Hexapod robot foot end trajectory planning method based on quintic polynomial interpolation of path passing points

Abstract

The invention belongs to the technical field of robot walking paths, and provides a hexapod robot foot end trajectory planning method based on quintic polynomial interpolation of path passing points. Comprising the following steps: step S10, acquiring an initial target angle theta n of each joint of the hexapod robot and a corresponding target angle theta m of each joint at specified time; step S20, outputting a coefficient aij of a quintic polynomial interpolation function based on theta n and theta m; and S30, based on a preset quintic polynomial interpolation function and the coefficient aij, outputting a foot end trajectory planning function of the robot. By means of a quintic polynomial interpolation function, calculation and simulation are carried out for many times, and the stability problems that when the hexapod robot walks, angular acceleration jumps, foot ends are prone to slipping, and the foot ends make contact with the ground late or early, so that fluctuation of the robot body in the vertical direction is large are solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of robot walking paths, and in particular relates to a hexapod robot foot end trajectory planning method based on quintic polynomial interpolation of path points. Background Art

[0002] With the advancement of human science and global economic growth, robotics research is no longer limited to fixed-point applications but is gradually expanding into areas such as space exploration, undersea resource development, disaster rescue, and military reconnaissance. Focusing on the problem of stable walking for multi-legged robots, domestic and international scholars have conducted extensive research on gait control schemes and foot trajectory planning. Zhang J et al. designed a crab-like flexible leg gait control scheme for adaptive locomotion in multi-legged robots, enabling the robots to adapt to various complex terrain conditions and adjust their speed and height. Hakamada S et al. proposed a passively driven support leg structure to address the problem of robot walking on uneven and rugged surfaces. Ba KX et al. proposed a novel one-dimensional force sensor calibration method to improve the accuracy of contact force solutions for legged robots. In summary, the commonly used robot foot trajectory planning function is a cubic polynomial interpolation function, which is simple to calculate. For example, the Chinese invention patent application number CN202410446275.1 discloses a motion planning method for a hexapod robot in rough terrain environments, which addresses the fields of robot path planning and trajectory planning. A support point-based stereo matching algorithm and a spatial decomposition method are used to construct a raster map of a rugged terrain environment. The two-point visual model theory is used in conjunction with the three-dimensional map information to guide RRT path planning to obtain the hexapod robot's motion path. A B-spline curve path optimization algorithm is used to optimize the path to obtain a smooth motion path for the hexapod robot. A combined triangulation algorithm is used to obtain a three-dimensional model of the terrain. A foothold function is established in conjunction with the planned travel path. A support vector machine learning method is used to obtain the foothold function and a foothold selection strategy. Footholds are selected, and trajectory planning is performed for the hexapod robot's support legs and swing legs from the perspective of stability analysis and optimal control during motion, thereby obtaining the robot's optimal motion trajectory. This motion planning method, which combines global path planning with local trajectory planning for the hexapod robot, improves the hexapod robot's stability and its ability to adapt to complex environments and operate independently in practical applications.

[0003] However, when a hexapod robot walks, there are jumps in angular acceleration, which can easily lead to stability problems such as foot slippage, late foot contact, and early foot contact, resulting in large fluctuations in the vertical direction of the body. Summary of the Invention

[0004] Based on this, it is necessary to provide a hexapod robot foot-end trajectory planning method based on quintic polynomial interpolation of path points to address the stability problems of the hexapod robot when walking, such as angular acceleration jumps, foot slippage, late foot contact, and early foot contact, which lead to large fluctuations in the vertical direction of the body.

[0005] To achieve the above object, the present invention adopts the following scheme:

[0006] A hexapod robot foot trajectory planning method based on quintic polynomial interpolation of path points comprises the following steps:

[0007] Step S10. Obtain the initial target angle θ of each joint of the hexapod robot n and the corresponding target angle θ of each joint at the specified time m ;

[0008] Step S20. Based on θ n and θ m , output the coefficient a of the quintic polynomial interpolation function ij ;

[0009] Step S30. Based on the preset quintic polynomial interpolation function and coefficient a ij , output the robot's foot trajectory planning function.

[0010] Preferably, step S10. Obtain the initial target angle θ of each joint of the hexapod robot n and the corresponding target angle θ of each joint at the specified time m ; Also includes the following steps:

[0011] Step S11. Obtain the coordinates of the starting point of the hexapod robot's foot, the preset step length L, and the safety distance H, and output the coordinates of the landing point of the hexapod robot's foot;

[0012] Step S12: Based on the starting point coordinates and landing point coordinates of the hexapod robot foot end, execute the hexapod robot kinematic model and output the path point coordinates of the hexapod robot foot end;

[0013] Step S13: Based on the starting point coordinates, path point coordinates and landing point coordinates of the hexapod robot foot end, the initial target angle θ of each joint of the hexapod robot is output. n and the corresponding target angle θ of each joint at the specified time m .

[0014] Preferably, the first segment of trajectory planning of the hexapod robot's foot from the starting point to the path point is a fifth-order polynomial interpolation function, and includes the following steps:

[0015] Step S31. Obtain θ n and θ m, based on the interpolation function f(t n )=θ n , output the angular velocity of each link of the robot leg at a specified time angular acceleration and the rate of change of angular acceleration

[0016] Step S32: Interpolation function based on the interpolation function and the angular velocity function of the hexapod robot at the path point and interpolation function of angular acceleration Output the angular velocity of the hexapod robot at the path point angular acceleration and the rate of change of angular acceleration All are 0;

[0017] Step S33. Based on step S31 and step S32, output the fifth-order polynomial interpolation function of the first segment trajectory planning; the fifth-order polynomial interpolation function of the first segment trajectory planning f(t1) = a0+a1t1+a2t1 2 +a3t1 3 +a4t1 4 +a5t1 5 ;

[0018] Among them, a0, a1, a2, a3, a4, and a5 are the coefficients of the fifth-order polynomial interpolation function, t1 is the time variable from the foot end to the path point, is the angular velocity function, is the angular acceleration function.

[0019] Preferably, the hexapod robot foot end is a fifth-order polynomial interpolation function of the second trajectory planning from the path point to the landing point, comprising the following steps:

[0020] Step S34. Based on the fifth-order polynomial interpolation function of the first trajectory planning, output the leg, foot, and joint angles of the hexapod robot's path points and the leg, foot, and joint angles of the hexapod robot at specified time nodes;

[0021] Step S35. Based on the interpolation function and the interpolation function of the angular velocity function and the interpolation function of the angular acceleration of the hexapod robot at the landing point, output the angular velocity, angular acceleration and angular acceleration change rate of the hexapod robot at the landing point as 0;

[0022] Step S36. Based on step S34 and step S35, output the fifth-order polynomial interpolation function of the second segment trajectory planning; wherein the fifth-order polynomial interpolation function of the second segment trajectory planning f(t2)=a0+a1t2+a2t2 2 +a3t2 3 +a4t2 4 +a5t25 ;

[0023] Step S37. Outputting a preset quintic polynomial interpolation function based on the quintic polynomial interpolation function of the first trajectory planning and the quintic polynomial interpolation function of the second trajectory planning;

[0024] Among them, a0, a1, a2, a3, a4, and a5 are the coefficients of the quintic polynomial interpolation function, t2 is the time variable from the path point to the landing point, is the angular acceleration function, is the rate of change function of angular acceleration.

[0025] Preferably, the coefficient a of the fifth-order polynomial interpolation function is ij for:

[0026]

[0027] where a ij where i=1, 2, a 1j The coefficients of the fifth-order polynomial interpolation function for the first trajectory planning, a 2j The coefficients of the fifth-order polynomial interpolation function are planned for the second trajectory, j = 1, 2, 3, 4, 5, which are the order numbers of the fifth-order polynomial coefficients, θ m is the angle of each leg link when the robot passes the path point, is the corresponding angular velocity.

[0028] Preferably, the preset quintic polynomial interpolation function is:

[0029]

[0030] in, Angular velocity function of the first trajectory planning function, Angular acceleration function of the first trajectory planning function, The angular acceleration rate of change function of the first trajectory planning function, The angular velocity function of the second trajectory planning function, The angular acceleration function of the second trajectory planning function, The angular acceleration rate of change function of the second trajectory planning function, t n1 , t n2 Respectively represent the time consumed by the two path planning.

[0031] The technical solution adopted in this application can achieve the following beneficial effects:

[0032] 1. Using a quintic polynomial interpolation function, multiple calculations and simulations were performed to address stability issues associated with hexapod walking, such as angular acceleration jumps, foot slippage, late or early foot contact, and large vertical fluctuations. Furthermore, the robot was able to avoid acceleration jumps when passing designated points while completing a predetermined step length.

[0033] 2. The function curve obtained by the trajectory planning function based on the quintic polynomial interpolation function of the path points has a smooth transition. There is no jump in angular velocity and angular acceleration at the time nodes of the path points. The hexapod robot can achieve stable triangular gait walking, and the fluctuation degree of the vertical direction of the fuselage during walking is less than 1mm, which meets the stability requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 Schematic diagram of the hexapod robot disclosed in the embodiment of the present application (a is a schematic diagram of the hexapod robot, b is a front view of a single leg of the hexapod robot, and c is a top view of a single leg of the hexapod robot).

[0035] Figure 2 This is a single-leg model of a hexapod robot disclosed in the embodiments of this application.

[0036] Figure 3 This is a schematic diagram of the foot trajectory planning scheme disclosed in an embodiment of this application.

[0037] Figure 4 Schematic diagram of the hexapod numbering and reference coordinate system disclosed in the embodiments of this application.

[0038] Figure 5 This is a kinematic analysis function diagram disclosed in an embodiment of the present application (a is a point cloud diagram of the space reachable by the foot end, b is a xoy plane projection diagram, and c is a yoz plane projection diagram).

[0039] Figure 6 Graphs showing the change in angle parameters of the traditional and improved quintic polynomial interpolation functions disclosed in the embodiments of the present application (a is the cubic polynomial angle curve for the passing point, b is the quintic polynomial angle curve for the passing point, c is the cubic polynomial angular velocity curve for the passing point, d is the quintic polynomial angular velocity curve for the passing point, e is the cubic polynomial angular acceleration curve for the passing point, f is the quintic polynomial angular acceleration curve for the passing point, g is the cubic polynomial angular acceleration change rate curve for the passing point, and h is the quintic polynomial angular acceleration change rate curve for the passing point).

[0040] Figure 7 This is the Simulink framework diagram disclosed in the embodiments of this application.

[0041] Figure 8These are the joint simulation result diagrams disclosed in the embodiments of this application (a is the fuselage fluctuation measurement result diagram at the Adams end, and b is the fuselage fluctuation measurement result diagram at the Simulink end).

[0042] Figure 9 This is a diagram of the Adams running results disclosed in the embodiments of this application.

[0043] Among them: protrusion 10, ground 20, shallow pit 30, first section trajectory planning 100, second section trajectory planning 200, starting point 310, path point 320, landing point 330, traditional trajectory 400. DETAILED DESCRIPTION

[0044] To facilitate understanding of the present application, a more comprehensive description of the present application will be provided below with reference to the accompanying drawings. The accompanying drawings illustrate preferred embodiments of the present application. However, the present application may be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a more thorough and comprehensive understanding of the disclosure of the present application.

[0045] It should be noted that when a device is considered to be "connected" to another device, it can be directly connected to the other device or there may be an intermediate device. The terms "interior," "top," "upper," "lower," "upper," "lower," and similar expressions used herein are for illustrative purposes only and do not represent the only implementation method.

[0046] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which this application pertains. The terms used herein in the specification of this application are intended only to describe specific embodiments and are not intended to limit this application. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0047] See also Figures 1 to 9 The present application provides a hexapod robot foot end trajectory planning method based on quintic polynomial interpolation of path points, comprising the following steps:

[0048] Step S10. Obtain the initial target angle θ of each joint of the hexapod robot n and the corresponding target angle θ of each joint at the specified time m ;

[0049] Step S20. Based on θ n and θ m , output the coefficient a of the quintic polynomial interpolation function ij ;

[0050] Step S30. Based on the preset quintic polynomial interpolation function and coefficient aij , output the robot's foot trajectory planning function.

[0051] Specifically, the robot of this application walks in coordination with six legs and feet. Each leg and foot has three rotating joints: the hip joint connecting the hip to the body, the knee joint connecting the hip to the leg, and the ankle joint connecting the leg to the foot. The foot position changes through the rotation of the joints. The angle changes of each joint are driven by a servo.

[0052] Furthermore, a hexapod robot model is established to analyze the kinematics of the hexapod robot, and the kinematic model is output; based on the kinematic model, the relationship between the hexapod robot's legs, feet, initial angles of each joint, foot-end coordinate positions, and the angles of each joint at the specified time node of the hexapod robot are output; based on the relationship between the hexapod robot's initial legs, feet, joint angles, foot-end coordinate positions, and the angles of each joint at the specified time node of the hexapod robot, the foot-end trajectory planning function of the hexapod robot is output; based on the hexapod robot's foot-end trajectory planning function, a simulation experiment on the hexapod robot's leg and foot motion trajectory planning is carried out.

[0053] First, a hexapod robot overall model and a three-joint leg and foot model were established. Kinematic analysis of the hexapod robot was conducted, revealing the relationship between the leg and foot joint angles and the foot end coordinate positions. Secondly, a trajectory planning function based on a quintic polynomial interpolation function passing through path points was developed. By constraining the joint angles, angular velocities, and angular accelerations of the hexapod robot, a general formula for the trajectory planning function was derived. This approach addresses the issues of ensuring the robot passes through designated points while completing a predetermined step length and avoiding acceleration jumps when passing through path points. Finally, a simulation model was established, and trajectory planning experiments were conducted on the hexapod robot using a triangular gait, using a quintic polynomial interpolation algorithm passing through path points.

[0054] This application adopts a technical solution of a hexapod robot foot end trajectory planning method based on quintic polynomial interpolation of path points to achieve the following beneficial effects:

[0055] 1. Using a quintic polynomial interpolation function, multiple calculations and simulations were performed to address stability issues associated with hexapod walking, such as angular acceleration jumps, foot slippage, late or early foot contact, and large vertical fluctuations. Furthermore, the robot was able to avoid acceleration jumps when passing designated points while completing a predetermined step length.

[0056] 2. The function curve obtained by the trajectory planning function based on the quintic polynomial interpolation function of the path points has a smooth transition. There is no jump in angular velocity and angular acceleration at the time nodes of the path points. The hexapod robot can achieve stable triangular gait walking, and the fluctuation degree of the vertical direction of the fuselage during walking is less than 1mm, which meets the stability requirements.

[0057] Based on the above scheme, step S10. Obtain the initial target angle θ of each joint of the hexapod robot n and the corresponding target angle θ of each joint at the specified time m ; Also includes the following steps:

[0058] Step S11. Obtain the coordinates of the starting point of the hexapod robot's foot, the preset step length L, and the safety distance H, and output the coordinates of the landing point of the hexapod robot's foot;

[0059] Step S12: Based on the starting point coordinates and landing point coordinates of the hexapod robot foot end, execute the hexapod robot kinematic model and output the path point coordinates of the hexapod robot foot end;

[0060] Step S13: Based on the starting point coordinates, path point coordinates and landing point coordinates of the hexapod robot foot end, the initial target angle θ of each joint of the hexapod robot is output. n and the corresponding target angle θ of each joint at the specified time m .

[0061] Specifically, a single-leg model of the robot is established based on the world coordinate system o-xyz, such as Figure 2 As shown in the figure, the hip joint, knee joint, and ankle joint are represented by O, A, and B respectively, C is the foot end, OA, AB, and BC represent the hip, leg, and foot of the robot respectively, A xy 、B xy 、C xy where θ is the angle between the robot's hip and the xoy plane. Since the robot's structure is already defined, θ is 0. α is the angle between the leg and foot projections in the xoy plane and the ox axis. β is the angle between the leg and the hip, and γ is the angle between the leg and the foot. A hexapod's legs and feet have only three revolute joints. The relationship between the foot's coordinates and the joint angles can be derived based on the structural parameters of each joint.

[0062] According to the robot leg and foot model, α, β, γ and the structural parameters of each leg and foot are known, and the projection length OC on the xoy plane is xy , find the coordinates of the foot end C [C X , C y , C z ].

[0063]

[0064] If the coordinates of point C are known, find the corresponding three joint angles: first find a, then find γ, and finally find β;

[0065] The formula for finding a first is:

[0066]

[0067] The formula for γ is:

[0068]

[0069] Finally, the formula for β is:

[0070]

[0071] Using the above formula and related parameters, the calculation of each leg is repeated and summed up to establish the kinematic model of the hexapod robot.

[0072] Based on the above scheme, the walking process of each step of the hexapod robot is divided into a starting point, a path point and a landing point, and is divided into a first-segment trajectory planning and a second-segment trajectory planning according to the starting point, the path point and the landing point; wherein, the first-segment trajectory planning is from the starting point to the path point, and completes the walking with the agreed step length, and the second-segment trajectory planning is from the path point to the landing point, and makes timely adjustments to the walking according to the complex terrain that may be encountered.

[0073] Figure 3 As shown, the red dashed line represents the planned trajectory. Each step of the robot's movement is divided into two parts: one for completing the agreed-upon step length, and the other for making timely adjustments to complex terrain that may be encountered. A safety distance H is set, and a path point based on the target point is derived. The corresponding joint angles are solved using the kinematic equations. After the robot's foot reaches the path point, it begins to descend from top to bottom. During this process, the foot's force sensor determines whether it has successfully contacted the ground and stops immediately to avoid unnecessary safety issues. The first trajectory is the trajectory planned from the hexapod's foot to the path point, and the second trajectory is the trajectory planned from the path point to the landing point. Both trajectories are controlled using a quintic polynomial interpolation function.

[0074] In the above scheme, the hexapod robot foot end from the starting point to the path point is a quintic polynomial interpolation function of the first segment trajectory planning, and includes the following steps:

[0075] Step S31. Obtain θ n and θ m , output the interpolation function f(t n )=θ n ;

[0076] Step S32. Based on the interpolation function, the angular velocity and angular acceleration of the legs, feet, and joints of the hexapod robot at the starting point and landing point are preset to be 0, and the interpolation function of the angular velocity function of the hexapod robot is output. and interpolation function of angular acceleration

[0077] Step S33. Based on step S31 and step S32, output the fifth-order polynomial interpolation function of the first segment trajectory planning; wherein the fifth-order polynomial interpolation function of the first segment trajectory planning f(t1)=a0+a1t1+a2t1 2 +a3t1 3 +a4t1 4 +a5t1 5 ;

[0078] Among them, a0, a1, a2, a3, a4, and a5 are the coefficients of the fifth-order polynomial interpolation function, t1 is the time variable from the foot end to the path point, is the angular velocity function, is the angular acceleration function.

[0079] The hexapod robot foot end is programmed with a quintic polynomial interpolation function for the second segment trajectory from the path point to the landing point, comprising the following steps:

[0080] Step S34. Based on the fifth-order polynomial interpolation function f(t1) of the first trajectory planning, output the leg, foot, and joint angles of the hexapod robot's path points and the leg, foot, and joint angles of the hexapod robot at specified time nodes;

[0081] Step S35. Based on the interpolation function, the angular velocity and angular acceleration of the legs, feet, and joints of the six-legged robot at the starting point and landing point are preset to 0, and the interpolation function of the angular acceleration of the six-legged robot is output. and the interpolation function of the rate of change of angular acceleration

[0082] Step S36. Based on step S34 and step S35, output the fifth-order polynomial interpolation function of the second segment trajectory planning; wherein the fifth-order polynomial interpolation function of the second segment trajectory planning f(t2)=a0+a1t2+a2t2 2 +a3t2 3 +a4t2 4 +a5t2 5 ;

[0083] Step S37. Outputting a preset quintic polynomial interpolation function based on the quintic polynomial interpolation function of the first trajectory planning and the quintic polynomial interpolation function of the second trajectory planning;

[0084] Among them, a0, a1, a2, a3, a4, and a5 are the coefficients of the quintic polynomial interpolation function, t2 is the time variable from the path point to the landing point, is the angular acceleration function, is the rate of change function of angular acceleration.

[0085] Based on the fifth-order polynomial interpolation function of the first segment trajectory planning and the fifth-order polynomial interpolation function of the second segment trajectory planning, the hexapod robot foot-end trajectory planning function (preset fifth-order polynomial interpolation function) is output.

[0086] Specifically, the robot foot movement process is that each joint rotates from one angle to the corresponding next angle within a specified time, and the speed and acceleration are constrained. The initial angle of each joint at the foot is defined as θ0. The target angle can be calculated by inverse kinematics. The initial angle is combined with the parameters of each joint of the robot to determine the foot coordinates. After adding the foot walking step length L, the coordinates of the next landing point are determined and the corresponding joint angles are inversely calculated from them, that is, the target angles of each joint, defined as θ n At this time, the path of the foot end can be represented by the interpolation function, and the time consumed by taking the corresponding step is t n , then:

[0087] To ensure the continuity of joint angular velocity and angular acceleration, the initial and final angular velocity and angular acceleration are set to 0:

[0088] According to the above two equations, we can get six equations for a joint, and solve a quintic polynomial with six unknowns. The variable is time t: f(t) = a0 + a1t + a2t 2 +a3t 3 +a4t 4 +a5t 5 , two segments of quintic polynomial interpolation functions are used to represent the two parts of the robot's walking process for each step: the time from the foot end to the path point, and the time from the foot end to the path point to the landing point, respectively. The time taken is t1 and t2, that is,

[0089] Due to the constraints of the quintic polynomial interpolation function itself, directly using it to plan the two segments of the trajectory before and after the waypoint will result in discontinuity in the angular velocity and angular acceleration between the two segments, both starting from zero. If the foot-end velocity and acceleration must not be zero upon reaching the waypoint, the quintic polynomial function must change the constraints of the two segments to achieve a smooth connection. Therefore, a quintic polynomial interpolation function passing through the waypoint is required to achieve continuity in angular velocity and angular acceleration without sudden changes.

[0090] Preferably, the coefficient a of the fifth-order polynomial interpolation function is ij for:

[0091]

[0092] where a ij where i=1, 2, a1j The coefficients of the fifth-order polynomial interpolation function for the first trajectory planning, a 2j The coefficients of the fifth-order polynomial interpolation function are planned for the second trajectory, j = 1, 2, 3, 4, 5, which are the order numbers of the fifth-order polynomial coefficients, θ m is the angle of each leg link when the robot passes the path point, is the corresponding angular velocity. The preset quintic polynomial interpolation function is:

[0093]

[0094] in, Angular velocity function of the first trajectory planning function, Angular acceleration function of the first trajectory planning function, The angular acceleration rate of change function of the first trajectory planning function, The angular velocity function of the second trajectory planning function, The angular acceleration function of the second trajectory planning function, The angular acceleration rate of change function of the second trajectory planning function, t n1 , t n2 Respectively represent the time consumed by the two path planning.

[0095] In the above scheme, the corresponding angle obtained by the inverse kinematic solution of the path point is set as θ m , define a ij is the coefficient of the quintic polynomial interpolation function, where i is 1 or 2, indicating the constraint function of the first or second segment trajectory planning, j is 0-5, indicating the sequence number of the quintic polynomial coefficient, and t n1 , t n2 They represent the time consumed by the two path planning segments respectively. Combined with the continuity requirement, the relevant speed parameters of the two segments are equalized when passing through the path points. The constraints of the new quintic polynomial interpolation function are:

[0096]

[0097] The new function has twelve equations and twelve unknowns, and has a corresponding unique solution. Assume that the time consumed by each planned path is the same, that is, t n1 =t n2 =t, the equation is solved to get:

[0098]

[0099] The coefficient a will be obtained ijSubstitute the quintic polynomial interpolation function to find the functional expression of the joint angle changing with time, and write an implementation program in Matlab software. Using the joint angles corresponding to the given initial point, path point, and landing point, the trajectory of each joint can be generated.

[0100] In another embodiment of the present application, a simulation experiment is conducted on the above scheme and the fifth-order polynomial interpolation function:

[0101] Step 1: Based on the hexapod robot model, number the six legs of the hexapod robot and establish a reference coordinate system OXY;

[0102] Step 2: Based on the reference coordinate system OXY and the hexapod robot foot trajectory planning function, a simulation experiment of the hexapod robot leg and foot motion trajectory planning is carried out.

[0103] The six legs of the hexapod robot are numbered sequentially, and a reference coordinate system OXY is established as follows: Figure 4 As shown:

[0104] Matlab software was used to perform kinematic analysis using the Monte Carlo method. Within the specified range of joint angles, the point set that the foot end could reach was obtained. The angles of the α angles of the six legs in the reference coordinate system were as follows: Figure 4 As shown, the initial values ​​of the other angles are the same. The initial parameter values ​​of the three joints of leg and foot 1 are shown in Table 1:

[0105] Table 1 Parameters of Leg 1

[0106]

[0107] Taking leg 1 as an example, the agreed ranges of the three angles α, β, and γ are [-pi / 2, 0], [0, pi / 2], and [0, pi] respectively. The simulation results of the reachable space of the foot end obtained by applying the kinematic analysis function are as follows: Figure 5 ,

[0108] Within the allowable range of the reachable space at the foot end, set the safety distance H = 20 mm and the step length L = 40 mm. The three-joint angles corresponding to the path point are inversely calculated based on the kinematic analysis function. The angle parameters of each leg and foot after taking the agreed step length are shown in Tables 2, 3, and 4. The angle change directions of legs 4, 5, and 6 are opposite to those of legs 1, 2, and 3.

[0109] Table 2 Results of the kinematic analysis function for leg 1

[0110]

[0111] Table 3 Results of the kinematic analysis function for leg 2

[0112]

[0113] Table 4 Results of the kinematic analysis function for leg 3

[0114]

[0115] Using the above parameters as initial values, and based on the initial and ending angles corresponding to each step, the trajectory planning function generates a cubic polynomial function and a quintic polynomial interpolation function for each path point, as well as corresponding visualization graphs of angles, angular velocities, angular accelerations, and rates of change of angular acceleration. The robot's legs are defined to reach each path point within 0.5 seconds and to touch the ground within the next 0.5 seconds, completing a single step, i.e., t = 0.5. After applying the designed planning function, the legs must achieve a smooth transition between the two actions within the two time periods. Taking joint A of leg 2 as an example:

[0116] The cubic polynomial interpolation function through the path point is:

[0117]

[0118] The corresponding angle parameter change curve is as follows Figure 6 As shown in (a), (c), (e), and (g), the quintic polynomial interpolation function passing through the path point is:

[0119]

[0120] The corresponding angle parameter change curve is as follows Figure 6 (b), (d), (f), and (h). Figure 6 ;

[0121] As can be seen, the quintic polynomial interpolation function effectively avoids the acceleration jump problem of the cubic polynomial interpolation function. The transition between the two segments of the angle parameter curve is very smooth, and the entire curve process is very stable. Although the initial angle of each leg is different, the kinematic analysis algorithm and trajectory planning function can successfully determine the foot end trajectory of each of the 18 joints of the hexapod within a single step.

[0122] Furthermore, the method further includes step S60. Based on the simulation experiment of the motion trajectory planning of the legs and feet of the hexapod robot, the rationality of the kinematic model and the trajectory planning function of the hexapod robot's foot end are verified.

[0123] Import the planning functions of each joint into Matlab software, complete the simulation operation in the Simulink module of Matlab software, write the planning functions of each joint into S-Function functions, use the modular information processing function of Simulink to drive the hexapod robot in Adams software to perform related simulation work, set the movement sequence function of each leg and foot of the triangular gait as the input, and build a Simulink framework diagram with the vertical direction fluctuation of the body and the degree of change of the joint angle as the output. The completed Simulink framework diagram is shown in Figure 7 , and use this framework diagram for simulation measurement.

[0124] The simulation results are as follows Figure 8 Figures (a) and (b) show the Adams and Simulink measurements of the hexapod's body fluctuations after the robot applied the trajectory planning function. A designed quintic polynomial interpolation function for path points was used as the driving function for each joint of each leg. The velocity and acceleration impacts caused by the driving function during leg lift, movement, and landing caused the body to fluctuate momentarily. The degree of vertical fluctuation was measured, and the Adams results were consistent with the Simulink results. This also verified the correct construction of the simulation framework. With the corresponding planning function applied, the robot's vertical fluctuations were less than 1 mm, including errors within the simulation. The main sources of fluctuations and errors are the accuracy of the results obtained from the kinematic analysis algorithm and the shape of the robot's foot. The co-simulation results show that the designed quintic polynomial planning function for path points is suitable for the designed hexapod robot, exhibits certain advantages, and can meet the stability requirements of the robot during walking.

[0125] The joint angles of the hexapod robot were successfully controlled on the Adams side, and the robot achieved a triangular gait within the agreed time. Figure 9 As shown, Figure 9 (a) shows that during the time from 0s to 0.5s, the robot's swinging legs 1, 3, and 5 reach their respective path points. At this time, legs 2, 4, and 6 serve as support legs to support the robot body. Figure 9 (b) shows that within 0.5s-1s, the three swinging legs fall vertically according to the constrained trajectory until they touch the ground; Figure 9 (c) shows that the robot completes one step in 1s-1.5s, and legs 1, 3, and 5 become supporting legs, while legs 2, 4, and 6 are lifted and reach the corresponding path points. Figure 9(d) shows the time between 1.5s and 2s for each swinging leg to land and transform into a supporting leg. This reciprocating motion enables the robot to walk steadily, and the model's pose transitions are very smooth between each time period, providing valuable support for adding relevant control to the robot's foot.

[0126] The above-described embodiments only express the way in which the equipment of the present application is arranged. The description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the patent application. It should be pointed out that a person skilled in the art can make a number of adjustments and improvements without departing from the concept of the present application, and these all fall within the scope of protection of the present application. Therefore, the scope of protection of the patent of the present application shall be based on the attached claims.

Claims

1. A hexapod robot foot trajectory planning method based on quintic polynomial interpolation of path points, characterized in that: The following steps are involved: Step S10. Obtain the initial target angle θ of each joint of the hexapod robot n and the corresponding target angle θ of each joint at the specified time m ; Step S20. Based on θ n and θ m , output the coefficient a of the quintic polynomial interpolation function ij ; Step S30. Based on the preset quintic polynomial interpolation function and coefficient a ij , output the robot's foot trajectory planning function.

2. The hexapod robot foot end trajectory planning method based on quintic polynomial interpolation of path points according to claim 1 is characterized in that: Step S10. Obtain the initial target angle θ of each joint of the hexapod robot n and the corresponding target angle θ of each joint at the specified time m ; Also includes the following steps: Step S11. Obtain the coordinates of the starting point of the hexapod robot's foot, the preset step length L, and the safety distance H, and output the coordinates of the landing point of the hexapod robot's foot; Step S12: Based on the starting point coordinates and landing point coordinates of the hexapod robot foot end, execute the hexapod robot kinematic model and output the path point coordinates of the hexapod robot foot end; Step S13: Based on the starting point coordinates, path point coordinates and landing point coordinates of the hexapod robot foot end, the initial target angle θ of each joint of the hexapod robot is output. n and the corresponding target angle θ of each joint at the specified time m .

3. The hexapod robot foot end trajectory planning method based on quintic polynomial interpolation of path points according to claim 2 is characterized in that: The first segment of trajectory planning of the hexapod robot from the starting point to the path point is a fifth-order polynomial interpolation function, and includes the following steps: Step S31. Obtain θ n and θ m , based on the interpolation function f(t n )=θ n , output the angular velocity of each link of the robot leg at a specified time angular acceleration and the rate of change of angular acceleration Step S32. Based on the interpolation function and the angular velocity function of the hexapod robot at the path point, the interpolation function number and interpolation function of angular acceleration Output the angular velocity of the hexapod robot at the path point angular acceleration and the rate of change of angular acceleration All are 0; Step S33. Based on step S31 and step S32, output the fifth-order polynomial interpolation function of the first segment trajectory planning; the fifth-order polynomial interpolation function of the first segment trajectory planning f(t1) = a0+a1t1+a2t1 2 +a3t1 3 +a4t1 4 +a5t1 5 ; Among them, a0, a1, a2, a3, a4, and a5 are the coefficients of the fifth-order polynomial interpolation function, t1 is the time variable from the foot end to the path point, is the angular velocity function, is the angular acceleration function.

4. The hexapod robot foot end trajectory planning method based on quintic polynomial interpolation of path points according to claim 3 is characterized in that: The hexapod robot foot end is programmed with a quintic polynomial interpolation function for the second segment trajectory from the path point to the landing point, comprising the following steps: Step S34. Based on the fifth-order polynomial interpolation function of the first trajectory planning, output the leg, foot, and joint angles of the hexapod robot's path points and the leg, foot, and joint angles of the hexapod robot at specified time nodes; Step S35. Based on the interpolation function and the interpolation function of the angular velocity function and the interpolation function of the angular acceleration of the hexapod robot at the landing point, output the angular velocity, angular acceleration and angular acceleration change rate of the hexapod robot at the landing point as 0; Step S36. Based on step S34 and step S35, output the fifth-order polynomial interpolation function of the second segment trajectory planning; wherein the fifth-order polynomial interpolation function of the second segment trajectory planning f(t2)=a0+a1t2+a2t2 2 +a3t2 3 +a4t2 4 +a5t2 5 ; Step S37. Based on the fifth-order polynomial interpolation function of the first segment trajectory planning and the fifth-order polynomial interpolation function of the second segment trajectory planning, output a preset fifth-order polynomial interpolation function; wherein a0, a1, a2, a3, a4, and a5 are the coefficients of the fifth-order polynomial interpolation function, t2 is the time variable from the path point to the landing point, is the angular acceleration function, is the rate of change function of angular acceleration.

5. The hexapod robot foot end trajectory planning method based on quintic polynomial interpolation through path points according to claim 4 is characterized in that: The coefficient a of the quintic polynomial interpolation function ij for: where a ij where i=1, 2, a 1j The coefficients of the fifth-order polynomial interpolation function for the first trajectory planning, a 2j The coefficients of the fifth-order polynomial interpolation function are planned for the second trajectory, j = 1, 2, 3, 4, 5, which are the order numbers of the fifth-order polynomial coefficients, θ m is the angle of each leg link when the robot passes the path point, is the corresponding angular velocity.

6. The hexapod robot foot end trajectory planning method based on quintic polynomial interpolation of path points according to claim 5 is characterized in that: The preset quintic polynomial interpolation function is: in, Angular velocity function of the first trajectory planning function, Angular acceleration function of the first trajectory planning function, The angular acceleration rate of change function of the first trajectory planning function, The angular velocity function of the second trajectory planning function, The angular acceleration function of the second trajectory planning function, The angular acceleration rate of change function of the second trajectory planning function, t n1 , t n2 Respectively represent the time consumed by the two path planning.

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