Hexapod robot foot end trajectory optimization design method based on Kriging model

Abstract

The invention discloses a six-foot robot foot end trajectory optimization design method based on a Kriging model, and the method comprises the steps: taking the trafficability and joint energy consumption of a foot end trajectory as optimization targets, and building a multi-target optimization model of the foot end trajectory of a six-foot robot; the core of the method is that a Kriging agent model is adopted to construct an approximate mapping relation between control parameters and performance indexes, so that the efficiency and precision of optimization calculation are improved, and the operation complexity is reduced; the approximate optimization problem is solved, so that a Pareto leading edge formed by a non-dominated solution is obtained; an optimal compromise solution meeting trafficability and energy consumption indexes is screened out through target normalization processing, so that the adaptability and energy efficiency performance of the hexapod robot in actual engineering tasks are improved; according to the method, the optimal design solution of the foot end track of the hexapod robot can be efficiently obtained, so that the motion stability of the hexapod robot is improved, and the method has wide engineering application value in the field of robot dynamics.

Description

Technical Field

[0001] This invention belongs to the field of foot trajectory optimization for legged robots, specifically involving a foot trajectory optimization design method for hexapod robots based on the Kriging model. It can be widely applied to application scenarios such as foot trajectory planning and energy consumption optimization for multi-legged robots in complex terrain. Background Technology

[0002] Foot trajectory planning is a crucial step in achieving stable gait control for hexapod robots, directly determining their stability and mobility in complex terrain. Proper planning not only enhances walking ability in rugged environments but also effectively reduces joint drive loads and extends system lifespan. Therefore, foot trajectory planning holds immense research significance in the field of hexapod robot motion control.

[0003] The existing methods for optimizing hexapod robot foot trajectory planning still have the following shortcomings:

[0004] 1. For existing hexapod robot foot trajectory planning, foot trajectories are generally designed using parametric methods such as spline functions. Some studies have introduced evolutionary algorithms (such as genetic algorithms and particle swarm optimization) or deep learning methods to optimize trajectory parameters, thereby improving trajectory performance and task adaptability. However, these methods usually suffer from slow convergence speed and reliance on a large number of training samples, making it difficult to meet the real-time control and rapid deployment requirements of hexapod robots in dynamic environments.

[0005] 2. Existing hexapod robot foot trajectory planning commonly uses third- or fourth-order Bézier curves. However, the setting and adjustment of control points for higher-order Bézier curves mainly rely on manual experience, lacking systematic optimization methods. This manual design approach is cumbersome, inefficient, and struggles to achieve effective trade-offs among multiple performance objectives (such as foot mobility, joint energy consumption, and motion stability). Especially when dealing with multi-legged collaboration and high-dimensional task parameter spaces, traditional trajectory design methods struggle to balance accuracy and computational overhead, exhibiting weak parameter generalization capabilities.

[0006] 3. Regarding existing methods for optimizing hexapod robot foot trajectory planning, some methods employ nonlinear transformation functions to nonlinearly transform and correct each motion component of the hexapod robot foot trajectory, such as the patent "Foot Trajectory Optimization Method for Reducing Hydraulic Robot Flow Rate" with publication number CN106773680A. However, the introduction of nonlinear transformation functions increases the computational complexity of trajectory planning, requiring nonlinear transformation of each motion component, which involves more mathematical operations and function evaluation, placing higher demands on the real-time control system.

[0007] In summary, achieving efficient collaborative optimization of multi-objective performance in hexapod trajectory planning and improving the efficiency and rationality of trajectory parameter design are key issues that need to be addressed in the field of hexapod robot motion control. Foot trajectories often involve a comprehensive trade-off between multiple performance indicators, such as mobility, joint energy consumption, and motion stability, which places higher demands on the accuracy and efficiency of trajectory parameter design. Especially in high-dimensional design spaces, traditional methods struggle to simultaneously balance multiple objectives and ensure the feasibility of trajectory execution. Therefore, developing a hexapod robot foot trajectory optimization design method based on the Kriging model can not only significantly improve the gait adaptability and motion performance of hexapod robots in complex environments but also provide a new solution for efficient collaboration between trajectory planning and execution systems, possessing significant engineering application value. Summary of the Invention

[0008] To overcome the above problems, this invention proposes a method for optimizing the trajectory of the hexapod robot's foot based on the Kriging model.

[0009] The technical solution adopted by this invention to solve its technical problem is: a method for optimizing the trajectory of the foot end of a hexapod robot based on the Kriging model, characterized by the following steps:

[0010] Step 1: Establish a multi-objective optimization design problem for the trajectory of the hexapod's foot. The multi-objective optimization design problem for the trajectory of the hexapod's foot includes the following steps:

[0011] Step 11: Select the passability F1 and joint energy consumption F2 of the hexapod robot's foot end as optimization objectives to construct a multi-objective optimization model for the trajectory of the hexapod robot's foot end;

[0012] Step 12: Within the footwork space, set the control point parameter vector of the eleventh-order Bézier curve as the optimization independent variable X, and determine the range of values ​​for the independent variable X; different values ​​of X correspond to different Bézier curve trajectories, and their variable ranges are shown in formula (1):

[0013] X L <X<X R Formula (1)

[0014] In the above formula, X is the independent variable of the working space at the end of the hexapod robot's foot. L X is the lower bound of the optimization variables within the workspace of the hexapod's feet. R The upper bound of the optimization variables within the workspace of the hexapod's feet;

[0015] Step 13: Establish a multi-objective optimization model for the trajectory of the hexapod's feet. The specific expression is as follows:

[0016] min{-F1(X),F2(X)} Formula (2) st v x (X)-v x ≤0 v y (X)-v y ≤0 |v s (X)|-v≥0 a x (X)-a x ≤0 a y (X)-a y ≤0 X L <X<X R

[0017] In the above formula, v x For the maximum velocity constraint of the hexapod robot's swinging leg tip in the x-direction, v y To constrain the maximum velocity of the hexapod robot's swinging leg tip in the y-direction, a x For the maximum acceleration constraint of the hexapod robot's swinging leg tip in the x-direction, a y The constraint is the maximum acceleration of the hexapod's swinging leg tip in the y-direction, where v is the hexapod's velocity, and X is the maximum acceleration of the hexapod's swinging leg tip in the y-direction. L X R These are the lower and upper bounds of the optimization variables within the workspace of the hexapod's foot.

[0018] Step 2: Use Latin Hypercube Design (LHD) to collect training and test set sample points in the independent variable parameter design space X;

[0019] Step 3: Select and use the Kriging model to construct an approximate model for energy consumption calculation in the trajectory optimization problem, and reconstruct the multi-objective optimization problem described by formula (2) using formula (3):

[0020] st v x (X)-v x ≤0 v y (X)-v y ≤0 |v s (X)|-v≥0 a x (X)-a x ≤0 a y (X)-a y ≤0 X L <X<X R

[0021] In the above formula, v x For the maximum velocity constraint of the hexapod robot's swinging leg tip in the x-direction, v y To constrain the maximum velocity of the hexapod robot's swinging leg tip in the y-direction, a x For the maximum acceleration constraint of the hexapod robot's swinging leg tip in the x-direction, a y The constraint is the maximum acceleration of the hexapod's swinging leg tip in the y-direction, where v is the hexapod's velocity, and X is the maximum acceleration of the hexapod's swinging leg tip in the y-direction. L X R These are the lower and upper bounds of the optimization variables within the workspace of the hexapod's foot.

[0022] Step 4: Use the coefficient of determination (R²) 2 The mean absolute percentage error (MAPE) and mean absolute percentage error (MAPE) are used as accuracy evaluation metrics for the Kriging model, and their expressions are shown in the following formula:

[0023]

[0024]

[0025] In the above formula, t represents the number of samples collected in the test set; F2(X k () represents the actual response value obtained from the simulation of the test sample; This represents the predicted value obtained through the Kriging model;

[0026] Step 5: Obtain the Pareto front composed of non-dominated solutions by solving the approximate optimization problem;

[0027] Step 6: Select the optimal compromise solution that satisfies the throughput and energy consumption indicators through objective normalization, as shown in formulas (6) and (7):

[0028]

[0029]

[0030] In the above formula, F1 norm (X) and The objective function F1(X) in the Pareto front is respectively... The normalized value, and F1 min (X) and F1 max (X) represent the minimum and maximum values ​​of F1(X), respectively. and They are respectively The minimum and maximum values.

[0031] The beneficial effects of this invention are:

[0032] 1. Regarding point 1 in the background technology, this invention parametrically models the control points of the Bézier curve and introduces a Kriging surrogate model to construct the mapping relationship between control parameters and performance indicators. This effectively reduces the problem of relying heavily on manual trial and error and experience-based adjustments in traditional trajectory design, and significantly improves the automation level and design efficiency of trajectory optimization.

[0033] 2. Regarding point 2 in the background technology, the present invention can simultaneously consider multiple key performance indicators such as foot trajectory passability, joint energy consumption and motion stability, and achieve multi-objective collaborative optimization in complex terrain, thereby improving the overall task adaptability and environmental adaptability of the hexapod robot.

[0034] 3. Regarding point 3 in the background technology, this invention constructs an approximate model of the energy consumption of the hexapod robot's foot trajectory using a Kriging model for parameter optimization analysis, thus avoiding the problem of low efficiency caused by repeatedly simulating and solving the original high-fidelity model.

[0035] Note: The above designs are not in any particular order, and each one makes the present invention different from the prior art and a significant advancement.

[0036] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0037] Figure 1 This is a flowchart of the Bézier curve control point optimization design method based on the Kriging model of the present invention;

[0038] Figure 2 This invention relates to the eleventh-order Bézier curve and its control points;

[0039] Figure 3 This is a comparison of the eleventh-order Bézier curve before and after optimization;

[0040] Figure 4 The Pareto front obtained for optimization;

[0041] Figure 5 It optimizes the speed of the anterior and posterior knee joints;

[0042] Figure 6 It optimizes the acceleration of the anterior and posterior knee joints;

[0043] Figure 7 It optimizes the acceleration in the y-direction before and after;

[0044] Figure 8 It optimizes the acceleration in the z-direction before and after.

[0045] Figure 9 Optimize the speed of the anterior and posterior knee joints;

[0046] Figure 10 Optimize the acceleration of the anterior and posterior knee joints. Detailed Implementation

[0047] The general method of the present invention will now be described with reference to the accompanying drawings:

[0048] like Figure 1 As shown, a method for optimizing the trajectory of the hexapod robot's feet based on the Kriging model includes the following steps:

[0049] Step 1: Establish a multi-objective optimization design problem for the trajectory of the hexapod's foot. The multi-objective optimization design problem for the trajectory of the hexapod's foot includes the following steps:

[0050] Step 11: Select the passability F1 and joint energy consumption F2 of the hexapod robot's foot end as optimization objectives to construct a multi-objective optimization model for the trajectory of the hexapod robot's foot end;

[0051] Step 12: Within the footwork space, set the control point parameter vector of the eleventh-order Bézier curve as the optimization independent variable X, and determine the range of values ​​for the independent variable X; different values ​​of X correspond to different Bézier curve trajectories, and their variable ranges are shown in formula (1):

[0052] X L <X<X R Formula (1)

[0053] In the above formula, X is the independent variable of the working space at the end of the hexapod robot's foot. L X is the lower bound of the optimization variables within the workspace of the hexapod's feet. R The upper bound of the optimization variables within the workspace of the hexapod's feet;

[0054] Step 13: Establish a multi-objective optimization model for the trajectory of the hexapod's feet. The specific expression is as follows:

[0055] min{-F1(X),F2(X)} Formula (2) st v x (X)-v x ≤0 v y (X)-v y ≤0 |v s (X)|-v≥0 a x (X)-a x ≤0 a y (X)-a y ≤0 X L <X<X R

[0056] In the above formula, v xFor the maximum velocity constraint of the hexapod robot's swinging leg tip in the x-direction, v y To constrain the maximum velocity of the hexapod robot's swinging leg tip in the y-direction, a x For the maximum acceleration constraint of the hexapod robot's swinging leg tip in the x-direction, a y The constraint is the maximum acceleration of the hexapod's swinging leg tip in the y-direction, where v is the hexapod's velocity, and X is the maximum acceleration of the hexapod's swinging leg tip in the y-direction. L X R These are the lower and upper bounds of the optimization variables within the workspace of the hexapod's foot.

[0057] Step 2: Use Latin Hypercube Design (LHD) to collect training and test set sample points in the independent variable parameter design space X;

[0058] Step 3: Select and use the Kriging model to construct an approximate model for energy consumption calculation in the trajectory optimization problem, and reconstruct the multi-objective optimization problem described by formula (2) using formula (3):

[0059] st v x (X)-v x ≤0 v y (X)-v y ≤0 |v s (X)|-v≥0 a x (X)-a x ≤0 a y (X)-a y ≤0 X L <X<X R

[0060] In the above formula, v x For the maximum velocity constraint of the hexapod robot's swinging leg tip in the x-direction, v y To constrain the maximum velocity of the hexapod robot's swinging leg tip in the y-direction, a x For the maximum acceleration constraint of the hexapod robot's swinging leg tip in the x-direction, a y The constraint is the maximum acceleration of the hexapod's swinging leg tip in the y-direction, where v is the hexapod's velocity, and X is the maximum acceleration of the hexapod's swinging leg tip in the y-direction. L X R These are the lower and upper bounds of the optimization variables within the workspace of the hexapod's foot.

[0061] Step 4: Use the coefficient of determination (R²) 2 The mean absolute percentage error (MAPE) and mean absolute percentage error (MAPE) are used as accuracy evaluation metrics for the Kriging model, and their expressions are shown in the following formula:

[0062]

[0063]

[0064] In the above formula, t represents the number of samples collected in the test set; F2(X k () represents the actual response value obtained from the simulation of the test sample; This represents the predicted value obtained through the Kriging model;

[0065] Step 5: Obtain the Pareto front composed of non-dominated solutions by solving the approximate optimization problem;

[0066] Step 6: Select the optimal compromise solution that satisfies the throughput and energy consumption indicators through objective normalization, as shown in formulas (6) and (7):

[0067]

[0068]

[0069] In the above formula, F1 norm (X) and The objective function F1(X) in the Pareto front is respectively... The normalized value, and F1 min (X) and F1 max (X) represent the minimum and maximum values ​​of F1(X), respectively. and They are respectively The minimum and maximum values.

[0070] To further illustrate the present invention in detail, a specific embodiment will be used to describe the solution below. Taking the optimized design of the foot trajectory of a biomimetic hexapod robot as an example, and implementing the present invention based on its technical solution, detailed implementation methods and specific operation processes are given. However, the scope of protection of the present invention is not limited to the following example.

[0071] like Figure 2 The image shows the eleventh-order Bézier curve at the foot of the biomimetic hexapod robot and its control points, which are the target of the method of this invention. According to... Figure 1 The process shown is implemented. A method for optimizing the trajectory of the hexapod's feet based on the Kriging model is proposed, targeting... Figure 2 The specific steps for illustrating the eleventh-order Bézier curve and its control points at the foot of the biomimetic hexapod robot are as follows:

[0072] Step 1: Establish a multi-objective optimization design problem for the hexapod robot's foot trajectory. This requires considering both the foot's motion performance and energy efficiency. Therefore, two representative indicators are selected for modeling. By reasonably setting control point parameters (as shown in Table 1), the stability of the foot's motion during the take-off and landing phases (P0-P2 and P9-P11) and the reasonable change in velocity direction during the swing phase (P3-P8) are ensured. The multi-objective optimization design problem for the hexapod robot's foot trajectory includes the following steps:

[0073] Table 1. Parameters of Control Points for Bézier Curves

[0074] Step 11: Select the passability F1 of the hexapod robot's foot end and the joint energy consumption F2 as optimization objectives. F1 is defined as the percentage of the trajectory segment that is higher than the set height threshold h = 0.08m. F2 is the energy consumption data of each joint of the swinging leg in one swing phase under the conditions of step length S = 0.15m, period T = 1s, and speed v = 0.15m / s.

[0075] Step 12: Within the footwork space, set the control point parameter vector of the eleventh-order Bézier curve as the optimization independent variable X, and determine the range of values ​​for the independent variable X; different values ​​of X correspond to different Bézier curve trajectories, and their variable ranges are shown in formula (8):

[0076] X L <X<X R Formula (8)

[0077] In the above formula, X = [x1,x2,x3,x4,x5,x6,x7,x8,x9] T X L = [-0.05, -0.05, 0, 0.13, 0.15, 0.02, 0.05, 0.05, 0.02] T X R =[0,0.02,0.15,0.2,0.2,0.12,0.15,0.15,0.12] T

[0078] Step 13: Establish a multi-objective optimization model for the trajectory of the hexapod's feet. The specific expression is as follows:

[0079] min{-F1(X),F2(X)} Formula (9) st v x (X)-0.5≤0 v y (X)-0.5≤0 |vs (X)|-0.15≥0 a x (X)-2≤0 a y (X)-8≤0 X L <X<X R

[0080] In the above formula, the maximum velocity constraint of the hexapod's swing leg tip in the x-direction is 0.5 m / s, the maximum velocity constraint of the hexapod's swing leg tip in the y-direction is 0.5 m / s, and the maximum acceleration constraint of the hexapod's swing leg tip in the x-direction is 2 m / s². 2 The maximum acceleration of the hexapod robot's swinging leg tip in the y-direction is constrained to 8 m / s². 2 v represents the hexapod robot's movement speed, which is 0.15 m / s. This speed can be modified based on subsequent simulations. X L X R These are the lower and upper bounds of the optimization variables within the workspace of the hexapod's foot.

[0081] Step 2: Use Latin Hypercube Design (LHD) to collect training and test set sample points in the independent variable parameter design space X;

[0082] Step 3: After constructing an approximate model for energy consumption calculation in the trajectory optimization problem using the Kriging model, the multi-objective optimization problem described by formula (9) can be reconstructed using formula (10) as follows:

[0083] st v x (X)-0.5≤0 v y (X)-0.5≤0 |v s (X)|-0.15≥0 a x (X)-2≤0 a y (X)-8≤0 X L <X<X R

[0084] In the above formula, the maximum velocity constraint of the hexapod's swing leg tip in the x-direction is 0.5 m / s, the maximum velocity constraint of the hexapod's swing leg tip in the y-direction is 0.5 m / s, and the maximum acceleration constraint of the hexapod's swing leg tip in the x-direction is 2 m / s². 2 The maximum acceleration of the hexapod robot's swinging leg tip in the y-direction is constrained to 8 m / s². 2v represents the hexapod robot's movement speed, which is 0.15 m / s. This speed can be modified based on subsequent simulations. X L X R These are the lower and upper bounds of the optimization variables within the workspace of the hexapod's foot.

[0085] Step 4: Use the coefficient of determination (R²) 2 The mean absolute percentage error (MAPE) and the mean absolute percentage error (MAPE) are used as accuracy evaluation indicators for the Kriging model, and their expressions are shown in the following formula;

[0086]

[0087]

[0088] In the above formula, t represents the number of samples collected in the test set; F2(X k () represents the actual response value obtained from the simulation of the test sample; This represents the predicted value obtained through the Kriging model;

[0089] Step 5: Obtain the Pareto front composed of non-dominated solutions by solving the approximate optimization problem;

[0090] Step 6: Select the optimal compromise solution that satisfies the throughput and energy consumption indicators through objective normalization, as shown in formulas (13) and (14):

[0091]

[0092]

[0093] In the above formula, F1 norm (X) and The objective function F1(X) in the Pareto front is respectively... The normalized value, and F1 min (X) and F1 max (X) represent the minimum and maximum values ​​of F1(X), respectively. and They are respectively The minimum and maximum values;

[0094] As shown in Table 2 and Figure 4 It can be seen that the passability of the optimized eleventh-order Bézier curve is 41.96%, which means that 41.96% of the trajectory exceeds 0.08m. Although it is lower than before optimization, most of the middle part of the foot swings forward exceeds 0.08m, so it still has good passability.

[0095] From Table 1 and Figure 5 and6 It can be seen that the total energy consumption of a single leg of the hexapod robot in one swing phase cycle after optimization is 5.34J, which is 0.46J lower than before optimization. The knee joint velocity and acceleration of leg 3 are lower than before optimization, especially in the latter half when the foot is about to land. This shows that the optimization can effectively reduce joint vibration when the foot lands, increase the service life of the joint, and improve the stability of the hexapod robot during movement.

[0096] Depend on Figure 7 , Figure 8 , Figure 9 , Figure 10 It can be seen that the speed of the hexapod robot's feet in the y-direction is significantly reduced when they lift and fall after optimization. This can effectively reduce the impact of the hexapod robot's legs when switching between the swinging and supporting phases. At the same time, the peak speeds in both the y and z directions are reduced. The acceleration in the y-direction is greatly reduced and becomes S-shaped after optimization. In addition to reducing the impact between the feet and the ground, this is closer to the movement characteristics of animals and helps to improve the stability of the hexapod robot's movement and its environmental adaptability.

[0097] Table 2 Optimization Results

[0098] The above detailed description is a specific description of feasible embodiments of the present invention. These embodiments are not intended to limit the patent scope of the present invention. All equivalent implementations or modifications that do not depart from the present invention should be included in the patent scope of this case.

Claims

1. A method for optimizing the trajectory of the hexapod robot's feet based on the Kriging model, characterized in that, Includes the following steps: Step 1: Establish a multi-objective optimization design problem for the trajectory of the hexapod's foot. The multi-objective optimization design problem for the trajectory of the hexapod's foot includes the following steps: Step 11: Select the robot's foot passability F1 and joint energy consumption F2 as optimization objectives to construct a multi-objective optimization model for the hexapod robot's foot trajectory; Step 12: Within the footwork space, set the control point parameter vector of the eleventh-order Bézier curve as the independent variable X, and determine its range of values; different values ​​of X correspond to different Bézier curve trajectories, and their range of variables is shown in formula (1): X L <X<X R Formula (1) In the above formula, X is the independent variable of the working space at the end of the hexapod robot's foot. L X is the lower bound of the optimization variables within the workspace of the hexapod's feet. R The upper bound of the optimization variables within the workspace of the hexapod's feet; Step 13: Establish a multi-objective optimization model for the trajectory of the hexapod's feet. The specific expression is as follows: min{-F1(X),F2(X)} formula (2) st v x (X)-v x ≤0v y (X)-v y ≤0|v s (X)|-v≥0 a x (X)-a x ≤0a y (X)-a y ≤0 X L <X<X R In the above formula, v x For the maximum velocity constraint of the hexapod robot's swinging leg tip in the x-direction, v y To constrain the maximum velocity of the hexapod robot's swinging leg tip in the y-direction, a x For the maximum acceleration constraint of the hexapod robot's swinging leg tip in the x-direction, a y The constraint is the maximum acceleration of the hexapod's swinging leg tip in the y-direction, where v is the hexapod's velocity, and X is the maximum acceleration of the hexapod's swinging leg tip in the y-direction. L X R These are the lower and upper bounds of the optimization variables within the workspace of the hexapod's foot. Step 2: Use Latin Hypercube Design (LHD) to collect training and test set sample points in the independent variable parameter design space X; Step 3: Select the Kriging model to construct an approximate model for energy consumption calculation in the trajectory optimization problem, and reconstruct the multi-objective optimization problem described by formula (2) using formula (3): st v x (X)-v x ≤0v y (X)-v y ≤0|v s (X)|-v≥0 a x (X)-a x ≤0a y (X)-a y ≤0 X L <X<X R In the above formula, v x For the maximum velocity constraint of the hexapod robot's swinging leg tip in the x-direction, v y To constrain the maximum velocity of the hexapod robot's swinging leg tip in the y-direction, a x For the maximum acceleration constraint of the hexapod robot's swinging leg tip in the x-direction, a y The constraint is the maximum acceleration of the hexapod's swinging leg tip in the y-direction, where v is the hexapod's velocity, and X is the maximum acceleration of the hexapod's swinging leg tip in the y-direction. L X R These are the lower and upper bounds of the optimization variables within the workspace of the hexapod's foot. Step 4: Use the coefficient of determination (R²) 2 The mean absolute percentage error (MAPE) and mean absolute percentage error (MAPE) are used as accuracy evaluation metrics for the Kriging model, and their expressions are shown in the following formula: In the above formula, t represents the number of samples collected in the test set; F2(X k () represents the actual response value obtained from the simulation of the test sample; This represents the predicted value obtained through the Kriging model; Step 5: Obtain the Pareto front composed of non-dominated solutions by solving the approximate optimization problem; Step 6: Select the optimal compromise solution that satisfies the throughput and energy consumption indicators through objective normalization, as shown in formulas (6) and (7): In the above formula, F1 norm (X) and The objective function F1(X) in the Pareto front is respectively... The normalized value, and F1 min (X) and F1 max (X) represent the minimum and maximum values ​​of F1(X), respectively. and They are respectively The minimum and maximum values.

2. The method for optimizing the trajectory of the hexapod robot's foot end based on the Kriging model according to claim 1, characterized in that, The basic steps for constructing the Kriging approximation model in step 2 are as follows: Step 1: The Gaussian function is used as the covariance function. The covariance function of Z(x) is shown in formula (8). Cov[Z(x i ),Z(x j )] = σ 2 R(θ,x i ,x j ) Equation (8) Step 2: Use the known response values ​​of the sample points and the distance between the prediction point and the sample points to infer the response value of the prediction point. Its general form is expressed by formula (9). In the above formula, is the Kriging approximation; G(x,β) is the global approximation function; β is the regression coefficient; f i Z(x) is typically a first- or second-order polynomial function; Z(x) is a random distribution function with a mean of 0 and a variance of σ. 2 ; Step 3: Express F2(X) using an approximate model as shown in Equation (10): In the above formula, A Kriging approximation model for calculating the energy consumption of the hexapod robot's foot trajectory.

3. The method for optimizing the trajectory of the hexapod robot's foot end based on the Kriging model according to claim 1, characterized in that, In step 11, foot passability F1 is defined as the percentage of the segment in the trajectory that is higher than the set height threshold h to the whole Bezier curve; joint energy consumption F2 is the energy consumption data of each joint of the swinging leg in one swing phase under the conditions of set step length S, period T, and speed v.

4. The method for optimizing the trajectory of the hexapod robot's foot end based on the Kriging model according to claim 1, characterized in that, In step 5, the Pareto front, composed of non-dominated solutions, is obtained, and a multi-objective genetic algorithm is used to solve the approximate optimization problem.

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