Design method of hexapod robot

Abstract

The application relates to a design method of a hexapod robot, and belongs to the field of robot design. In order to solve the problem that the existing robots often appear unstable, slip or fail to cross obstacles under complex terrains such as slopes, cross slopes and gullies, and lack systematic size-terrain constraint analysis, the passing ability of the robot under the limit working condition cannot be guaranteed. Based on the space layout of the body and the supporting legs of the designed hexapod robot, the geometric size parameters of the hexapod robot and the working space of the supporting legs, the analytical constraint relationship between the geometric size parameters of the hexapod robot and the terrain parameters is established for the walking working condition of the hexapod robot, and then the geometric size parameters of the hexapod robot are designed based on the analytical constraint relationship. The hexapod robot designed based on the method can ensure the stable motion passing ability of the hexapod robot in the complex terrain, while maintaining the structural strength and overall stability, and can significantly enhance the terrain adaptability to the complex outdoor environment.

Description

Technical Field

[0001] This invention belongs to the field of robot design, and in particular relates to a design method for a hexapod robot. Background Technology

[0002] With the development of robotics technology, legged robots have gradually become a research hotspot for mobile platforms in unstructured environments due to their superior terrain adaptability. Compared with wheeled and tracked robots, hexapods, with their larger number of legs and wider support range, offer higher stability margins and load-bearing capacity compared to quadruped robots. Furthermore, the redundant degrees of freedom of hexapods not only endow them with greater gait diversity and fault tolerance but also enable them to exhibit superior adaptability when simultaneously dealing with complex geometric and physical terrains. Compared to most existing commercially available legged robots, heavy-duty hexapods have significant advantages in payload capacity and endurance, making them promising for applications in disaster relief, material transportation, and remote area operations.

[0003] Existing hexapod robots perform well on flat ground and with simple obstacles, but they often experience instability, slippage, or obstacle-crossing failures in complex terrains such as slopes, cross slopes, ravines, gravel, and snow. Most designs lack systematic dimensional-terrain constraint analysis, failing to guarantee the robot's traversal capabilities under extreme conditions. Summary of the Invention

[0004] In view of this, the present invention provides a design method for a hexapod robot, which can establish analytical constraint relationships between the geometric parameters of the hexapod robot and the terrain parameters for the walking conditions of the hexapod robot, and then design the geometric parameters of the hexapod robot based on the analytical constraint relationships.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0006] A design method for a hexapod robot includes:

[0007] Based on the spatial layout of the body and supporting legs of the proposed hexapod robot, the geometric parameters of the hexapod robot, and the working space of the supporting legs, analytical constraint relationships between the geometric parameters of the hexapod robot and the terrain parameters are established for the walking conditions of the hexapod robot. Then, the geometric parameters of the hexapod robot are designed based on the analytical constraint relationships.

[0008] The walking conditions include one or more of the following: slope climbing, cross-slope walking, crossing ditches, crossing obstacles, slope turning, and ditches-obstacle combinations. For slope climbing, cross-slope walking, and slope turning conditions, analytical constraints are determined by stability margins. For crossing ditches and crossing obstacles conditions, analytical constraints are determined by the limit width across the ditch and the limit height over the obstacle, respectively. For ditches-obstacle combinations, analytical constraints are determined by the limit width across the ditch and the limit height over the obstacle.

[0009] Furthermore, stability margin under slope climbing conditions Where: S is the stability margin, S0 is the maximum stability margin, and E S It is the projection point of the center of mass onto the inclined plane, F S It is the intersection of the projection of the centroid along the vertical direction and the inclined plane. The slope angle, The pitch angle is the angle of the center of mass. The height of the center of mass.

[0010] Furthermore, the analytical constraint relationships determined through stability margin are as follows:

[0011] ,

[0012] Where: P is the distance between two adjacent sets of support legs; The pitch angle is the angle of the center of mass. This represents the longitudinal offset distance of the hexapod's center of mass.

[0013] Furthermore, the stability margin under the cross-slope walking condition is ,in: The transverse slope angle; It is the angle formed by the supporting triangle of the three supporting legs of the hexapod robot on the slope; For maximum stability margin, The maximum stride length of the supporting leg in the X direction; The installation spacing between the two support legs in each group; The roll angle at the center of mass; This represents the lateral offset distance of the centroid.

[0014] Furthermore, the analytical constraint relationships determined through stability margin are as follows:

[0015] ,

[0016] Where: P is the distance between two adjacent sets of support legs; R is the installation spacing between the two support legs in each group; X The maximum stride length of the supporting leg in the X direction; The roll angle at the center of mass; This represents the lateral offset distance of the centroid. The height of the center of mass.

[0017] Furthermore, the analytical constraint relationship determined by the limiting ditch width under the ditch-crossing condition is as follows:

[0018] ,

[0019] in, The maximum width across the trench for the front leg; This represents the maximum span width of the middle leg. R represents the maximum span width of the hind leg, and P is the distance between two adjacent sets of supporting legs; X The maximum stride of the supporting leg in the X direction.

[0020] Furthermore, the analytical constraint relationship determined by the ultimate obstacle-crossing height under obstacle-crossing conditions is as follows:

[0021] The maximum obstacle-crossing height of the hexapod robot's front legs is as follows:

[0022] ,

[0023] in, R is the maximum stride length of the supporting leg in the X direction. Y To support the maximum stride of the leg in the Y direction, H1 is the distance from the top of the robot to the extreme position of the leg's movement space, and H is the height of the robot's body;

[0024] The maximum obstacle-crossing height of the legs of a hexapod robot is as follows:

[0025] ,

[0026] in, R is the maximum stride length of the supporting leg in the X direction. Y To support the maximum stride of the leg in the Y direction, H1 is the distance from the top of the robot to the extreme position of the leg's movement space, and H is the height of the robot's body;

[0027] The maximum obstacle-crossing height of the hexapod robot's hind legs is as follows:

[0028] ,

[0029] in, R is the maximum stride length of the supporting leg in the X direction. Y The maximum stride of the supporting leg in the Y direction is defined by H1, which is the distance from the top of the robot to the extreme position of the leg in the motion space, and H is the height of the robot body; P is the distance between two adjacent sets of supporting legs.

[0030] The maximum obstacle-crossing height for a hexapod robot is:

[0031] .

[0032] Furthermore, the stability margin under slope turning conditions is: ,in: It is the longitudinal slope angle; The height of the center of mass; For maximum stability margin; It is the angle at which the robot turns around the outside normal of the slope. It is the included angle that supports the triangle. It is the vertical projection of the center of mass onto the slope surface. These are the boundary points supporting the triangle. It represents the position of the boundary point of the supporting triangle after rotation.

[0033] Furthermore, the analytical constraint relationships determined through stability margin are as follows:

[0034] ,

[0035] Where P is the distance between two adjacent sets of support legs; The maximum stride length of the supporting leg in the X direction; The installation spacing between the two support legs in each group; It is the angle at which the robot turns around the outside normal of the slope.

[0036] Furthermore, the analytical constraint relationships determined by the limiting trench width and the limiting obstacle clearance height under the combined trench-obstacle condition are as follows:

[0037] when When, the expression is as follows:

[0038] ,

[0039] Will When, the expression is as follows:

[0040] ,

[0041] in, R is the pitch angle of the hexapod robot's center of mass; Y The maximum stride length of the supporting leg in the Y direction; H1 represents the maximum stride of the supporting leg in the X direction; H1 is the distance from the top of the robot to the extreme position of the leg's movement space; and H is the height of the robot's body.

[0042] The beneficial effects of this invention compared to the prior art are:

[0043] This invention, based on the spatial layout of the body and supporting legs of a proposed hexapod robot, the robot's geometric parameters, and the working space of the supporting legs, establishes analytical constraints between the robot's geometric parameters and terrain parameters for the robot's walking operation. Then, based on these constraints, the robot's geometric parameters are designed to ensure stable movement and maneuverability in complex terrains. The hexapod robot designed using this method significantly enhances its adaptability to complex outdoor environments while maintaining structural strength and overall stability. Attached Figure Description

[0044] The accompanying drawings, which form part of this invention, are provided to give a further understanding of the invention.

[0045] Figure 1 This is a schematic diagram showing the overall layout relationship between the body and supporting legs of the hexapod robot of the present invention.

[0046] Figure 2 Define the relevant geometric dimensions of the body and supporting legs of the hexapod robot, where (a) represents the geometric dimensions of the front, middle and hind legs of the hexapod robot, and (b) represents the geometric dimensions of the two legs in each group.

[0047] Figure 3 This study analyzes the passability of a hexapod robot in slope climbing conditions.

[0048] Figure 4 Analysis of the passability of a hexapod robot in the case of walking on a cross slope.

[0049] Figure 5 The following is a passability analysis of a hexapod robot in the condition of crossing a ditch, where (a) is the passability analysis of the front legs of the hexapod robot in the condition of crossing a ditch; (b) is the passability analysis of the middle legs of the hexapod robot in the condition of crossing a ditch; and (c) is the passability analysis of the hind legs of the hexapod robot in the condition of crossing a ditch.

[0050] Figure 6 The following is an analysis of the passability of a hexapod robot under obstacle crossing conditions, where (a) is the passability analysis of the front legs of the hexapod robot under obstacle crossing conditions; (b) is the passability analysis of the middle legs of the hexapod robot under obstacle crossing conditions; and (c) is the passability analysis of the hind legs of the hexapod robot under obstacle crossing conditions.

[0051] Figure 7 The following is a passability analysis of a hexapod robot in a slope turning condition, where (a) is the passability analysis under a three-dimensional structural schematic diagram of the hexapod robot, and (b) is the passability analysis of the hexapod robot in a top-down view.

[0052] Figure 8The following is a passability analysis of a hexapod robot in a combination of ravines and obstacles, where (a) is a passability analysis of the hexapod robot in a three-dimensional structural schematic diagram, and (b) is a passability analysis of the hexapod robot in a side view state.

[0053] Figure 9 The results are multibody dynamics simulations of a hexapod robot under typical working conditions.

[0054] Figure 10 This experiment verifies the mobility of a hexapod robot in a slope climbing scenario.

[0055] Figure 11 This experiment verifies the mobility of a hexapod robot in a cross-slope climbing condition.

[0056] Figure 12 This experiment verifies the mobility of a hexapod robot in ditch crossing conditions.

[0057] Figure 13 This experiment verifies the mobility of a hexapod robot under obstacle-crossing conditions. Detailed Implementation

[0058] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0059] See Figures 1 to 9 The design method of a hexapod robot in this embodiment includes the following design steps:

[0060] S1. Determine the spatial layout of the proposed hexapod robot's body and supporting legs, the geometric parameters of the hexapod robot, and the working space of the supporting legs:

[0061] S11, Determine the spatial layout of the hexapod robot's body and supporting legs: See [link / reference] Figure 1 and Figure 2 The hexapod robot of this embodiment includes a body and supporting legs. The body has a cuboid structure, and the supporting legs are six in number and divided into three groups. These three groups of supporting legs are arranged along the length of the body, and from front to back, they are designated as front legs, middle legs, and rear legs. Two supporting legs in each group are arranged side-by-side on both sides of the body along its width. Figure 1 The six supporting legs are numbered as follows: the left front leg is number 4, the right front leg is number 1, the left middle leg is number 5, the right middle leg is number 2, the left hind leg is number 6, and the right hind leg is number 3.

[0062] S12, Set the geometric parameters of the hexapod robot related to terrain constraints: The set geometric parameters are as follows Figure 2 As shown, L is the length of the robot's body, and W is the width of the robot's body. H is the installation spacing between the two support legs in each group; H is the height of the robot body; P is the spacing between two adjacent groups of support legs; and H1 is the distance from the top of the robot to the extreme position of the leg movement space.

[0063] S13, Determine the working space of the supporting leg: The working space refers to the range of motion of each supporting leg, such as... Figure 2 As shown, the rectangular dashed box below each support leg represents the working space of each support leg. Since the front, middle, and rear legs have the same structure and the spacing between adjacent support legs is the same, their working spaces are identical. Let the length direction of the fuselage be the X-direction, the height direction be the Y-direction, and the width direction be the Z-direction, where R... X R Y R Z γ1 represents the maximum stride length of the supporting leg in the X, Y, and Z directions, respectively; γ2 represents the outward swing angle of the supporting leg; and γ1 represents the inward swing angle of the supporting leg.

[0064] S2. For the walking conditions of the hexapod robot, analytical constraint relationships between the geometric parameters of the hexapod robot and the terrain parameters are established respectively. Then, the geometric parameters of the hexapod robot are designed based on the analytical constraint relationships:

[0065] Based on the walking requirements of hexapod robots in complex outdoor environments, typical terrains are classified and modeled. These typical terrains include slopes, gullies, and vertical obstacles. The hexapod robot's walking conditions on these typical terrains are diverse, specifically including slope climbing, lateral walking, gully crossing, obstacle crossing, slope turning, and gully-obstacle combination conditions. Mathematical modeling is performed for each condition. For slope climbing, lateral walking, and slope turning, static stability margin is used as the stability evaluation index for the hexapod robot. The stability margin determines the analytical constraint relationship between the hexapod robot's geometric parameters and terrain parameters under these three conditions. For gully crossing, the maximum gully crossing width is used as the analytical constraint relationship between the hexapod robot's geometric parameters and terrain parameters; for obstacle crossing, the maximum obstacle crossing height is used as the analytical constraint relationship; and for the gully-obstacle combination condition, the maximum gully crossing width and maximum obstacle crossing height are used as the analytical constraint relationships between the hexapod robot's geometric parameters and terrain parameters. These analytical constraint relationships determine the geometric parameters of the hexapod robot that can stably move under different conditions.

[0066] The analytical constraint relationships between the geometric parameters and terrain parameters of the hexapod robot under different working conditions are obtained below:

[0067] (1) Slope climbing conditions:

[0068] The stability of a hexapod robot climbing a slope is related to its center of mass height, forward displacement of the center of mass, and pitch angle. The terrain parameter affecting the robot's climbing stability is the slope angle. The stability margin of the robot under slope climbing conditions is:

[0069] (1)

[0070] Where: S is the stability margin, S0 is the maximum stability margin, and E S It is the projection point of the center of mass onto the inclined plane, F S It is the intersection of the projection of the centroid along the vertical direction and the inclined plane. The slope angle, The pitch angle is the angle of the center of mass. The height of the center of mass.

[0071] when When the robot reaches a critical stable state, the maximum climbing angle under this critical stable state should be calculated. The analytical constraint relationship with the robot's geometric parameters is calculated using the following formula:

[0072] (2)

[0073] Where: P is the distance between two adjacent sets of support legs; This represents the longitudinal offset distance of the hexapod's center of mass.

[0074] This leads to the analytical constraint relationship between the geometric parameters of the hexapod robot and the terrain parameters under slope climbing conditions. Based on this analytical constraint relationship, the geometric parameters of the hexapod robot under different climbing angles can be designed.

[0075] (2) Crossing a slope:

[0076] The stability of a hexapod robot when crossing a slope mainly depends on the support of its legs on the lower side of the slope and the position of its center of mass projection. The terrain parameter affecting the robot's stability when crossing the slope is the slope angle. Assume that during the slope crossing process, the right front leg, right middle leg, and right hind leg are on the lower side of the slope, while the left front leg, left middle leg, and left hind leg are on the upper side. That is, legs 1, 2, and 3 are on the lower side of the slope, and legs 4, 5, and 6 are on the upper side (e.g., ...). Figure 1 (The arrangement of the supporting legs is shown). Since the working space for leg movement is extremely limited when leg 1 or leg 3 on the lower side of the slope supports the slope alone, easily leading to instability, this gait is generally avoided. Therefore, this embodiment does not calculate the analytical constraint relationship between the geometric parameters and terrain parameters of the hexapod robot in this gait.

[0077] This embodiment only considers the minimum stability range of the hexapod robot when leg number 2 on the lower side of the slope supports the slope alone. For example... Figure 4 As shown, when the hexapod robot adjusts its center of mass height on a slope, its stability margin is:

[0078] (3)

[0079] in: The transverse slope angle; It is the angle formed by the supporting triangle composed of legs 2, 4, and 6 on the slope.

[0080] Considering the outward support of the side leg on the slope, the maximum stability margin It can be expressed by the following formula:

[0081] (4)

[0082] in: The maximum stride length of the supporting leg in the X direction; The installation spacing between the two support legs in each group; The roll angle at the center of mass; This represents the lateral offset distance of the centroid. The height of the center of mass.

[0083] Substituting formula (4) into formula (3) yields the analytical constraint relationship between the maximum slope angle and the robot's geometric parameters when the hexapod robot traverses a slope. The calculation formula is as follows:

[0084] (5)

[0085] This leads to the analytical constraint relationship between the geometric parameters of the hexapod robot and the terrain parameters when traversing a slope. Based on this analytical constraint relationship, the geometric parameters of the hexapod robot when traversing slopes at different slope angles can be designed.

[0086] (3) Crossing ravines:

[0087] In natural environments, gully terrain is prevalent. Since deep gullies cannot provide effective support points for a six-legged robot, this embodiment uses this type of situation as an example for detailed explanation. This embodiment specifies the trench width... The width of the ditch serves as a crucial factor in the robot's dimensional constraints and influences its stability when crossing it. When a hexapod robot crosses such a ditch, it must maintain its own stability and move from one side to the other using two supporting legs in each leg group simultaneously. A successful crossing is achieved only when the front, middle, and hind legs all successfully cross the ditch. Therefore, calculating the maximum crossing width requires separately calculating the limit crossing widths for the front, middle, and hind legs. The calculation formula is as follows:

[0088] (6)

[0089] (7)

[0090] (8)

[0091] in, The maximum width across the trench for the front leg; This represents the maximum span width of the middle leg. R represents the maximum span width of the hind leg, and P is the distance between two adjacent sets of supporting legs; X The maximum stride of the supporting leg in the X direction.

[0092] Pick , and The minimum value in the equation is used as the analytical constraint relationship between the geometric dimension parameters and terrain parameters of the robot when crossing ditches. The calculation formula is as follows:

[0093] (9)

[0094] This leads to the analytical constraint relationship between the geometric parameters and terrain parameters of the hexapod robot when crossing ditches. Based on this analytical constraint relationship, the geometric parameters of the hexapod robot under different ditch widths can be designed.

[0095] (4) Obstacle crossing conditions:

[0096] Stepped obstacles are a common type of obstacle, and the main challenge for hexapod robots in overcoming them lies in the obstacle's height. When calculating the obstacle-crossing height of a hexapod robot, the maximum obstacle-crossing heights of the front legs, middle legs, and hind legs should be measured separately, and the minimum of these three values ​​should be taken as its maximum obstacle-crossing height. Furthermore, when determining the maximum obstacle-crossing height of a hexapod robot, the angle between the supporting legs and the body, as well as the body's pitch angle, must also be considered.

[0097] The obstacle-crossing height of the hexapod robot's front legs is shown below:

[0098] (10)

[0099] in: The obstacle-crossing height of the hexapod robot's front legs; It is the angle between the front legs and the fuselage. It is the foot support point of the foreleg. It is the foot support point of the middle leg.

[0100] During obstacle crossing, the hexapod robot should first keep its front legs off the ground and positioned at the upper right limit of its workspace, with the four rear legs providing ground support. Then, the robot begins to tilt its head back from a horizontal position, gradually increasing the pitch angle, while the landing point of its middle legs moves towards the rear of its workspace. When the middle legs reach the rear limit position of its workspace (e.g., ...), ... Figure 6 (as shown in a) To reach the maximum value, according to geometric relationships, we can obtain:

[0101] (11)

[0102] (12)

[0103] in, R is the maximum stride length of the supporting leg in the X direction. Y The maximum stride length of the supporting leg in the Y direction.

[0104] At this point, the position of the robot's hind legs can still be adjusted, allowing the pitch angle of the robot body to continue increasing until the stability margin of the center of mass projection is exactly zero. (Using O...) C Draw a circle with diameter C2, intersecting the workspace of the hind legs at point P1. Point P1 is the position where the robot's stability margin is zero. C2P1 represents the position on the horizontal ground. C P1 represents the projection of the centroid onto the vertical direction, such as... Figure 6 As shown in a. According to ΔO C C2P1, ΔC2M1P1, ΔO C The relationship between the side lengths of P1N1, and the maximum pitch angle of the robot body, can be expressed as follows:

[0105] (13)

[0106] Substituting formulas (11), (12), and (13) into formula (10) yields the maximum obstacle clearance height for the forelegs:

[0107] (14)

[0108] During obstacle crossing, the hexapod robot's middle leg must ensure full contact with the top of the obstacle and provide stable support, since the front legs have already crossed it. The robot's obstacle-crossing height is maximized when the middle leg is at its upper right limit position within its workspace. As the robot's pitch angle increases, when the hind leg reaches its lower left limit position within its workspace, the stability margin of the center of mass projection is exactly zero. Figure 6 As shown in b, at this point, the obstacle-crossing height of the robot's middle leg reaches its maximum value. The obstacle-crossing height of the middle leg is calculated based on geometric relationships:

[0109] (15)

[0110] in: The obstacle-crossing height of the robot's legs; It is the angle between the mid-mounted legs and the fuselage. It is the foot support point of the middle leg. It is the foot support point of the hind leg.

[0111] It can be concluded through calculation :

[0112] (16)

[0113] To ensure the robot can be stably supported, the following should be met: ,Right now:

[0114] (17)

[0115] It is the point on the ground projected from the robot's center of mass. It is the point on the ground projected from the upper right corner of the robot's leg's workspace.

[0116] The expression for the maximum obstacle-crossing height of the middle leg of a hexapod robot is as follows:

[0117] (18)

[0118] During obstacle crossing, the hexapod robot's front and middle legs should have successfully crossed the obstacle and are stably supported on top of it. Under these support conditions, the hexapod robot has a stability margin greater than zero, and the robot will not become unstable even after the hind legs lose contact with the ground, as shown in Figure 6c.

[0119] When the stability margin of the hexapod robot is zero, the expression for the obstacle-crossing height of its hind legs is as follows:

[0120] (19)

[0121] in: The obstacle-crossing height of the robot's hind legs; It is the angle between the hind legs and the fuselage.

[0122] The angle between the hind legs and the fuselage The maximum values ​​are as follows:

[0123] (20)

[0124] (twenty one)

[0125] When the robot's pitch angle reaches its maximum, point C2 at the end of the middle leg should be located at the upper left limit of its workspace. Based on geometric relationships, the maximum value of the robot's pitch angle can be calculated as follows:

[0126] (twenty two)

[0127] Substituting formulas (19), (20), (21), and (22) into formula (18) yields the maximum obstacle-clearing height of the hind legs:

[0128] (twenty three)

[0129] The minimum obstacle-crossing height among the front, middle, and hind legs of the hexapod robot is taken as the analytical constraint relationship between the robot's geometric parameters and terrain parameters under obstacle-crossing conditions. The calculation formula is as follows:

[0130] (twenty four)

[0131] This leads to the analytical constraint relationship between the geometric parameters of the obstacle-crossing height of the hexapod robot and the terrain parameters under obstacle-crossing conditions. Based on this analytical constraint relationship, the geometric parameters of the hexapod robot under different obstacle heights can be designed.

[0132] (5) Slope turning condition:

[0133] When a hexapod robot moves on a slope, it must simultaneously possess good longitudinal slope adaptability and lateral anti-rollover stability. To evaluate its motion stability at any slope angle, the maximum slope at which the robot can maintain stable motion while rotating at any angle around the external normal of the slope needs to be determined. During slope turning, the robot's gait should remain symmetrical about the rotation axis. At this point, the robot's stability margin S is determined by the minimum stable interval within the entire turning cycle. Similar to slope climbing and traversing slopes, if S < 0 at any moment during the motion cycle, instability will occur. Only when the projection F of the robot's center of mass is zero will instability be achieved. R It always rests on the support triangle A formed by the feet of legs #2, #4, and #6. R B R C R Within range (e.g.) Figure 7 As shown in a), the six-legged robot can achieve stable turning on the slope.

[0134] During the turning process on a slope, the stability margin of the hexapod robot's center of mass is:

[0135] (25)

[0136] It is the longitudinal slope angle. The height of the center of mass.

[0137] When the stability margin of the centroid is zero, the projection point of the centroid onto the inclined plane is exactly located in triangle A. R B R C R The edge A R C R Above. Assuming the robot's rotation angle around the external normal of the slope is ψ, the maximum stability margin S0 of the hexapod robot is:

[0138] (26)

[0139] in, It is the angle at which the robot turns around the outside normal of the slope. It is the included angle that supports the triangle. It is the vertical projection of the center of mass onto the slope surface. These are the boundary points supporting the triangle. It represents the position of the boundary point of the supporting triangle after rotation.

[0140] The solution for the maximum slope angle can be transformed into a calculation. The length problem under the minimum stable interval. The minimum stable interval of a hexapod robot during its turning process is analyzed below. When the robot moves on a slope, the projection of its center of mass onto the slope plane generates a downward component force along the slope. In the support phase, the minimum stable interval occurs when legs 2 and 6 are at the front limit position of the workspace, while leg 4 is at the rear limit position of the workspace. At this point, the support area formed by the supporting legs reaches its minimum, as shown in Figure 7(b). Based on geometric relationships, we obtain... , The expression relating to the geometric parameters of the hexapod robot:

[0141] (27)

[0142] (28)

[0143] The analytical constraint relationship between the longitudinal slope angle and the robot's geometric parameters is solved for a hexapod robot turning on a slope. The calculation formula is as follows:

[0144] (29)

[0145] This leads to the analytical constraint relationship between the geometric parameters and terrain parameters of the hexapod robot under slope turning conditions. Based on this analytical constraint relationship, the geometric parameters of the hexapod robot under different longitudinal slope angles can be designed.

[0146] (6) Combined gully-obstacle working condition:

[0147] When a hexapod traverses complex terrain, it needs to cope not only with individual ditches or obstacles, but also with combinations of ditches and obstacles. This paper analyzes the calculations for a "ditch in front, obstacle behind" terrain as an example. In this terrain, the robot first crosses the ditch, then traverses the obstacle. This terrain can be represented by the ditch width L. R and obstacle height H step These two terrain parameters are defined.

[0148] Figure 8 This demonstrates the process of a hexapod robot traversing a ditch and an obstacle. To ensure the robot doesn't collide with the ground during obstacle crossing, its legs must have sufficient crossing width and lift. Simultaneously, the projection of the center of mass onto the ground should always lie within the supporting polygon formed by the supporting legs. As the pitch angle of the center of mass increases, the maximum obstacle-crossing height of the hexapod robot also increases. However, due to the influence of leg layout and workspace, the ditch-crossing width of the hexapod robot will decrease accordingly. Therefore, it is necessary to establish the pitch angle α of the center of mass. COM Obstacle clearance height H step and trench width L R The analytical relationship between them allows for the determination of any centroid pitch angle α. COM At that time, it can accurately calculate the maximum obstacle height H that the robot can cross. step and the corresponding maximum trench width L R .

[0149] We consider a hexapod robot capable of successfully traversing a ditch (obstacle) when all its supporting legs can cross it stably. In other words, the minimum obstacle-crossing height among the front, middle, and hind legs determines the maximum obstacle the hexapod robot can cross. Therefore, we will analyze the obstacle-crossing height and ditch width of the hind legs. According to the stability criterion, when the front and middle legs support the ground and the hind legs are raised, the projection of the center of mass must lie within the support polygon formed by the front and middle legs. When the projection point is on the edge of the support polygon, the stability margin of the hexapod robot reaches a critical value. Only when the middle and hind legs are as far apart as possible can the hexapod robot cross higher and farther obstacles. Assume the pitch angle of the hexapod robot's center of mass is α. C The hexapod robot reached the critical position where the stability margin was zero, and the relative distance between C2 and C3 was the greatest. At this point, the end point C2 of the middle leg coincided with the vertex P3 of the obstacle, and point R3 was located at point O. C On the extension of C2, such as Figure 8 As shown in (b), the expression for the obstacle-crossing height of the hexapod robot is as follows:

[0150] (30)

[0151] For any given pitch angle α C In this case, the angle ϕ between the hind leg and the fuselage can be expressed as follows:

[0152] (31)

[0153] Based on geometric relationships, the length of C2C3 can be expressed as:

[0154] (32)

[0155] Substituting formulas (30) and (31) into formula (29), we obtain the obstacle-crossing height H of the hexapod robot. step The analytical relationship between it and its dimensional parameters is as follows:

[0156] (33)

[0157] When the distal end point C3 of the hind leg is located at the lower left limit of its workspace, the hexapod robot can cross the furthest distance across the ditch. Therefore, the expression for the width of the ditch crossed by the hexapod robot can be obtained:

[0158] (33)

[0159] Due to the limited workspace of its legs, the pitch angle of the hexapod robot's center of mass is subject to certain ranges. During obstacle crossing with the hind legs, the front and middle legs are responsible for supporting the ground, with the position of point C2 at the end of the middle leg directly limiting the pitch angle. The value of . Specifically, when the fuselage is parallel to the horizontal plane, The minimum value is reached; and when point C2 is at the upper left limit of the workspace, Then it reaches its maximum value. Based on this, the range of variation of the center-of-mass pitch angle can be clearly defined as follows:

[0160] (34)

[0161] (35)

[0162] Will Substituting (33) and (34), we get:

[0163] (36)

[0164] Will Substituting (33) and (34), we get:

[0165] (37)

[0166] This leads to the analytical constraint relationship between the geometric parameters and terrain parameters of the hexapod robot under the condition of front ditch and rear obstacle. Based on this analytical constraint relationship, the geometric parameters of the hexapod robot under different ditch widths and different obstacle heights can be designed.

[0167] Therefore, this embodiment can derive an expression for the analytical constraint relationship between terrain parameters and robot geometric parameters under different working conditions. Transforming complex terrain conditions into direct constraints for robot dimensional design ensures stable mobility and maneuverability of the robot in complex terrain during the design phase. The hexapod robot designed based on this method significantly enhances its adaptability to complex outdoor environments while maintaining structural strength and overall stability.

[0168] To obtain the mobility performance of the hexapod robot under different typical working conditions, a dynamic simulation analysis was performed on the robot, and the performance requirements parameters of each joint motor were determined based on the simulation results. In this embodiment, the main task requirements set for the hexapod robot include: a maximum walking speed of 5 km / h; a maximum turning angle of 180°; a maximum climbing angle of 30°; a maximum lateral walking angle of 20°; a maximum ditch width of 1 m; and a maximum obstacle clearance height of 1 m.

[0169] Based on the aforementioned task requirements and constraints, initial parameter values ​​for the simulation analysis of the hexapod robot were first set (as shown in Table 1). Subsequently, using the constructed Vortex-based dynamics simulation platform, the simulation was performed... Figure 9 Simulation demonstrations were conducted for six working conditions (a) to (f) respectively, from... Figure 9 As can be seen, the hexapod robot can move stably under these six typical working conditions.

[0170]

[0171] Based on this, envelope analysis was performed on the motion trajectory and mechanical response of each joint to extract the maximum displacement range, velocity range, and peak force of the joints under different working conditions. The final drive requirement parameters are shown in Table 2. Therefore, this implementation method clearly defines the performance requirements of each joint under six task requirements and provides reliable data for subsequent motor selection and hardware system integration.

[0172]

[0173] Based on the constraints between the terrain parameters and the robot's geometric parameters for the four working conditions mentioned above (climbing slopes, walking on cross slopes, and crossing ditches), this embodiment produced a physical robot and conducted experimental verification.

[0174] 1) Slope climbing experiment:

[0175] like Figure 10 As shown, the hexapod robot underwent a climbing experiment on a longitudinal slope. In this embodiment, the slope was set at 35°, and the slope was constructed using a metal frame with an adjustable slope angle. During the experiment, the hexapod robot adopted a three-gait walking mode to improve overall stability. Specific parameters were: leg lift height Hsw = 0.12m, stride length S = 0.4m, and gait period TM = 2.5s. During walking, the upper leg was mainly bent, while the lower leg was fully extended to keep the center of mass projection within the supporting polygon area. The experimental results show that the hexapod robot can stably climb a 35° slope without slipping or overturning, verifying the stable walking capability of this invention under steep slope conditions.

[0176] 2) Cross slope experiment:

[0177] As shown in Figure 11, a hexapod robot was tested for lateral walking on a transverse slope. The experimental scenario was equivalent to a 20° transverse slope. The robot was placed on a single-sided bridge using a crane, with its three inner legs supporting the slope and its three outer legs supporting the ground. To ensure stability, at least two legs on the lower side of the slope were supported simultaneously during the robot's movement. A three-gait pattern was used, with a stride length S = 0.4 m and a gait period TM = 1.5 s. Due to the upward tilt of the robot, the movement space of the legs on the upper side of the slope was limited, and their leg lift height was set to Hsw = 0.1 m. The experimental results show that the hexapod robot can stably complete movement under a 20° transverse slope with minimal overall vibration, verifying its adaptability to lateral terrain.

[0178] 3) Trench crossing experiment:

[0179] like Figure 12 As shown, a hexapod robot was tested crossing a ditch. In this embodiment, the ditch was 1.0m wide, and ground tape was used to simulate unsteppable areas. The robot crossed the ditch step by step using a specific gait: first, the two front legs crossed the ditch, then the body moved forward and the middle leg moved to the edge of the ditch, crossing it again step by step; finally, the hind legs crossed the ditch to complete the experiment. The gait parameters set for the experiment were: leg lift height Hsw = 0.12m, gait period TM = 2.0s, and stride length dynamically adjusted according to the width of the ditch. The experimental results show that the hexapod robot can successfully cross a 1.0m wide ditch without instability or falling, proving its strong terrain-crossing ability.

[0180] 4) Obstacle course experiment:

[0181] like Figure 13As shown, a hexapod robot underwent an experiment to cross a 1.0m high protruding obstacle. Before the experiment, the robot adjusted the posture of its front leg joints to provide sufficient space for movement. The crossing process consisted of several stages: the front legs were raised and placed on top of the obstacle, and the robot moved forward to bring its center of mass into a stable region; after the front legs crossed the obstacle, the middle legs were raised and crossed in turn; the hind legs were placed on the obstacle first, and after the robot moved forward again and stabilized, the hind legs crossed the obstacle in turn. A special gait planning method was used in the experiment, with a gait period TM = 4.0s to ensure process stability. The experimental results showed that the hexapod robot successfully crossed the 1.0m high protruding obstacle, verifying the robot's reliability and adaptability in complex obstacle environments.

[0182] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions created by the present invention, and are not intended to limit the scope of protection of the present invention. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions created by the present invention without departing from the essence and scope of the technical solutions created by the present invention.

Claims

1. A design method for a hexapod robot, characterized in that, include: Based on the spatial layout of the body and supporting legs of the proposed hexapod robot, the geometric parameters of the hexapod robot, and the working space of the supporting legs, analytical constraint relationships between the geometric parameters of the hexapod robot and the terrain parameters are established for the walking conditions of the hexapod robot. Then, the geometric parameters of the hexapod robot are designed based on the analytical constraint relationships. The walking conditions include one or more of the following: slope climbing, cross-slope walking, crossing ditches, crossing obstacles, slope turning, and ditches-obstacle combinations. For slope climbing, cross-slope walking, and slope turning conditions, analytical constraints are determined by stability margins. For crossing ditches and crossing obstacles conditions, analytical constraints are determined by the limit ditch width and the limit obstacle height, respectively. For ditches-obstacle combinations, analytical constraints are determined by the limit ditch width and the limit obstacle height. Among them, stability margin under slope climbing conditions Where: S is the stability margin, S0 is the maximum stability margin, and E S It is the projection point of the center of mass onto the inclined plane, F S It is the intersection of the projection of the centroid along the vertical direction and the inclined plane. The slope angle, The pitch angle is the angle of the center of mass. The height of the center of mass; The analytical constraints determined by the stability margin are as follows: ， Where: P is the distance between two adjacent sets of support legs; This represents the longitudinal offset distance of the hexapod's center of mass. Among them, the stability margin under the cross-slope walking condition is ,in: The transverse slope angle; It is the angle formed by the supporting triangle formed by the three supporting legs of the hexapod robot on the slope. For maximum stability margin, The maximum stride length of the supporting leg in the X direction; The installation spacing between the two support legs in each group; The roll angle at the center of mass; This represents the lateral offset distance of the centroid. The analytical constraints determined by the stability margin are as follows: ； The analytical constraint relationship determined by the ultimate span width under the ditch-crossing condition is as follows: ， in, The maximum width across the trench for the front leg; The maximum span width of the middle leg; The maximum width across the ditch for the hind legs; The analytical constraint relationship determined by the ultimate obstacle-crossing height under obstacle-crossing conditions is as follows: The maximum obstacle-crossing height of the hexapod robot's front legs is as follows: ， Where H1 is the distance from the top of the robot to the extreme position of the leg movement space, and H is the height of the robot body; The maximum obstacle-crossing height of the legs of a hexapod robot is as follows: ， Among them, R Y The maximum stride length of the supporting leg in the Y direction; The maximum obstacle-crossing height of the hexapod robot's hind legs is as follows: ， The maximum obstacle-crossing height for a hexapod robot is: ； Among them, the stability margin under the slope turning condition is ,in: It is the longitudinal slope angle; For maximum stability margin; It is the angle at which the robot turns around the outside normal of the slope. It is the included angle that supports the triangle. It is the vertical projection of the center of mass onto the slope surface. These are the boundary points supporting the triangle. It represents the position of the boundary point of the supporting triangle after rotation; The analytical constraints determined by the stability margin are as follows: ； The analytical constraint relationships determined by the ultimate ditch-obstacle combination condition, based on the ultimate ditch-crossing width and ultimate obstacle-crossing height, are as follows: when When, the expression is as follows: ， Will When, the expression is as follows: 。

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