A multi-constraint based multi-objective optimization design method for hexapod robot

Abstract

A kind of multi-constraint-based hexapod robot multi-objective optimization design method, the present application solves the problem that the optimization method of foot type robot does not consider real field terrain conditions, which can cause task failure due to drive overload, structural interference or foot end skidding when foot type robot moves in field environment.The present application uses terrain passability constraints to combine the terrain conditions to be executed by hexapod robot, terrain indicators and geometric parameters to be optimized to calculate the optimal body size of hexapod robot under terrain passability constraints, and then according to the leg size constraints of hexapod robot, the minimum values of joint peak stress and joint peak power under leg size constraints are used as optimization objectives to obtain the optimal leg size by using non-dominated sorting algorithm.The optimal structure of hexapod robot is obtained.The present application optimizes the body size and leg structure size of hexapod robot by terrain adaptability constraints and multiple real physical constraints.The present application belongs to the field of robot design.

Description

Technical Field

[0001] This invention relates to the field of robot design, and more specifically to a multi-objective optimization design method for a hexapod robot based on multiple constraints. Background Technology

[0002] In recent years, with advancements in sensing, control, and execution technologies, legged robots have seen initial applications in scenarios such as inspection, security, and logistics. However, existing commercially available legged robots are mostly geared towards light-load tasks, lacking stability and dynamic performance in high-load, high-interference outdoor environments. Most existing legged robot design methods employ a modular strategy, first determining the overall structural layout and then independently optimizing the leg mechanisms. These methods focus on optimizing the leg structure layer, such as adjusting leg length ratios, link dimensions, drive layout, or improving foot trajectory to reduce energy consumption. However, these methods often neglect the coupling relationship between the leg structure and the overall robot layout, lacking a systematic holistic optimization perspective, often leading to parameter mismatches between structure and mechanism. In practical applications, the reachability and load capacity of the legs are affected not only by leg length and link arrangement but also by system parameters such as body size, center of gravity height, and leg spacing. The selection of body size parameters directly affects the center of gravity distribution and workspace range, while the leg link ratio determines the joint load and power requirements. Therefore, existing optimization methods often suffer from insufficient space utilization, degraded dynamic performance, abnormal joint stress, or excessive actuation limits, restricting the reliability and applicability of robots in field operations. Furthermore, most existing optimization designs only consider geometric or kinematic constraints, often assuming idealized operating environments that fail to fully reflect real-world terrain conditions. In practical applications, robots need to adapt to complex terrains such as slopes, cross slopes, ravines, and vertical obstacles. Each working condition places different demands on the robot's posture stability, foot reachability, and force distribution. The actual operation of hexapod robots is limited by physical constraints such as joint travel, actuator power, mechanism interference, and foot-ground contact conditions. Ignoring these constraints in the design may result in theoretically superior optimization results and feasible simulations, but in actual tasks, problems such as actuation overload, structural interference, or foot slippage may lead to task failure. Summary of the Invention

[0003] In order to address the problem that optimization methods for legged robots fail to consider real-world terrain conditions, which may lead to task failure due to drive overload, structural interference, or foot slippage when the legged robot is moving and operating in the field, this invention proposes a multi-objective optimization design method for hexapod robots based on multiple constraints.

[0004] The technical solution adopted in this invention is:

[0005] It includes the following steps:

[0006] S1. Determine the geometric parameters to be optimized for the hexapod robot;

[0007] S2. Determine the kinematic relationship between the foot and leg joints of the hexapod robot;

[0008] S3. Construct terrain passability constraints. Given the terrain conditions, terrain indices, and range of geometric parameters to be optimized for the hexapod robot, calculate the optimal body size of the hexapod robot under the terrain passability constraints in conjunction with S2.

[0009] S4. Based on S1 and S3, set the leg size constraints of the hexapod robot, with the optimization objective being to minimize the peak joint force and peak joint power under the leg size constraints. The optimal leg size is obtained using a non-dominated sorting algorithm.

[0010] The optimal size and structure of the hexapod robot are obtained based on S3 and S4.

[0011] The beneficial effects of this invention are as follows:

[0012] This invention optimizes the body dimensions and leg structure dimensions of a hexapod robot by comprehensively considering multiple constraints, including terrain mobility constraints and real-world physical constraints. It proposes an optimization method that simultaneously coordinates the overall structural layout and leg configuration of the hexapod robot, overcoming the performance bottlenecks of traditional decoupled designs. The constraints of typical outdoor terrain ensure reliable mobility and adaptability under complex working conditions. Furthermore, this invention integrates geometric, kinematic, dynamic, and physical constraints to guarantee the feasibility and stability of the optimized design in actual manufacturing and operation. While ensuring stability and mobility, it reduces joint stress and power consumption, enabling efficient and stable operation of the heavy-duty hexapod robot in outdoor tasks and improving task completion rates. Attached Figure Description

[0013] Figure 1 This is a flowchart of the present invention;

[0014] Figure 2 This is a schematic diagram showing the structural layout and geometric dimensions of a hexapod robot;

[0015] Figure 3 yes Figure 2 Side view;

[0016] Figure 4 This is a schematic diagram of the leg structure of a hexapod robot;

[0017] Figure 5 This is a simplified diagram of the leg mechanism of a hexapod robot;

[0018] Figure 6 This is a schematic diagram of the range of motion of the leg joints of a hexapod robot;

[0019] Figure 7 It is the constraint of the center of mass during the process of a hexapod robot climbing a slope;

[0020] Figure 8 It is the constraint of the center of mass of the hexapod robot during the process of crossing the cross slope;

[0021] Figure 9 This is a schematic diagram of the interference constraint on the thickness of the leg link. Figure 1 ;

[0022] Figure 10 This is a schematic diagram of the interference constraint on the thickness of the leg link. Figure 2 ;

[0023] Figure 11 This is a schematic diagram of collision constraints when the knee joint is above the ground. Detailed Implementation

[0024] Specific implementation method one: Combining Figures 1-11 This embodiment describes a multi-objective optimization design method for a hexapod robot based on multiple constraints. It includes the following steps:

[0025] S1. Since the hexapod robot needs to perform material transportation and complex environment movement in the field, this invention selects a decoupled leg configuration for the hexapod robot. Based on the leg structure characteristics of the hexapod robot, the geometric parameters to be optimized are determined. The geometric parameters to be optimized include the longitudinal leg spacing of the hexapod robot. lateral leg spacing The distance between the center of gravity and the extreme position of the leg workspace Leg mounting height Footwork space dimensions Length of thigh (link AE) Length of the lower leg (connecting rod CE) Scaling ratio of the legs ,like Figures 2 to 5 As shown.

[0026] S2. Based on the leg structure and kinematic relationships of the hexapod robot, the kinematic relationship between the foot and the leg joint is obtained. The specific process is as follows:

[0027] like Figure 5 and Figure 6 As shown, for the scaled-down leg configuration of a hexapod robot, the first... The generalized coordinates of a leg joint space can be represented as:

[0028] (1)

[0029] in, For joint variables, Horizontal joint exist The position of the axis Vertical joint exist The position of the axis Transverse joint around rotational joint Angle of rotation This indicates transpose.

[0030] Based on the scaling properties of the leg mechanism, the foot coordinates The position vector in the foot coordinate system can be represented as:

[0031] (2)

[0032] in, It represents the multiplication sign.

[0033] Based on equations (1) and (2), and according to the kinematic relationship, the foot coordinates can be obtained. The position vector in the base coordinate system is as follows:

[0034] (3)

[0035] in, The coordinates of the foot in the base coordinate system are shown. The y-coordinate of the origin of the foot coordinate system in the base coordinate system. This represents the z-axis coordinate of the origin of the foot coordinate system in the base coordinate system. The base coordinate system is the coordinate system of the connection between the leg and the body.

[0036] Foot trajectory of a six-legged robot:

[0037] This invention employs a fifth-order polynomial function to plan the foot trajectory, ensuring that position, velocity, and acceleration remain continuous and smooth throughout the gait cycle. This planning method helps achieve shock-free and vibration-free motion, thereby reducing shock and vibration phenomena in the hexapod robot's mechanical system. The motion trajectories of the horizontal and vertical joints can be obtained through joint inverse kinematics, as follows:

[0038] (4)

[0039] in, Horizontal joint Position coordinates throughout the gait cycle, The coordinates of the foot's position throughout the gait cycle. Vertical joint Position coordinates throughout the gait cycle, , This refers to the gait cycle.

[0040] Dynamic equations:

[0041] Given the foot trajectory and kinematic relationships, the dynamic equations of the hexapod robot need to be solved to obtain the joint forces required to achieve movement. Based on the Euler-Lagrange formulas, the system dynamic model can be established as follows:

[0042] (5)

[0043] in, For the quality matrix, The second derivative of the generalized coordinate vector. For generalized coordinate vectors, The first derivative of the generalized coordinate vector. For the Coriolis force matrix, The gravity term matrix, To drive the joint to bear force, For Jacobian matrices, For foot-ground contact force.

[0044] S3. Construct terrain traversal constraints, and provide the terrain conditions and corresponding terrain indices for the hexapod robot to execute, as well as the range of geometric parameters to be optimized. Combine this with S2 to calculate the longitudinal leg spacing of the hexapod robot under the terrain traversal constraints. lateral leg spacing The distance between the center of gravity and the extreme position of the leg workspace Leg mounting height and foot end working space dimensions The specific process is as follows:

[0045] S31. Given the terrain conditions to be performed by the hexapod robot, including slopes, cross slopes, gullies, and obstacles, the terrain indices include the hexapod robot's maximum slope climbing angle. Maximum cross slope crossing angle Maximum gully spanning distance and the distance across the greatest obstacle And the longitudinal leg spacing of a six-legged robot lateral leg spacing The distance between the center of gravity and the extreme position of the leg workspace Leg mounting height Footwork space dimensions The range of values ​​is shown in Table 1 for ease of calculation. and Take those that are equal in size.

[0046] Table 1

[0047]

[0048] S32. Based on S31, construct terrain traversability constraints. These constraints are primarily related to the hexapod robot's ability to traverse terrain during its movement. In the process of searching for a suitable solution set of geometric parameters to be optimized, the hexapod robot's movement must meet the design requirements of climbing slopes, traversing cross slopes, crossing ditches, and overcoming obstacles. Therefore, this invention collectively refers to these four terrain conditions as terrain traversability constraints, namely:

[0049] (6)

[0050] in, for Reference value, for Reference value, for Reference value, for The reference value. From equation (6), it can be seen that... and The design of the hexapod robot is not only closely related to its body dimensions, but also affected by the position of its center of mass and its posture. Therefore, in order to analyze the impact of the hexapod robot's center of mass adjustment process on the body dimension design results, this invention introduces a set of intermediate variables. , The longitudinal offset distance of the centroid. For the height of the center of mass, The pitch angle of the center of mass. The lateral offset distance of the centroid. Let be the roll angle of the center of mass. Based on the intermediate variable, the constraint relationship between the range of change in the center of mass height and the geometric dimensions of the aircraft can be derived.

[0051] (a) Constraints on the center of mass adjustment range during the process of a hexapod robot climbing a slope:

[0052] When the hexapod's legs are at the top of the workspace, the height of its center of mass from the ground is at its minimum. Take the minimum value. Conversely, when the hexapod's legs are at the bottom of the workspace, the hexapod's center of mass height is... Take the maximum value. Therefore, we can obtain:

[0053] (7)

[0054] longitudinal offset distance of centroid The range of values ​​is limited by the horizontal distance of the workspace, and the constraints are as follows:

[0055] (8)

[0056] When the hexapod robot's hind legs are at the bottom of the workspace and its front legs are at the top, the hexapod robot's center of mass pitch angle is... Take the maximum value, center of mass pitch angle The range of values ​​for is as follows:

[0057] (9)

[0058] Next, through analysis and Changes The influence of this leads to the following inequalities:

[0059] (10)

[0060] Combining equations (7) to (10) yields the constraints on the values ​​of the adjustable parameters of the centroid of the hexapod robot during slope climbing, such as... Figure 7 As shown.

[0061] (ii) Constraints on the range of center of mass pose adjustment for a hexapod robot traversing a cross slope:

[0062] Figure 8 Intermediate variables are given The value range of is related to the dimensions of the hexapod robot. When the hexapod robot traverses a cross slope, the vertical position of its center of mass is related to the upper and lower limits of its leg workspace. Therefore, The range of variation can still be represented by equation (7).

[0063] When considering only the rolling motion (pitch, roll, yaw) of the hexapod robot, The value of is related to the position of the support points on both sides of the cross slope. It can be calculated based on geometric relationships. The range of variation is as follows:

[0064] (11)

[0065] When adjusting the lateral offset distance of the center of gravity, the swing angle of the outriggers cannot exceed the range limit of the lateral joint. Therefore, the following relationship exists:

[0066] (12)

[0067] in, Let M be the minimum rotation angle of the rotary joint. This represents the maximum rotation angle of the rotary joint M.

[0068] Similarly, and Constrained The values ​​of and the relationship between the three are as follows:

[0069] (13)

[0070] In summary, the range of the center of mass pose adjustment of the hexapod robot during the process of crossing the cross slope is constrained by equations (11) to (13).

[0071] When crossing ravines and obstacles, the centroid takes the maximum value under geometric constraints.

[0072] S33. Calculate the longitudinal leg spacing of the hexapod robot while simultaneously satisfying the terrain passability constraints, the minimum value of the hexapod robot's envelope volume, and the maximum value of the leg workspace, based on the terrain passability constraints. lateral leg spacing The distance between the center of gravity and the extreme position of the leg workspace Leg mounting height and foot end working space dimensions The specific process is as follows:

[0073] S331. Based on the terrain passability constraint (Equation (6)), calculate the longitudinal leg spacing of the hexapod robot under the terrain passability constraint. lateral leg spacing The distance between the center of gravity and the extreme position of the leg workspace Leg mounting height and foot end working space dimensions The initial value.

[0074] S332. The body volume parameters of the hexapod robot directly reflect the overall structural compactness of the robot. A smaller volume not only helps reduce energy consumption and improve mobility, but also enhances the hexapod robot's passability in narrow and rugged environments. Therefore, this invention calculates the envelope volume of the hexapod robot based on the preliminary values ​​in S331. for:

[0075] (14)

[0076] S333, based on the footwork space dimensions of S331 The preliminary values ​​are used to calculate the working space range of the hexapod robot's leg structure.

[0077] The leg workspace reflects the reach of the feet in space and directly determines the gait flexibility of a hexapod robot. A larger workspace facilitates diverse movement patterns and enhances the robot's adaptability to unstructured terrain. Simultaneously, a larger reachable area allows for broader control strategies, contributing to both stability and movement efficiency. Leg structure workspace range The expression is:

[0078] (15)

[0079] in, These are the weighting coefficients.

[0080] S334, satisfying the envelope volume of the hexapod robot At the minimum value, when equation (15) is negative, the range of the workspace accessible by the leg structure is larger, thus obtaining the maximum value of the workspace range of the hexapod robot's legs. The envelope volume of the hexapod robot is used as the basis for this calculation. Minimum value and leg workspace range The maximum value is the optimization target. The longitudinal leg spacing of the hexapod robot is gradually optimized according to equations (6) to (15). lateral leg spacing The distance between the center of gravity and the extreme position of the leg workspace Leg mounting height and foot end working space dimensions The value of is used to obtain the longitudinal leg spacing that simultaneously satisfies equations (6), (14), and (15). lateral leg spacing The distance between the center of gravity and the extreme position of the leg workspace Leg mounting height and foot end working space dimensions Thus, the optimal body size of the hexapod robot was obtained.

[0081] Under typical terrain conditions, this invention aims to minimize the body volume of the hexapod robot and maximize the working space coverage of its legs. By combining terrain passability and posture stability constraints, it obtains the optimized result of the global structural layout of the hexapod robot.

[0082] S4. Based on the geometric parameters of the hexapod robot's legs in S3 and the geometric parameters to be optimized, set the leg size constraints for the hexapod robot. The optimization objective is to minimize the peak force and peak power of the leg joints under these constraints. The optimal thigh length is obtained using the Non-Dominated Sort Algorithm (NSGA-II). calf length Scaling ratio of the legs The specific process is as follows:

[0083] The optimization framework for leg structure focuses on finding the optimal leg design parameters, including thigh length. calf length Scaling ratio of the legs This invention utilizes foot trajectory parameters As input conditions, a dynamic performance index is constructed with the optimization objectives of minimizing joint forces and minimizing joint power. Further considerations are given to workspace constraints, knee joint interference limitations, actuator parameter limitations, and geometric constraints. The optimal body dimensions from the first level of optimization are used as the dimensional constraints for this stage. Furthermore, the design result should satisfy the necessity constraint that the hexapod robot can walk smoothly. Under these constraints, the Non-Dominated Sorting Algorithm (NSGA-II) is used to solve the problem, ultimately obtaining the leg configuration with optimal performance within the known workspace. The optimization process will be analyzed in detail below.

[0084] First, considering the basic requirements of the hexapod robot's legs in terms of geometry, motion, control, and mechanics, the constraints for the leg optimization process are determined from the perspectives of geometric dimensions, workspace, kinematic feasibility, actuator stroke and speed limits, and interference constraints. These constraints include geometric constraints, workspace constraints, kinematic constraints, joint amplitude constraints, foot-ground force constraints, and interference constraints.

[0085] 1. Geometric constraints

[0086] Geometric constraints reflect the basic configuration of a mechanical structure and determine the rationality of the optimization result selection. In the leg mechanism of a hexapod robot, the dimensions of the leg links must satisfy a triangular configuration; otherwise, a closed-loop chain cannot be formed. That is, during the movement of the leg, the three sides AB, AD, and BD can always form a complete triangle. Therefore, the geometric constraint expression is:

[0087] (16)

[0088] in, Horizontal joint exist The position of the axis Vertical joint exist The position of the axis.

[0089] 2. Workspace constraints

[0090] The first level of optimization has determined the range of the footworkspace size, reflecting the basic capabilities required for the hexapod robot to walk and support itself in complex terrain. Therefore, the leg structure in the second level of optimization must ensure that its motion capabilities fully cover this workspace. To ensure the hexapod robot has omnidirectional motion capabilities, this invention defines the actuator's motion range as symmetrical about its origin, thus:

[0091] (17)

[0092] in, , , , Horizontal joint exist The maximum distance the axis moves. Horizontal joint exist The minimum distance the axis moves. Vertical joint exist The maximum distance the axis moves. Vertical joint exist The minimum distance the axis moves. This represents the maximum rotation angle of the rotary joint M. This represents the minimum rotation angle of the rotary joint M.

[0093] 3. Joint amplitude limiting constraint

[0094] When a hexapod robot walks on complex terrain, such as climbing slopes or overcoming obstacles, it typically needs to adopt specific gaits to ensure its mobility. These postures can cause the actuator parameters to approach or even exceed their limits. As the core actuator for foot trajectory tracking and posture control, the actuator's maximum stroke determines the reach of the joints, its speed capability directly affects the dynamic response of trajectory tracking, and the forces applied to the joints affect the hexapod robot's mobility and load-bearing capacity. Ignoring these physical limitations during optimization may result in generated foot trajectories exceeding the actuator's motion capabilities, leading to problems such as tracking errors, torque overload, or even mechanical damage. Limiting the actuator's range, speed, and forces yields the following:

[0095] (18)

[0096] in, This represents the lower limit of the joint range. For joint variables, This represents the upper limit of the joint range. For generalized joint velocity, This is the upper limit of joint velocity. For generalized joint forces, This represents the upper limit of joint force.

[0097] 4. Kinematic constraints

[0098] The generation of foot trajectories is typically task-oriented, while the actual execution of these trajectories depends on the kinematic characteristics of the leg mechanism. Without constraints, the foot may fail to reach the intended position or cause the joints to exceed their range of motion. Introducing kinematic constraints ensures both the feasibility and control stability of the trajectory, thereby achieving effective coordination between structural design and motion control. This invention uses the foot trajectory of a hexapod robot walking rapidly on flat ground as the design input. During flat ground walking, the lateral joints of the hexapod robot remain stationary, thus yielding the following kinematic constraints:

[0099] (19)

[0100] in, The coordinates are for the foot end.

[0101] 5. Foot-ground force constraint

[0102] In complex terrain or high-speed motion, properly constraining the magnitudes of normal and tangential forces can effectively prevent overload and insufficient local support, enhancing the overall robustness and safety of the hexapod robot. Therefore, this invention introduces physical constraints related to foot-ground interaction forces during the optimization process. For terrains with different physical properties, a unified normal contact force model can be used to represent them:

[0103] (20)

[0104] in, For normal contact force, This is the stiffness coefficient. The subsidence index is 1. The damping coefficient is... The subsidence index is 2. This is the speed index.

[0105] The tangential mechanical model can be represented as follows:

[0106] (twenty one)

[0107] in, For tangential contact force, This is the cohesion coefficient. The radius of the foot tip, It is the internal friction angle. This is the tangential displacement. Shear displacement modulus This is the bulldozing resistance coefficient. It is the hyperbolic tangent function. This is the bulldozing resistance index.

[0108] Given the maximum normal subsidence and maximum tangential displacement Then, the corresponding foot-ground force constraint conditions are as follows:

[0109] (twenty two)

[0110] in, The contact force vector, The contact force is the tangential force along the x-direction. The tangential contact force is along the y-direction. The upper limit of contact force, for The transpose of .

[0111] 6. Interference constraints

[0112] To avoid physical collisions or spatial overlaps between components during the movement of the hexapod robot, this invention introduces interference constraints during the optimization design process. In the leg design, this invention analyzes the reachable workspace and mobility of the hexapod robot's leg structure. When performing multi-condition motion analysis on the hexapod robot, only the motion performance at the mechanism level is considered. However, actual leg components have thickness, and interference may occur between links when they move to their extreme positions. Figure 9 As shown, when the vertical slider A and the horizontal slider B are closest... At this time, the distance between link AE and link BF can be expressed as follows:

[0113] (twenty three)

[0114] in, The distance between AE and BF is the minimum distance between vertical slider A and horizontal slider B. For connecting rods, The angle between AE and BD. This is the vertical distance from slider A to the origin.

[0115] when At times, such as Figure 10 As shown, the vertical slider A is the furthest from the horizontal slider B. Similarly, the distance between connecting rods AE and BF can be calculated as follows:

[0116] (twenty four)

[0117] in, The distance between AE and BF is the maximum distance between the vertical slider A and the horizontal slider B. The angle between AE and BD. This represents the maximum horizontal travel. This represents the maximum vertical travel distance.

[0118] Equations (23) and (24) represent different positions of the leg mechanism within the same dimension, and the thickness of the leg link is affected by... and The minimum value is a constraint. It's easy to see that the thickness of the thigh link is greatest when the two are equal. Therefore, the following relationship can be obtained:

[0119] (25)

[0120] When the legs of a hexapod robot are in the support phase, the position of the knee joints should be restricted. Without this restriction, the legs may "land on their knees" during the support phase, affecting gait stability and compromising the robot's posture control and terrain adaptability. Therefore, as... Figure 11 As shown, this invention introduces the geometric constraint of "knee higher than foot" in the optimization of the leg structure, which helps to ensure the rationality of the mechanism's movement and obtains the corresponding inequality constraints:

[0121] (26)

[0122] in, For horizontal drive motor displacement, This is for vertical drive motor displacement.

[0123] While satisfying the aforementioned six constraints, this invention focuses on improving the energy efficiency and actuator driving capability of a hexapod robot during actual operation. Joint driving force and power, as core indicators for measuring actuator performance, directly relate to factors such as motor selection, driving efficiency, and load-bearing capacity. Therefore, this invention optimizes leg structure parameters to minimize joint force and power, effectively reducing energy consumption and joint load, while also improving the stability and reliability of the hexapod robot during movement in complex environments.

[0124] Peak joint stress :

[0125] In the optimization of the leg structure of a hexapod robot, lower joint forces help reduce the load requirements of the actuators and decrease mechanical wear in the transmission system. Furthermore, reduced joint forces also contribute to improving the stability and response accuracy of the motion control system. Therefore, this invention takes minimizing the peak joint forces as the objective of the second level of optimization, as shown in the following expression:

[0126] (27)

[0127] in, To optimize weights, For joint force vectors, For gait period, This refers to the robot's runtime.

[0128] Peak joint power :

[0129] Joint power reflects the matching relationship between joint forces and speeds, and is a direct indicator for evaluating the energy consumption level of a drive system. Minimizing joint power can significantly reduce energy consumption and extend endurance, making it suitable for field operations with high runtime requirements. In this invention, the joint power of a hexapod robot can be expressed in the following form:

[0130] (28)

[0131] in, For joint velocity vectors, for The transpose of .

[0132] In hexapod robot design, increasing the body size is beneficial for improving stability and workspace coverage, but it also significantly increases overall mass and inertia, leading to increased joint driving force and energy consumption. Conversely, excessive pursuit of a compact design can easily result in insufficient workspace at the feet, affecting its ability to cross obstacles and adjust posture. Therefore, this invention proposes a two-layer optimization design method for the coordinated optimization of the overall size and leg dimensions of a hexapod robot. The first layer, while satisfying terrain passability constraints (such as climbing slopes, climbing cross slopes, crossing ravines, and obstacle crossing capabilities), aims to make the body structure of the hexapod robot as compact as possible and maximize the workspace. The second layer, within the leg workspace determined in the first layer, optimizes the leg mechanism parameters by combining leg dynamic performance and physical feasibility constraints, thereby constructing a complete and task-oriented hexapod robot design method.

[0133] To achieve the optimal trade-off between structural compactness, workspace coverage, and dynamic performance in a hexapod robot, this invention employs a multi-objective optimization algorithm to systematically solve for key design parameters. The process is as follows: Figure 1As shown, traditional single-objective optimization methods often struggle to simultaneously address the complex interrelationships between multiple performance metrics. Multi-objective optimization, however, can establish a balance between different objectives, generating a set of representative Pareto optimal solutions and providing more options for robot design. Considering that hexapod robots need to simultaneously meet multiple performance requirements in practical applications, such as minimizing volume, maximizing footwork space, and optimizing drive efficiency, a non-dominated sorting genetic algorithm (NSGA-II) based on evolutionary principles is selected as the optimization framework. Combined with the objective function and constraints in this invention, the robot's structure and mechanism parameters are efficiently solved, thereby achieving multi-performance collaborative optimization design.

[0134] Example

[0135] The objective of this invention is to find the optimal solution for a set of dimensional parameters. Firstly, in the first layer of optimization, parameters including the longitudinal leg spacing are selected. lateral leg spacing The distance between the center of gravity and the extreme position of the leg workspace Leg mounting height and foot workspace dimensions The structural parameters, including those mentioned above, are used as design variables. The input condition is the terrain passability index. With the optimization objectives of minimizing the envelope volume of the hexapod robot and maximizing the workspace of its legs, terrain adaptability constraints are constructed by combining the passability requirements of typical terrains such as slopes, cross slopes, ditches, and obstacles. Simultaneously, design constraints such as geometric relationships and posture stability are introduced. A non-dominated sorting genetic algorithm is used to solve the above objectives and constraints to obtain the optimal combination of body design parameters at the structural level.

[0136] Subsequently, using the optimal workspace range obtained in the first optimization layer as a known condition, the second optimization layer is entered. In this layer, the thigh length of the leg is used as the basis for further optimization. calf length and scaling ratio To optimize the variables, the joint variable is the displacement of the horizontal drive motor. and vertical drive motor displacement The input condition for the second-level optimization process is the trajectory parameters of the foot. A dynamic performance index is constructed with joint force and joint power as optimization objectives. Further consideration is given to workspace constraints, knee joint interference limitations, actuator parameter limitations, and geometric constraints to form a complete leg design. Under these constraints, the Non-Dominated Sort Algorithm (NSGA-II) is used to solve the problem, ultimately obtaining the leg configuration with optimal performance within the known workspace. The pseudocode for this optimization process is shown below:

[0137]

[0138] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A multi-objective optimization design method for a hexapod robot based on multiple constraints, characterized in that: It includes the following steps: S1. Determine the geometric parameters to be optimized for the hexapod robot, including the longitudinal leg spacing of the hexapod robot. lateral leg spacing The distance between the center of gravity and the extreme position of the leg workspace Leg mounting height Footwork space dimensions Thigh length calf length Scaling ratio of the legs ; S2. Determine the kinematic relationship between the foot and leg joints of the hexapod robot. The specific process is as follows: Based on the leg structure and kinematic relationship of the hexapod robot, the kinematic relationship between the foot and the leg joint of the hexapod robot is obtained as follows: （1） in, The coordinates of the foot in the base coordinate system are shown. Transverse joint around rotational joint Angle of rotation Horizontal joint exist The position of the axis Vertical joint exist The position of the axis The y-coordinate of the origin of the foot coordinate system in the base coordinate system. The z-axis coordinate of the origin of the foot coordinate system in the base coordinate system. Indicates the multiplication sign; S3. Construct terrain passability constraints. Given the terrain conditions, terrain indices, and range of geometric parameters to be optimized for the hexapod robot, combine with S2 to calculate the optimal body size of the hexapod robot that satisfies the terrain passability constraints. The specific process is as follows: S31. The terrain conditions to be performed by the hexapod robot include slopes, cross slopes, ditches, and obstacles. Terrain parameters include the hexapod robot's maximum slope climbing angle. Maximum cross slope crossing angle Maximum gully spanning distance and the distance across the greatest obstacle ; The range of geometric parameters to be optimized includes the longitudinal leg spacing of the hexapod robot. lateral leg spacing The distance between the center of gravity and the extreme position of the leg workspace Leg mounting height Footwork space dimensions The range of values; S32. Construct terrain accessibility constraints based on S31. The expression for the terrain accessibility constraints is: （2） in, The longitudinal offset distance of the centroid. For the height of the center of mass, The pitch angle of the center of mass. for Reference value, The lateral offset distance of the centroid. The roll angle of the center of mass. for Reference value, for Reference value, for Reference value; S33. Calculate the longitudinal leg spacing of the hexapod robot while simultaneously satisfying the terrain passability constraints, the minimum value of the hexapod robot's envelope volume, and the maximum value of the leg workspace range, based on the terrain passability constraints. lateral leg spacing The distance between the center of gravity and the extreme position of the leg workspace Leg mounting height and foot workspace dimensions , lengthen leg spacing lateral leg spacing The distance between the center of gravity and the extreme position of the leg workspace Leg mounting height and foot workspace dimensions As the optimal body size for a hexapod robot; S4. Based on S1 and S3, set the leg size constraints of the hexapod robot, with the optimization objective being to minimize the peak joint force and peak joint power under the leg size constraints. The optimal leg size is obtained using a non-dominated sorting algorithm. The optimal size and structure of the hexapod robot are obtained based on S3 and S4.

2. The multi-objective optimization design method for a hexapod robot based on multiple constraints according to claim 1, characterized in that: During the process of climbing a slope, the hexapod robot's center of mass is subject to the following constraints regarding terrain traversal: （3） （4） （5） （6）。 3. The multi-objective optimization design method for a hexapod robot based on multiple constraints according to claim 2, characterized in that: When the hexapod robot traverses a cross slope, its center of mass is subject to the following constraints regarding terrain passability: （7） （8） （9） in, Let M be the minimum rotation angle of the rotary joint. This represents the maximum rotation angle of the rotary joint M.

4. The multi-objective optimization design method for a hexapod robot based on multiple constraints according to claim 3, characterized in that: The specific process of S33 is as follows: S331. Calculate the longitudinal leg spacing of the hexapod robot under terrain passability constraints. lateral leg spacing The distance between the center of gravity and the extreme position of the leg workspace Leg mounting height and foot workspace dimensions The initial value; S332. Calculate the envelope volume of the hexapod robot based on S331. : （10） S333, based on the footwork space dimensions of S331 Preliminary calculation of the working space range of the hexapod robot's legs : （11） in, These are the weighting coefficients; S334. Under the condition of satisfying the minimum envelope volume of the hexapod robot, the maximum value of the working space range of the hexapod robot's legs is taken when Equation (11) is negative. Taking the minimum envelope volume of the hexapod robot and the maximum working space range of the legs as the optimization objectives, the longitudinal leg spacing of the hexapod robot is gradually optimized according to Equations (2) to (11). lateral leg spacing The distance between the center of gravity and the extreme position of the leg workspace Leg mounting height and foot workspace dimensions The value of is used to obtain the longitudinal leg spacing that simultaneously satisfies equations (2), (10), and (11). lateral leg spacing The distance between the center of gravity and the extreme position of the leg workspace Leg mounting height and foot workspace dimensions This is the optimal body size for a six-legged robot.

5. The multi-objective optimization design method for a hexapod robot based on multiple constraints according to claim 4, characterized in that: The leg size constraints in S4 include geometric constraints, workspace constraints, joint amplitude constraints, kinematic constraints, foot-ground force constraints, and interference constraints. (1) Geometric constraints: （12） (2) Workspace constraints: （13） in, , , , Horizontal joint exist The maximum distance the axis moves. Horizontal joint exist The minimum distance the axis moves. Vertical joint exist The maximum distance the axis moves. Vertical joint exist The minimum distance the axis moves. This represents the maximum rotation angle of the rotary joint M. This represents the minimum rotation angle of the rotary joint M. (3) Joint amplitude limiting constraints: （14） in, This represents the lower limit of the joint range. For joint variables, This represents the upper limit of the joint range. For generalized joint velocity, This is the upper limit of joint velocity. For generalized joint forces, This represents the upper limit of joint force. (4) Kinematic constraints: （15） in, The coordinates are those of the foot end; (5) Foot-ground force constraint: （16） in, The contact force vector, For normal contact force, The contact force is the tangential force along the x-direction. The tangential contact force is along the y-direction. The upper limit of contact force, for Transpose of; (6) Interference constraints: （17） in, For horizontal drive motor displacement, This is for vertical drive motor displacement.

6. The multi-objective optimization design method for a hexapod robot based on multiple constraints according to claim 5, characterized in that: The peak joint force in S4 The expression is: （18） in, To optimize weights, For joint force vectors, For gait period, For robot running time, ; The peak power of the joint The expression is: （19） in, For joint velocity vectors, for The transpose of .

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