A parameter optimization-based robust constraint tracking control method for biped robots

Abstract

The present application relates to biped robot control technical field, especially relate to a kind of robust constraint tracking control method of biped robot based on parameter optimization.The present application uses improved inverted pendulum model, while making full use of the advantages of single mass model, still can reflect the important characteristics of biped robot, avoid a series of errors and interference problems due to model oversimplification.The key parameters of the improved inverted pendulum model are set to be variable in the present application, which is convenient for adjusting its dynamic characteristics.The present application designs a kind of robust constraint control method, considers the motion equation of the limited mechanical system of equality constraint and inequality constraint, and makes the control input satisfy Gauss principle and d'Alembert principle, so as to produce moderate control force in the real world to meet system performance.

Description

Technical Field

[0001] This invention relates to the field of bipedal robot control technology, and in particular to a robust constraint tracking control method for bipedal robots based on parameter optimization. Background Technology

[0002] Bipedal robots are a class of robots that mimic human walking and standing. With their humanoid design, flexible movement capabilities, and high degree of autonomy, they exhibit unique advantages in many fields. To maintain stability during bipedal robot walking and simplify gait planning and balance control, the inverted pendulum model has been applied to bipedal robot gait design. It views 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 calculations. This model has been widely used in bipedal robot research and has achieved good control results.

[0003] However, the traditional inverted pendulum model still has some shortcomings. First, the center-of-mass trajectory obtained from the traditional inverted pendulum model is not smooth enough, resulting in an overly stiff gait and significant impact force with the ground during actual movement, which does not meet the requirements of a compliant gait. Second, the traditional inverted pendulum model simplifies the complex bipedal robot into a point mass and a massless linkage system. This oversimplification ignores the interference from unmodeled parts such as arms and legs, as well as the interactions within the robot's joints. This may lead to an inaccurate or unsuitable gait in practical applications, causing the final motion to deviate from the reference motion and affecting the robot's stability.

[0004] Furthermore, robotic systems are not simple, unconstrained systems. During actual motion, they are subject to a series of constraints, such as structural constraints imposed by their own structure, or functional constraints introduced to fulfill a specific intended function. These constraints can be further categorized into equality constraints and inequality constraints. The additional control forces introduced by inequality constraints can hinder the performance of equality constraints, increasing the complexity of the control problem and posing additional challenges to control design. Existing robust control research mainly focuses on trajectory tracking problems, i.e., equality constraints, while research on inequality constraints is not in-depth. There remains no effective solution for deriving and analyzing the motion of mechanical systems under both types of constraints simultaneously. Summary of the Invention

[0005] This invention discloses a robust constraint tracking control method for bipedal robots based on parameter optimization, the specific method of which is as follows:

[0006] Simplify the structure of bipedal robots;

[0007] A dynamic model is constructed for the simplified structure;

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

[0009] Optimize the center-of-gravity motion trajectory of the bipedal robot;

[0010] Calculate the zero-torque point of the bipedal robot's motion process based on the optimized center-of-mass trajectory of the bipedal robot;

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

[0012] The parameters of the bipedal robot are optimized based on the fitness function.

[0013] Furthermore, the specific methods are as follows:

[0014] Based on the optimized parameters of the bipedal robot, a servo controller was designed to control the bipedal robot.

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

[0016] Furthermore, the structure of the bipedal robot is simplified, and the specific methods are as follows:

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

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

[0019]

[0020] In the formula, θ is the swing angle of the inverted pendulum. The angular velocity of the inverted pendulum's swing. Let be the angular acceleration of the inverted pendulum, l be the pendulum length, k be the stiffness of the virtual spring, B be the damping coefficient of the virtual damper, and m be the mass.

[0021] Furthermore, the calculated trajectory of the bipedal robot's center of mass 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, respectively; α and β are the coefficients of the differential equation; and θ(0) and β are the coefficients of the differential equation. These are the initial conditions for the swing angle and the swing angular velocity, respectively, i.e., their magnitudes at time 0.

[0025] Furthermore, the motion trajectory of the bipedal robot's center of mass is optimized using a higher-order spline interpolation polynomial. The optimized 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) represents the motion trajectory 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 and ankle joints at the initial moment, the half-step length S, and the period T.

[0029] Furthermore, the zero-torque point during the bipedal robot's motion is calculated using the following formula:

[0030]

[0031] In the formula, zmp x The position of the zero torque point in the x-direction. and α and β 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 is specifically formulated as follows:

[0033]

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

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

[0036]

[0037] In the formula, F e and F i Let M be the equality constraint force and the inequality constraint force, respectively. M is the inertia matrix, A is the constraint matrix, b is the equality constraint vector, F is the force under the unconstrained condition, and r is the adjustable vector.

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

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

[0040] 2. This invention sets the key parameters of the improved inverted pendulum model to be variable, which facilitates the adjustment of its dynamic characteristics. The improved particle swarm optimization algorithm enables the bipedal robot to achieve a gait trajectory with the maximum stability margin, thus ensuring the stability of its motion to the greatest extent.

[0041] 3. In order to achieve stable control of bipedal robots under constraints, this invention designs a robust constraint control method. This method gives the motion equation of a constrained mechanical system that simultaneously considers equality constraints and inequality constraints, and makes the control input satisfy Gauss's principle and d'Alembert's principle, thereby generating an appropriate control force in the real world to meet the system performance requirements.

[0042] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0043] The accompanying drawings of this invention are described below.

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

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

[0046] Figure 3 This is a schematic diagram of the actual motion of a bipedal robot within a cycle.

[0047] Figure 4 Flowchart for improving the particle swarm optimization algorithm.

[0048] Figure 5 This is a schematic diagram of the servo controller algorithm flow. Detailed Implementation

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

[0050] A robust constraint tracking control method for bipedal robots 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 motion of the bipedal robot is not considered; only its forward-backward motion is taken into account, meaning the robot's center of mass only moves within 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, the motion of the robot's center of mass in the linear inverted pendulum model is rather stiff, its trajectory is not smooth enough, and it generates a large impact force, affecting the stability of the motion. The virtual spring in the improved inverted pendulum model can be used to simulate the compliant gait of a bipedal robot. Based on this model, the trajectory curve of the bipedal robot's center of mass is smoother, with less rigid impact, and more consistent with the robot's actual motion trajectory. Friction between the joints of the bipedal robot also affects the trajectory of the center of mass; the virtual damper in the improved inverted pendulum model can offset this effect to some extent. By modifying the key parameters of the model, the dynamic characteristics of the inverted pendulum can be easily adjusted, minimizing the interference caused by unmodeled dynamics, such as leg and arm swing.

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

[0054] By analyzing the proposed inverted pendulum model, q = θ is chosen as the generalized coordinate system to describe the inverted pendulum system, where θ represents the angle of the pendulum's swing. We first establish an unconstrained dynamic model, neglecting the torque τ at the ankle joint. Since the virtual damper in the system cannot be considered an energy storage element like a virtual spring, additional generalized dissipative forces are introduced. Through the analysis of the kinetic and potential energy of the inverted pendulum, the Lagrange equation is established, thus completing the robot's dynamic model. The Lagrange dynamic 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 pendulum's swing angle θ, pendulum length l, and the radian s through which the center of mass rotates satisfy the following relationship:

[0058]

[0059] The system's kinetic energy can be expressed as:

[0060]

[0061] The system potential energy 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 into L = K – U, we get:

[0064]

[0065] The dissipation force caused by virtual damping can be approximately obtained 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 get:

[0069]

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

[0071] In step S3, when the rotation angle of the inverted pendulum is small, sinθ = θ can be approximated, and the above equation becomes:

[0072]

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

[0074]

[0075] To facilitate subsequent writing, We can obtain:

[0076]

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

[0078]

[0079] Generally speaking, the damping coefficient of the system is not very large, so we assume p here. 2 -4q<0, therefore 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 satisfy the initial condition θ(0) and Substituting t=0 into θ(t) and available:

[0084] θ(0)=C1

[0085]

[0086] Solving

[0087] C1=θ(0)

[0088]

[0089] In summary, the trajectory of the turning angle θ can be obtained as follows:

[0090]

[0091] Based on the established inverted pendulum model, the trajectory of the center of mass can be easily obtained:

[0092]

[0093]

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

[0095] In step S4, when the robot's movement speed is low, the influence of inertia on the robot can be ignored, and the robot's center of mass can be approximated as coinciding with the hip joint. Therefore, the center of mass trajectory can be optimized using the hip joint trajectory calculation method. Since the trajectory of the hip joint, i.e., the center of mass, is calculated based on an inverted pendulum model, it differs somewhat from the actual movement, but still has high reference value. Trajectory points at certain moments can be selected as constraints. Combined with the constraints that the robot needs to follow during actual movement, a high-order polynomial can be obtained to accurately fit the hip joint's movement trajectory. This results in a smoother trajectory curve that better matches the robot's actual movement trajectory. It also avoids excessive impact forces on the ground due to unreasonable acceleration at the moment the robot lifts and lowers its feet, which would affect the stability of the movement.

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

[0097]

[0098] To make the trajectory curve smoother, the continuity condition must also be met.

[0099]

[0100] During the robot's movement, its velocity first increases and then decreases. Due to the symmetry of the robot's gait, the initial and final acceleration values ​​are equal but opposite in direction. Therefore, we can obtain...

[0101]

[0102] Based on the above four constraints, a cubic interpolation polynomial can be constructed. However, since this paper has already obtained an approximate trajectory of the hip joint based on the inverted pendulum model, a selection can be made from this approximate trajectory. The position, velocity, and acceleration at any given time are used as constraints, i.e.

[0103]

[0104] The sixth-order interpolation polynomial of the hip joint's 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] Where 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 and ankle joints at the initial moment, the half-step length S, and the period T.

[0107] The hip joint's trajectory in the z-direction changes relatively little and has little impact on the robot's motion stability; therefore, it does not need to be overly precise and can still be represented by z(t), i.e.

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

[0109] S5. Calculate the zero-torque point of the bipedal robot's motion process based on the optimized center-of-mass trajectory of the bipedal robot.

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

[0111]

[0112] h is the centroid locus, f i It is the contact force at the foot, p i It is f i The corresponding contact point, N is the angular momentum of the entire robot relative to its center of mass.

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

[0114]

[0115] Considering the change in angular momentum would introduce many inconveniences to the calculation; therefore, we assume...

[0116] On a flat surface, for all contact points in the z-axis direction... Therefore, Newton's equations can be written in component form.

[0117]

[0118] Dividing the above equation by the following equation yields

[0119]

[0120] because Expanding and simplifying the above expression by its components, we get...

[0121]

[0122] The right side of the equation defines the center of pressure in the xy plane, i.e.

[0123]

[0124] zmp x,y Zero torque point position

[0125] Since the gravitational acceleration g only acts in the z-direction,

[0126] g x,y =0

[0127] Substituting into the above equation, we can obtain

[0128]

[0129] Considering only the x-direction, we have

[0130]

[0131] Right now

[0132]

[0133] Based on the calculation results in step S4, the position of the zero torque point in the x-direction can be easily determined. x .

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

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

[0136] The calculation of stability margin considers two factors: first, the maximum distance between the zero-moment point and the midpoint of the support foot within a cycle, which reflects the limit state of stability margin; and second, the average distance between the zero-moment point and the midpoint of the support foot within a cycle, which reflects the average state of stability margin.

[0137] Therefore, the following formula is established to reflect the stability of the robot during its motion.

[0138]

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

[0140] If only the stability of the robot is considered in the iteration of the particle swarm optimization algorithm, the searched parameters k and B may be too large, causing the robot to fail to run. Therefore, the fitness function also considers the motion speed and energy loss.

[0141] Using the velocity of the robot's hip joint to represent the robot's motion velocity, the following formula is established.

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

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

[0144]

[0145] Since the model does not yet consider the torque τ at the ankle joint, τ = 0 in the first cycle iteration; the controller designed later will calculate the torque value of the ankle joint in the next motion cycle, so the value of τ in subsequent cycle iterations will not be zero, but rather the torque value calculated by the controller.

[0146] Generally, particle swarm optimization (PSO) always maximizes the fitness function. A larger P1 value results in a smaller stability margin for the robot, while a larger P3 value leads to higher energy consumption. Therefore, the fitness function P of PSO can be written as...

[0147]

[0148] S7. Optimize the calculation of the parameters of the bipedal robot based on the fitness function.

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

[0150]

[0151]

[0152]

[0153] in Let be the velocity of the i-th particle in the k-th generation in d-dimensional space. Let be the position of the i-th particle in the k-th generation in d-dimensional space, w be the inertial weight, c1 and c2 be two constants, and rand1 and rand2 be two random parameters uniformly distributed in the range [0,1]. For the optimal solution of the i-th particle in the first k generations, g d (k) represents the optimal solution for all particles in the first k generations, v max The boundary velocity of the particle.

[0154] Traditional particle swarm optimization (PSO) algorithms are prone to slow convergence in the later stages of iteration or getting trapped in local convergence. To avoid these issues, we improve upon the traditional PSO algorithm to better suit the requirements of parameter optimization.

[0155] In traditional particle swarm optimization (PSO) algorithms, only the globally optimal particle is used to update the positions of candidate particles. Candidate particles are attracted to the optimal particle, thus ignoring valuable information provided by other particles. In this situation, particles often get trapped in local optima instead of searching for better new regions. To address this issue, we select the globally optimal particle, along with other particles, as the influence source for candidate particles. The specific method is as follows:

[0156] After each iteration, all n particles are sorted in descending order of their fitness values, denoted as f. s 1(k)>f s 2(k)>…>f s n(k), f s Let i(k) represent the fitness value of the i-th particle in the k-th iteration. We select λ particles in descending order of 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 number of iterations, determined by the following formula.

[0157]

[0158] In the formula, 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] Let represent the influence coefficient of neighboring particle j on candidate particle i in the k-th iteration. It is directly proportional to the contribution and inversely proportional to the distance, and is defined as follows:

[0162]

[0163] Let be the ranking parameter, representing 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] Let be the distance parameter, representing the Euclidean distance between neighboring particle j and candidate particle i in the d-dimensional solution space (d=2 in this invention), defined by the following formula:

[0166]

[0167] The inertia weight w should not be fixed. In the early stages of iteration, w should be small to encourage particles to freely explore new regions; in the later stages of iteration, w should be large to promote convergence to the optimal solution as quickly as possible. Here, a linearly varying weight is used, and the formula for w changing with the number of iterations is as follows:

[0168]

[0169] Usually, w is taken. max =0.9, w min =0.4

[0170] Since the two random parameters rand1 and rand2 are generated independently, sometimes both parameters can be too large or too small simultaneously. If both are too large, the particle will rely too much on its own and the group's experience, easily getting trapped in a local optimum; if both are too small, the particle will not fully utilize its own and the group's experience, making convergence difficult. Therefore, we need to design new random parameters based on rand1 and rand2.

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

[0172]

[0173] Based on the improved particle swarm optimization algorithm described above, the optimal values ​​of parameters k and B, which maximize the stability margin, can be found by iteratively searching the values ​​of S, S1, and T.

[0174] The flowchart of the improved particle swarm optimization algorithm is as follows: Figure 4 As 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] Where q is the generalized coordinate of the system, M is the positive definite inertia matrix, F is the generalized active force matrix, i.e. the force given without any constraints, and t is time. Let be the generalized acceleration of the mechanical system. To avoid confusion, we will denote the acceleration of an unconstrained mechanical system as 'a'. In this current unconstrained mechanical system,

[0179] However, robots are often subject to various constraints during actual movement. For example, tracking the desired trajectory to ensure the expected function is met during operation requires the introduction of equality constraints; in addition, it is necessary to limit the joint angles of the robot to ensure the normal operation of the system, which requires the introduction of inequality constraints.

[0180] Suppose 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 the equality constraints are sufficiently smooth, we can obtain the matrix form of the equality constraint equations by taking their first or second derivative with respect to time.

[0184]

[0185] in For the constraint matrix, A c1-dimensional vector

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

[0187] ​The presence of constraints causes changes in the system's acceleration. In Newtonian and Lagrange mechanics, force is the only factor that can change the system's acceleration; therefore, the dynamic equations of a constrained system are written as follows:

[0188]

[0189] and These are equality constraint forces and inequality constraint forces, respectively.

[0190] Since the bipedal robot studied in this invention does not consider non-ideal constraints, it is only necessary to calculate the ideal constraint force vector. This can be seen from the dynamic equations proposed by Udwadia and Kalaba.

[0191]

[0192] Where "+" represents the Moore-Penrose generalized inverse matrix.

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

[0194]

[0195] If a system introduces both equality and inequality constraints simultaneously, they may interfere with each other, preventing both constraints from being satisfied at the same time. Therefore, after determining the equality constraints, we need to manage the inequality constraints to ensure they do not interfere with each other. We represent 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 simultaneously subject to equality and inequality constraints can be expressed as:

[0199]

[0200] Multiplying both sides by matrix A, we get:

[0201]

[0202] and

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

[0204] therefore

[0205]

[0206] This means that introducing inequality constraints of this structure will not affect equality constraints, and the inequality constraint force is...

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

[0208] From the established Lagrange equations, the unconstrained equations of the bipedal robot in generalized coordinates can be written as:

[0209]

[0210] Combining system dynamics equations

[0211]

[0212] We can obtain:

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

[0214]

[0215] To satisfy the equality and inequality constraints, the torque applied to the robot's ankle joint needs to be...

[0216]

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

[0218] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do 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 parameter-optimization-based robust constraint tracking control method for biped robots, characterized by, The specific method is as follows: Simplify the structure of the biped robot; Construct a dynamics model for the simplified structure; Plan a center of mass trajectory of the biped robot; Optimize the center of mass trajectory of the biped robot; According to the optimized center of mass trajectory, calculate the zero moment point of the biped robot during movement; According to the zero moment point, construct a fitness function of the optimization algorithm; According to the fitness function, optimize the parameters of the biped robot; According to the optimized parameters of the biped robot, design a servo controller to control the biped robot; Simplify the structure of the biped robot, the specific method is as follows: On the basis of the inverted pendulum, add a virtual spring and a virtual damper at the center of mass of the inverted pendulum of the biped robot; The constructed dynamics model has the following specific formula: wherein is the inverted pendulum swing angle, is the inverted pendulum swing angular velocity, is the inverted pendulum swing angular acceleration, is the pendulum length, is the virtual spring stiffness, is the virtual damper damping coefficient, is the mass; The planned center of mass trajectory of the biped robot has the following specific formula: wherein, and are the trajectories of the center of mass in the x and z directions, respectively, and are the coefficients of the differential equations, and are the initial conditions of the swing angle and the swing angular velocity, i.e. their values at time 0. The optimized center of mass trajectory of the biped robot uses high-order spline interpolation polynomials, and the specific formula after optimization is as follows: In the formula, With Respectively, the motion trajectory of the hip joint in the x direction and the z direction, 、 、 、 、 、 、 The polynomial coefficients are determined by the spring coefficient k, the damping coefficient B, the horizontal distance between the hip joint and the ankle joint at the initial time , Half step length S, period T; The specific formula for calculating the zero moment point of the biped robot during movement is as follows: In the formula, The position of the zero torque point in the x-direction. and , where are the accelerations of the hip joint in the x and z directions, respectively, and g is the acceleration due to gravity; The fitness function has the following specific formula: wherein, is the fitness function, , , are the stability margin, the motion velocity and the energy consumption part in the fitness function, respectively, is the distance from the robot ankle to the center of the foot sole, is the ankle torque; The specific formula for designing the servo controller is as follows: wherein and are the equality and inequality constraint forces, respectively, is the inertia matrix, is the constraint matrix, is the equality constraint vector, is the unconstrained force, is the adjustable vector.

2. The parameter-optimization-based robust constraint tracking control method for biped robots as claimed in claim 1, wherein, The optimized parameters of the biped robot include the damping coefficient of the virtual damper and the stiffness of the virtual spring.

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