs and arms.

[0053] S2. Construct a dynamic model for the simplified structure.

[0054] By analyzing the proposed inverted pendulum model, q=θ is selected as the generalized coordinate to describe the inverted pendulum system, where θ represents the swing angle of the inverted pendulum. We first establish an unconstrained dynamic model, that is, the torque τ at the ankle joint is not considered. Since the virtual damper in the system cannot be regarded as an energy storage element like a virtual spring, additional generalized dissipative forces will be introduced. By analyzing the kinetic energy and potential energy of the inverted pendulum, the Lagrangian equation is established, thus completing the dynamic model of the robot. The Lagrangian dynamics formula is:

[0055]

[0056] Where L = K–U, K is kinetic energy, U is potential energy, and Q is the generalized dissipative force caused by the existence of virtual damping.

[0057] In the inverted pendulum model, the following relationship is satisfied between the inverted pendulum swing angle θ, the pendulum length l, and the arc s of the center of mass rotation:

[0058]

[0059] The kinetic energy of the system can be expressed as:

[0060]

[0061] The potential energy of the system can be expressed as:

[0062]

[0063] Where U1 and U2 represent the gravitational potential energy of the inverted pendulum and the elastic potential energy of the spring, respectively, and k is the stiffness of the virtual spring. Substituting L = K – U, we get:

[0064]

[0065] The dissipative force caused by virtual damping can be approximated by the following formula:

[0066]

[0067] B is the damping coefficient of the virtual damper.

[0068] Substituting the above formula into the Lagrange equation, we can get:

[0069]

[0070] S3. Plan the trajectory of the center of mass of the biped robot.

[0071] In step S3, when the inverted pendulum rotation angle is small, sinθ=θ can be approximately obtained, and the above equation is transformed into:

[0072]

[0073] Written in standard form as a second-order homogeneous linear differential equation with constant coefficients

[0074]

[0075] In order to facilitate subsequent writing, We can get:

[0076]

[0077] Solve this equation based on the structure of solutions to second-order homogeneous linear differential equations with constant coefficients:

[0078]

[0079] Generally speaking, the damping coefficient of the system will not be too large, so it is assumed here that p 2 -4q<0, so the structure of its solution is:

[0080] θ(t)=e αt [C1cos(βt)+C2sin(βt)]

[0081] Where C1 and C2 are arbitrary constants.

[0082]

[0083] In order to make the solution satisfy the initial conditions θ(0) and Substituting t = 0 into θ(t) and available:

[0084] θ(0)=C1

[0085]

[0086] Solved

[0087] C1=θ(0)

[0088]

[0089] In summary, the trajectory of the rotation angle θ is:

[0090]

[0091] According to the established inverted pendulum model, the motion trajectory of the center of mass can be easily obtained:

[0092]

[0093]

[0094] S4. Optimize the trajectory of the center of mass of the bipedal robot.

[0095] In step S4, when the robot moves at a low speed, the influence of inertia on the robot can be ignored, and the center of mass of the robot can be approximately regarded as coinciding with the hip joint, so the center of mass trajectory can be optimized by the hip joint trajectory calculation method. Since the trajectory of the hip joint, i.e., the center of mass, is calculated based on the inverted pendulum model, there is a certain difference compared with the actual movement situation, but it still has a high reference value. The trajectory points at certain moments can be selected as constraints. Combined with the constraints that the robot needs to follow during the actual movement process, a high-order polynomial can be obtained to accurately fit the motion trajectory of the hip joint. The motion trajectory curve obtained in this way is smoother and more in line with the actual motion trajectory of the robot. At the same time, it can also avoid the robot from generating a large impact force with the ground due to unreasonable acceleration at the moment of lifting and landing, affecting the stability of the movement.

[0096] The actual movement of the biped robot in a period T is as follows: Figure 3 As shown in the figure, the robot's left and right legs swing alternately with a constant step length. The half-step length of the movement is S. The horizontal distance between the hip joint and the ankle joint at the initial moment is S1. The coordinate system is established with the ankle joint as the coordinate origin. The motion trajectory should satisfy the following constraints:

[0097]

[0098] In order to make the trajectory curve smoother, the continuity condition must also be met

[0099]

[0100] During the robot's movement, the speed increases first and then decreases. According to the symmetry of the robot's gait, the acceleration values ​​at the initial moment and the end moment are equal and opposite in direction, so we can get

[0101]

[0102] According to the above four constraints, a cubic interpolation polynomial can be constructed. However, since this paper has obtained an approximate trajectory of the hip joint based on the inverted pendulum model, we can select The position, velocity, and acceleration at the moment are used as constraints, that is,

[0103]

[0104] The six-order interpolation polynomial of the hip joint motion trajectory in the x direction can be obtained from the seven constraints:

[0105] x h (t) = a6t 6 +a5t 5 +a4t 4 +a3t 3 +a2t 2 +a1t+a0

[0106] Among them, a0, a1, a2, a3, a4, a5, and a6 are polynomial coefficients, which are determined by the spring coefficient k, the damping coefficient B, the horizontal distance S1 between the hip joint and the ankle joint at the initial moment, the half-step length S, and the period T.

[0107] The motion trajectory of the hip joint in the z direction changes little, which has little effect on the stability of the robot's motion. Therefore, it does not need to be too precise and can still be expressed by z(t), that is,

[0108] z h (t) = z(t)

[0109] S5. Calculate the zero torque point of the bipedal robot's motion process according to the bipedal robot's motion trajectory along the optimized center of mass.

[0110] In step S5, the robot is modeled using Newton's equations and Euler's equations as follows:

[0111]

[0112] h is the trajectory of the center of mass, f i is the foot end contact force, p i Yes i The corresponding contact point, N is the angular momentum of the entire robot relative to the center of mass.

[0113] From the above two equations, we can get

[0114]

[0115] If the change of angular momentum is considered, it will bring a lot of inconvenience to the calculation. Here we assume that

[0116] On a flat surface, the coordinates of all contact points in the z-axis direction are So Newton's equations can be written in the form of components

[0117]

[0118] Dividing the above formula by the following formula, we can get

[0119]

[0120] because Expanding the above formula by components and simplifying it, we can get

[0121]

[0122] The right side of the equation is the definition of the pressure center on the xy plane, that is

[0123]

[0124] zmp x,y The zero moment point position

[0125] And because the gravitational acceleration g acts only in the z direction,

[0126] g x,y =0

[0127] Substituting into the above formula, we can get

[0128]

[0129] Considering only the x direction, we have

[0130]

[0131] Right now

[0132]

[0133] According to the calculation result in step S4, the position amp of the zero moment point in the x direction can be easily obtained. x .

[0134] S6. Construct a fitness function of the optimization algorithm based on the zero moment point.

[0135] In step S6, in order to make the movement of the bipedal robot as smooth as possible, we need to make the zero moment point (ZMP) as close to the midpoint of the supporting leg as possible. Here, the improved particle swarm optimization algorithm is used to iteratively search for the optimal values ​​of parameters k and B to achieve a larger stability margin, smaller energy consumption and a moderate movement speed.

[0136] The calculation of the stability margin takes two factors into consideration: one is the maximum value of the distance between the zero moment point and the midpoint of the support foot within a cycle, which reflects the limit state of the stability margin; the other is the average distance between the zero moment point and the midpoint of the support foot within a cycle, which reflects the average state of the stability margin.

[0137] Therefore, the following formula is established to reflect the stability of the robot during movement:

[0138]

[0139] Where D is the distance from the robot's ankle joint to the center of the sole

[0140] If only the stability of the robot is considered in the iteration of the particle swarm algorithm, it is very likely that the searched parameters k and B will be too large, causing the robot to be unable to operate. Therefore, the movement speed and energy loss are also considered in the fitness function.

[0141] Use the speed of the robot's hip joint to represent the robot's movement speed and establish the following formula

[0142] P2=6a6t 5 +5a5t 4 +4a4t 3 +3a3t 2 +2a2t+a1

[0143] The formula for calculating the robot's energy loss is as follows:

[0144]

[0145] Because the torque τ at the ankle joint is not considered in the model, τ=0 in the first cycle iteration; the torque value of the ankle joint in the next motion cycle will be calculated in the controller designed subsequently, so the τ value in the subsequent cycle iterations is not zero, but the torque value calculated by the controller.

[0146] Generally speaking, the particle swarm algorithm always maximizes the fitness function. The larger the P1 value, the smaller the stability margin of the robot. The larger the P3 value, the greater the energy consumption of the robot. Therefore, the fitness function P of the particle swarm algorithm can be written as

[0147]

[0148] S7. According to the fitness function, optimize and calculate the parameters of the biped robot.

[0149] In step S7, the characteristics of particles in the particle swarm algorithm are their positions and moving speeds in the solution space of the cost function. In the traditional particle swarm algorithm, when the i-th particle of the k-th generation in the d-dimensional space evolves to the k+1-th generation, the position of the particle is updated iteratively according to the following formula:

[0150]

[0151]

[0152]

[0153] in is the velocity of the i-th particle in the k-th generation in the d-dimensional space, is the position of the i-th particle in the k-th generation in the d-dimensional space, w is the inertia weight, c1 and c2 are two constants, rand1 and rand2 are two random parameters uniformly distributed in the range [0,1], is the optimal solution of the i-th particle in the previous k generations, g d (k) is the optimal solution of all particles in the previous k generations, v max is the boundary velocity of the particle.

[0154] The traditional particle swarm algorithm can easily lead to slow convergence in the later stages of iteration or fall into the trap of local convergence when iterating. In order to avoid these phenomena, we improve the traditional particle swarm algorithm to meet the needs of parameter optimization.

[0155] In the traditional particle swarm algorithm, only the global optimal particle is used to update the position of the candidate particle. The candidate particle is attracted by the optimal particle, thus ignoring the valuable information provided by other particles. In this case, the particles often fall into the local optimal trap instead of searching for a better new area. To solve this problem, we select the global optimal particle and other particles as the influencing source of the candidate particle. The specific method is as follows:

[0156] After each iteration, all n particles are sorted from large to small according to their fitness values, denoted as f s 1(k)>f s 2(k)>…>f s n(k),f s i(k) represents the fitness value of the i-th particle in the k-th iteration. We select λ particles from large to small according to the fitness value to update the position of candidate particle i. These λ particles are defined as the neighboring particles of candidate particle i, and the value of λ decreases linearly with the increase of the number of iterations, which is determined by the following formula:

[0157]

[0158] Where ir is the current iteration number and ir_max is the maximum iteration number.

[0159] The particle velocity iteration formula is improved to

[0160]

[0161] It represents the influence coefficient of neighboring particle j on candidate particle i in the kth iteration, which is proportional to the contribution and inversely proportional to the distance, and is defined as follows:

[0162]

[0163] is a ranking parameter, which indicates the contribution of neighboring particle j to candidate particle i. Its value depends on its relative fitness with all neighboring particles of candidate particle i and is defined as:

[0164]

[0165] is a distance parameter, which represents the Euclidean distance between neighboring particle j and candidate particle i in the d-dimensional solution space (the present invention takes d=2), and is defined by the following formula:

[0166]

[0167] The inertia weight w should not be fixed. In the early stage of iteration, w should be small to encourage particles to freely explore new areas. In the later stage of iteration, w should be large to promote particles to converge to the optimal solution as soon as possible. Here, a linearly changing weight is used. The formula for the change of w with the number of iterations is as follows:

[0168]

[0169] Usually take w max =0.9, w min =0.4

[0170] Since the two random parameters rand1 and rand2 are generated independently, sometimes both parameters will be too large or too small at the same time. If both are too large, the particles will be too dependent on their own experience and group experience, and will easily fall into a local optimal state; if both are too small, the particles will not fully utilize their own experience and group experience, and will be difficult to converge. Therefore, we need to design new random parameters based on rand1 and rand2.

[0171] In summary, the particle velocity iteration formula is:

[0172]

[0173] According to the improved particle swarm algorithm, the optimal values ​​of parameters k and B when the stability margin is maximum can be searched through the iterative search of the values ​​of S, S1, and T.

[0174] The improved particle swarm algorithm flow chart is as follows Figure 4 shown.

[0175] S8. Based on the optimized bipedal robot parameters, design a servo controller to control the bipedal robot.

[0176] In step S8, for an unconstrained mechanical system, its dynamic equation can be expressed as

[0177]

[0178] Among them, q is the generalized coordinate of the system, M is the positive definite inertia matrix, F is the generalized active force matrix, that is, the given force without any constraints, and t is the time. is the generalized acceleration of the mechanical system. To avoid confusion, we denote the acceleration of the unconstrained mechanical system as a. In the current unconstrained mechanical system,

[0179] However, robots are often subject to various constraints during actual motion. For example, tracking the desired motion trajectory to ensure that the expected functions are met during operation requires the introduction of equality constraints; in addition, the robot's joint angles need to be restricted to ensure the normal operation of the system, which requires the introduction of inequality constraints.

[0180] Assume that the robot is subject to the following c1 equality constraints and c2 inequality constraints:

[0181]

[0182] a i <f i (q) i ,i=1,2,…,c2

[0183] Assuming that the equality constraint is smooth enough, we let it take one or two derivatives with respect to time to obtain the equality constraint equation in matrix form:

[0184]

[0185] in is the constraint matrix, is a c1-dimensional vector

[0186] The system acceleration at this time q e Additional acceleration introduced for equality constraints

[0187] ​The existence of constraints will cause changes in the acceleration of the system. In Newtonian and Lagrangian mechanics, force is the only factor that can change the acceleration of the system, so the dynamic equation of the constrained system is written as

[0188]

[0189] and They are equality constraints and inequality constraints respectively.

[0190] Since the biped robot studied in this invention does not consider non-ideal constraints, it is only necessary to calculate the ideal constraint force vector. According to the dynamic equation expression proposed by Udwadia and Kalaba, it can be known that

[0191]

[0192] Where “+” represents the Moore-Penrose generalized inverse matrix

[0193] Then the additional acceleration introduced by the equality constraint is

[0194]

[0195] If a system introduces both equality constraints and inequality constraints at the same time, they may interfere with each other, resulting in the inability to satisfy both equality constraints and inequality constraints at the same time. Therefore, after the equality constraints are determined, we need to control the inequality constraints to ensure that the two do not interfere with each other. We express the additional acceleration introduced by the inequality constraints as

[0196] q i =(IA + A)r

[0197] Where r is a c2-dimensional adjustable vector.

[0198] The acceleration of a system subject to both equality and inequality constraints can be expressed as:

[0199]

[0200] Multiplying both sides by matrix A yields:

[0201]

[0202] and

[0203] AHr i =A(IA + A)r=(A-AA + A)r=(AA)r=0

[0204] therefore

[0205]

[0206] This means that the inequality constraints introduced into this structure do not affect the equality constraints. The inequality constraint force is

[0207] F i =Mq i =M(IA + A)r

[0208] From the established Lagrange equation, we can know that the unconstrained equation of the biped robot in generalized coordinates can be written as:

[0209]

[0210] Combined with system dynamics equations

[0211]

[0212] We can get:

[0213] M(q,t)=ml 2

[0214]

[0215] In order to satisfy the equality and inequality constraints, the torque applied to the ankle joint of the robot needs to be

[0216]

[0217] like Figure 5 As shown in Figure 2, the servo constraint control based on this algorithm can complete the robot's trajectory tracking control task while ensuring the maximum stability margin, and the torque can be adjusted in real time through r to meet the trajectory requirements.

[0218] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A robust constraint tracking control method for a biped robot based on parameter optimization, characterized in that: The specific method is as follows: Simplify the structure of bipedal robots; Construct dynamic models for simplified structures; Plan the trajectory of the center of mass of a bipedal robot; Optimize the trajectory of the center of mass of a bipedal robot; According to the biped robot's motion trajectory along the optimized center of mass, the zero moment point of the biped robot's motion process is calculated; Construct the fitness function of the optimization algorithm based on the zero moment point; According to the fitness function, the parameters of the biped robot are optimized and calculated.

2. The robust constraint tracking control method for a biped robot based on parameter optimization according to claim 1, characterized in that: The specific method is as follows: According to the optimized parameters of the bipedal robot, a servo controller is designed to control the bipedal robot.

3. The robust constraint tracking control method for a biped robot based on parameter optimization according to claim 1, characterized in that: The optimized biped robot parameters include: virtual damper damping coefficient and virtual spring stiffness.

4. The robust constraint tracking control method for a biped robot based on parameter optimization according to claim 1, characterized in that: Simplify the bipedal robot structure. The specific method is as follows: Based on the inverted pendulum, a virtual spring and a virtual damper are added at the mass center of the biped robot inverted pendulum.

5. The robust constraint tracking control method for a biped robot based on parameter optimization as claimed in claim 4, characterized in that: The specific formula of the constructed kinetic model is as follows: Where θ is the swing angle of the inverted pendulum, is the angular velocity of the inverted pendulum, is the angular acceleration of the inverted pendulum, l is the pendulum length, k is the stiffness of the virtual spring, B is the damping coefficient of the virtual damper, and m is the mass.

6. The robust constraint tracking control method for a biped robot based on parameter optimization as claimed in claim 5, characterized in that: The planned trajectory of the center of mass of the bipedal robot is as follows: In the formula, x(t) and z(t) are the trajectories of the center of mass in the x and z directions, α and β are the coefficients of the differential equation, and θ(0) and They are the initial conditions of the swing angle and the swing angular velocity, that is, their sizes at time 0.

7. The robust constraint tracking control method for a biped robot based on parameter optimization as claimed in claim 6, characterized in that: To optimize the trajectory of the center of mass of the bipedal robot, a high-order spline interpolation polynomial is used. The optimized specific formula is as follows: x h (t)=a6t 6 +a5t 5 +a4t 4 +a3t 3 +a2t 2 +a1t+a0 z h (t)=z(t) In the formula, x h (t) and z h (t) are the motion trajectories of the hip joint in the x and z directions, respectively. a0, a1, a2, a3, a4, a5, and a6 are polynomial coefficients, which are determined by the spring coefficient k, the damping coefficient B, the horizontal distance S1 between the hip joint and the ankle joint at the initial moment, the half-step length S, and the period T.

8. The robust constraint tracking control method for a biped robot based on parameter optimization as claimed in claim 7, characterized in that: Calculate the zero torque point of the biped robot's motion process. The specific formula is as follows: In the formula, zmp x is the position of the zero moment point in the x direction, and are the accelerations of the hip joint in the x and z directions respectively, and g is the acceleration due to gravity.

9. The robust constraint tracking control method for a biped robot based on parameter optimization as claimed in claim 8, characterized in that: Fitness function, the specific formula is as follows: Where P is the fitness function, P1, P2, and P3 are the stability margin, motion speed, and energy consumption parts of the fitness function, respectively, D is the distance from the robot's ankle joint to the center of the sole, and τ is the ankle joint torque.

10. The robust constraint tracking control method for a biped robot based on parameter optimization according to claim 2, characterized in that: Design the servo controller. The specific formula is as follows: In the formula, F e and F i are the equality constraint force and inequality constraint force respectively, M is the inertia matrix, A is the constraint matrix, b is the equality constraint vector, F is the force in the unconstrained case, and r is the adjustable vector.

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