Trajectory generation and tracking control method and system for leg-arm collaborative robot dancing

Abstract

The application relates to the technical field of leg-arm collaborative robots, and provides a trajectory generation and tracking control method and system for leg-arm collaborative robot dancing, which comprises the following steps: acquiring dancing actions of a leg-arm collaborative robot animation model in animation software; performing trajectory extraction and trajectory optimization on the dancing actions to obtain a trunk trajectory, a mechanical arm trajectory, a mechanical leg foot end trajectory and a foot bottom force which conform to robot dynamics; after priority grading of tasks of the trunk, the mechanical arm and the mechanical leg, calculating positions, velocities and accelerations of the tasks of all levels through zero space mapping; based on the accelerations of the tasks of all levels and the foot bottom force of the mechanical leg foot end, obtaining joint torques through a robot whole body dynamics equation after relaxation optimization of a trunk dynamics equation of the leg-arm collaborative robot, obtaining a control rate of the joint torques in combination with the positions and velocities of the tasks of all levels, and completing reproduction of the dancing actions. The trajectory generation efficiency is improved, and the dancing actions can be reproduced as much as possible under the premise of stability of the robot.

Description

Technical Field

[0001] This invention belongs to the field of legged-arm collaborative robot technology, and particularly relates to a method and system for generating and tracking the trajectory of a legged-arm collaborative robot dancing. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] Legged-arm collaborative robots are a new type of intelligent mobile robot system with active operation capabilities, consisting of a legged mobile platform with a robotic arm attached. They combine the strong terrain adaptability of legged robots with the powerful operational capabilities of robotic arms, showing great promise in disaster relief, logistics warehousing, and other fields. The realization of legged-arm collaborative robots dancing will allow them to break through traditional industrial production scenarios and expand into more fields such as entertainment performances, changing the usability of robots in the real world.

[0004] Several issues need to be considered to enable leg-arm collaborative robots to dance:

[0005] Firstly, there's the trajectory generation for multiple ends. A legged-arm collaborative robot has three ends: legs, torso, and robotic arm. Trajectory planning algorithms can generate multi-end trajectories based on a given objective function. However, achieving aesthetic appeal and overall coordination in a legged-arm collaborative robot's dance requires sophisticated planning algorithm design, and different dance movements necessitate different algorithms, leading to high difficulty and low efficiency. Using real-world biological motion capture methods can generate multi-end task trajectories with dance-like aesthetics, but this method demands sophisticated equipment and has a significant learning curve. Reinforcement learning can avoid the complexity of trajectory planning algorithms and the learning curve of motion capture, but it often requires substantial training time, resulting in low efficiency, and deploying physical prototypes is challenging.

[0006] Secondly, there's the modeling of legged collaborative robots. Adding a robotic arm to a legged robot necessitates considering the interactions between the robot and the ground, and between the robotic arm and the robot body. This makes the system's dynamics exceptionally complex, significantly increasing the difficulty of system modeling. For legged collaborative robots, modeling methods can be categorized into distributed modeling and overall modeling, depending on whether the robot body and robotic arm are modeled separately. Distributed modeling treats the robotic arm's influence on the robot body as an external disturbance. While this simplifies the modeling, the uncertainty of the disturbance makes overall robot control particularly challenging. Furthermore, because the overall joint configuration of a legged collaborative robot changes significantly during a dance, offline dynamics modeling cannot reflect the robot's true dynamic relationships, necessitating the more complex online dynamics modeling.

[0007] Thirdly, there is the stability of the leg-arm collaborative robot. Stability is the primary issue faced by all robots. In dance movements, the robot involves changes in the posture of its legs, torso, and robotic arms. The goal is to achieve the preset dance movement tracking control as much as possible while preventing robot instability. Summary of the Invention

[0008] To address the technical problems mentioned above, this invention provides a method and system for trajectory generation and tracking control of a legged collaborative robot dancing. It uses animation software to edit, generate, and optimize the dance movements of the legged collaborative robot. Compared with mainstream trajectory generation methods such as trajectory planning algorithms, biological motion capture, and reinforcement learning, this method reduces the equipment threshold and complexity, improves trajectory generation efficiency, and ensures that the robot can reproduce dance movements as stably as possible by prioritizing the multi-task end of the legged robot and using zero-space mapping for whole-body control.

[0009] To achieve the above objectives, the present invention adopts the following technical solution:

[0010] The first aspect of the present invention provides a method for trajectory generation and tracking control of a legged-arm collaborative robot dancing, comprising:

[0011] To obtain the dance movements of the leg-arm collaborative robot animation model in the animation software;

[0012] The dance motion is subjected to trajectory extraction and trajectory optimization to obtain the torso trajectory, robotic arm trajectory, robotic leg foot trajectory, and robotic leg foot force that conform to robot dynamics.

[0013] After prioritizing the tasks of the torso, robotic arm, and robotic leg, the position, velocity, and acceleration of each task are calculated by combining the torso trajectory, robotic arm trajectory, robotic leg foot trajectory, and robotic leg foot force through null space mapping.

[0014] Based on the acceleration of each task and the plantar force at the end of the mechanical leg, the joint torque is obtained through the robot's whole-body dynamics equation after relaxation optimization of the torso dynamics equation of the leg-arm collaborative robot.

[0015] Using joint torque as a feedforward quantity, combined with the position and speed of each task, proportional-derivative control is performed on the robot's joints to obtain the control rate of the joint torque, thus completing the reproduction of the dance movement.

[0016] Furthermore, the robot's whole-body dynamics equations are as follows:

[0017]

[0018] Among them, M 24×24 Let C be the robot mass distribution matrix. 24×1G is the generalized Coriolis force matrix. 24×1 Let f be the generalized gravity matrix. out,changed =f out +δf, f is obtained through zero-space iteration. out For the plantar force at the end of the mechanical leg, δf and Both are relaxation optimization solutions that satisfy the torso dynamics equations, J out Let τ represent the Jacobian matrix. 24×1 This indicates the joint torque.

[0019] Furthermore, the constraints for trajectory optimization include: rigid body dynamics model, force constraints when the foot is supported, force constraints when the foot is suspended, friction cone constraints at the foot, position constraints when the foot is supported, and position constraints at the end of the robotic arm.

[0020] Furthermore, the null space mapping includes: task-level null space mapping, position-level null space mapping, and acceleration-level null space mapping.

[0021] Furthermore, the torso, robotic arm, and robotic leg are each composed of several rigid bodies, which are connected by joints.

[0022] Furthermore, the null space mapping is based on the Jacobian matrix of each task;

[0023] The Jacobian matrix is ​​obtained by deriving the mapping relationship from Cartesian space to joint space of the leg-arm collaborative robot through the principle of virtual work.

[0024] Furthermore, the priority classification is in the following order: supporting leg, torso, robotic arm, and swing leg.

[0025] A second aspect of the present invention provides a trajectory generation and tracking control system for a leg-arm collaborative robot dancing, comprising:

[0026] The data acquisition module is configured to acquire the dance movements of the leg-arm collaborative robot animation model in the animation software.

[0027] The trajectory extraction module is configured to: extract and optimize the trajectory of the dance movement to obtain the torso trajectory, robotic arm trajectory, robotic leg foot end trajectory, and robotic leg foot end force that conform to robot dynamics.

[0028] The null space mapping module is configured to: prioritize the tasks of the torso, robotic arm, and robotic leg, and then calculate the position, velocity, and acceleration of each task level by combining the torso trajectory, robotic arm trajectory, robotic leg foot trajectory, and robotic leg foot force through null space mapping.

[0029] The relaxation optimization module is configured to: based on the acceleration and plantar force at the end of the mechanical leg at each level of task, obtain the joint torque through the robot's whole-body dynamics equation after relaxation optimization of the torso dynamics equation of the leg-arm collaborative robot;

[0030] The control module is configured to use joint torque as a feedforward quantity, combine it with the position and speed of each task, perform proportional-derivative control on the robot's joints to obtain the control rate of the joint torque, and complete the reproduction of the dance movement.

[0031] A third aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the trajectory generation and tracking control method for a leg-arm collaborative robot dancing as described above.

[0032] A fourth aspect of the present invention provides a computer device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps in the trajectory generation and tracking control method for a leg-arm collaborative robot dancing as described above.

[0033] Compared with the prior art, the beneficial effects of the present invention are:

[0034] This invention uses animation software to edit, generate, and optimize the dance movements of a leg-arm collaborative robot. Compared with mainstream trajectory generation methods such as trajectory planning algorithms, biological motion capture, and reinforcement learning, it reduces the equipment threshold and complexity, and improves the efficiency of trajectory generation.

[0035] This invention prioritizes the multi-tasking end of the legged robot and performs full-body control via zero-space mapping, ensuring that the robot can reproduce dance movements as stably as possible.

[0036] This invention introduces spatial vectors, kinematic trees, and advanced dynamics algorithms to perform overall modeling of the leg-arm collaborative robot, ensuring the accuracy of the dynamics model during robot dance. Attached Figure Description

[0037] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0038] Figure 1 This is a schematic diagram of the legged-arm collaborative robot structure according to Embodiment 1 of the present invention;

[0039] Figure 2 This is a flowchart of the trajectory generation and tracking control method for a leg-arm collaborative robot dancing according to Embodiment 1 of the present invention;

[0040] Figure 3 This is a skeletal relationship diagram of the robot animation model according to Embodiment 1 of the present invention;

[0041] Figure 4 This is a schematic diagram of the robot kinematics tree according to Embodiment 1 of the present invention;

[0042] Figure 5 This is a schematic diagram of the robot coordinate system according to Embodiment 1 of the present invention;

[0043] Figure 6 The robot single rigid body coordinate system T in Embodiment 1 of the present invention λ(i)，i With T i Relationship diagram. Detailed Implementation

[0044] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0045] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0046] Example 1

[0047] This embodiment provides a method for trajectory generation and tracking control of a legged and arm-assisted collaborative robot dancing.

[0048] This embodiment provides a trajectory generation and tracking control method for a leg-arm collaborative robot dancing. The trajectory generation method makes robot dance design and trajectory generation more efficient. Designers can interactively create and modify robot movements through visual effects, and obtain multi-terminal trajectories that satisfy the robot's torso dynamics after trajectory optimization. The tracking control method ensures that the robot can reproduce dance movements as accurately as possible while maintaining overall stability.

[0049] This embodiment provides a trajectory generation and tracking control method for a legged-arm collaborative robot dancing, wherein the legged-arm collaborative robot, such as... Figure 1 As shown, it includes a 6-DOF robotic arm and a quadruped robot with 12 DDOF.

[0050] The trajectory generation and tracking control method for a legged-arm collaborative robot dancing provided in this embodiment firstly introduces a technical path for editing, generating, and optimizing the robot's dance movements using the animation software Blender. Compared with mainstream trajectory generation methods such as trajectory planning algorithms, biological motion capture, and reinforcement learning, this method lowers the equipment threshold and complexity while improving trajectory generation efficiency. Secondly, by introducing spatial vectors, kinematic trees, and advanced dynamic algorithms, the legged-arm collaborative robot is modeled holistically, ensuring the accuracy of the dynamic model during the robot's dance. Finally, by prioritizing the multi-task ends of the legged-arm robot and implementing zero-space mapping for full-body control, the robot is ensured to reproduce the dance movements as accurately as possible while maintaining stability.

[0051] The method for trajectory generation and tracking control of a legged-arm collaborative robot dancing provided in this embodiment is as follows: Figure 2 As shown, the specific steps are as follows:

[0052] Step 1: Build an animation model of the Blender legged collaborative robot.

[0053] Exporting STL files of all components of the legged collaborative robot from the 3D CAD software SolidWorks, and then importing these STL files into the Blender animation software, Blender uses the principle of "skinned animation" to control the model's motion, that is, binding mesh entities to a specific "skeleton." A skeleton consists of a series of connected bones, each with a position and orientation. Bones can be combined into a hierarchical structure to form a skeleton. Rotating, translating, and scaling the bones in the skeleton controls the shape and movement of the associated model or object. In the design of the legged collaborative robot, the skeleton is used to represent the robot's four legs, one robotic arm, and body structure, as well as to control their movements.

[0054] To ensure the accuracy of the legged collaborative robot model in Blender, the number and hierarchical structure of the skeleton were designed accordingly. The robot model consists of 31 bones, including 6 control bones used to control the left and right forelegs, left and right hind legs, the robotic arm, and the torso. Each leg includes 4 component bones, the robotic arm includes 7 component bones, and the torso consists of 2 component bones. The skeleton relationship diagram is shown below. Figure 3 As shown, the skeletons of the parts on the legs and robotic arms are nested hierarchically through parent-child relationships, and rotational constraints are applied to each bone. Then, by controlling the movement of six control bones, the robot's torso, legs, and arms can be visualized and designed into dance motions.

[0055] Step 2: Multi-task trajectory extraction and optimization. Trajectory extraction and optimization are performed on the dance motion to obtain the torso trajectory, robotic arm trajectory, robotic leg foot trajectory, and robotic leg foot plantar force, all satisfying single rigid body dynamics.

[0056] After the robot's dance movements were designed, a Python-based trajectory extraction and visualization plugin was developed to extract the robot's multi-task trajectory, providing data support for subsequent trajectory optimization and tracking control.

[0057] The robot trajectory extracted from animation software typically only conforms to the robot's kinematic relationships. Therefore, optimizing the animation trajectory ensures it conforms to robot dynamics, while also making the animation trajectory as close as possible to the optimized trajectory. To this end, the following optimization problem is constructed:

[0058]

[0059] In the objective function, the input is the trajectory exported by the animation software, which serves as a reference. The output is the trajectory that satisfies the constraints, representing the optimization solution.

[0060] Taking the robot's torso trajectory as an example, the robot's trajectory changes continuously during movement. Here, we define a very small time interval dt, during which the trajectory remains unchanged, and the robot's torso trajectory only changes after the time interval dt. dt represents the time interval between the previous torso trajectory and the next torso trajectory. Similarly, x... N It can be understood as the optimized trajectory of the torso at the Nth time step dt, and of course, it also represents the trajectory at the last time step.

[0061] ①x ref The reference torso trajectory exported for the animation trajectory. The "ref" in the lower right corner is short for "reference," meaning reference value. ref =[roll,pitch,yaw,comx,comy,comz,dr,dp,dyaw,dx,dy,dz,g] 1×13 x ref The symbols in the diagram have the following meanings: torso attitude angles: roll, pitch, yaw; torso center of mass position vectors: comx, comy, comz; torso attitude angular velocity vectors: dr, dp, dyaw; torso center of mass velocity vectors: dx, dy, dz; g represents gravitational acceleration. x represents the torso trajectory that satisfies the constraints after optimization. N,ref The reference torso trajectory derived from the animation trajectory at the last time point is shown. (Note: The endpoint of the robot's torso motion trajectory is quite important due to factors such as motion transitions, so it is extracted as a separate optimization metric.) The x-axis of the last time point N is marked.ref That is, x N,ref x N This represents the torso trajectory at the last time point after optimization, when the constraints are satisfied.

[0062] ②p ref The positions of the robotic arm's end effector and each foot end are derived from the animation trajectory, serving as the reference trajectory p. ref =[x1,y1,z1,x2,y2,z2,x3,y3,z3,x4,y4,z4,x arm ,y arm ,z arm ]. p ref The symbols in the vector represent the following: x1, y1, z1 represent the position vector of the right foreleg foot; x2, y2, z2 represent the position vector of the left foreleg foot; x3, y3, z3 represent the position vector of the right hind leg foot; x4, y4, z4 represent the position vector of the left hind leg foot; x arm ,y arm ,z arm Let be the position vector of the robotic arm's end effector. p represents the optimized trajectory of the robotic arm's end effector and each foot end, satisfying the constraints.

[0063] ③f ref =[f RF T ,f LF T ,f RH T ,f LH T ] 1×12 For the force of contact between the robot's feet and the ground, f RF For example, The x, y, and z values ​​in the lower right corner represent the direction of the linear plantar force of the right front leg (RF). Animation software only deals with the robot's kinematics (position, velocity) and cannot derive f. ref The value of f, here. ref The value of is defined as follows: if the leg touches the ground (without swinging in the air), the linear force of the leg in the z direction is equal to the robot's mass divided by the number of legs touching the ground, and the linear forces in the x and y directions are 0. f is the ground-touching force that satisfies the constraints after optimization.

[0064] ④Q x Q p Q f Q N These are the parameters x, p, f, and x in the objective function, respectively. N Optimize weight parameters (e.g., increase Q) x The value of Q is reduced. p Q f QN This can make the entire optimization process focus more on solving the torso trajectory.

[0065] The optimization constraint settings mainly consider the robot's dynamics. To improve the optimization solution speed, the pose transformations of the quadrupeds and robotic arms are ignored, and only the state variable x of the torso is considered. k The contact force f between the four legs and the ground k As input, a simplified single-rigid-body dynamics model of the legged-arm collaborative robot is constructed:

[0066]

[0067] in,

[0068]

[0069]

[0070] Among them, A(12,13)=1, i body For the representation of trunk inertia in the world system, r i Represents the relative position of the foot tip (i) to the center of mass, m body This represents the mass of the robot's fuselage. Because the trajectory exported by the animation software satisfies kinematic relationships, no constraints are imposed on the robot's kinematics. For other constraints, f... k,z,stance ≥0 represents the force constraint in the z-direction when the foot is supported, f k,z,swing =0 means the force in the z-direction is 0 when the foot is suspended in the air. -μf k,z ≤f k,x ≤μf k,z -μf k,z ≤f k,y ≤μf k,z The friction cone constraint at the foot end ensures the stability of the fuselage. k,foot,z,satance =0 represents the position when the foot is supporting the weight, p arm,z >0 represents the position constraint at the end effector of the robotic arm. k That is, f, where the subscript k represents the kth time step. k That is, f is the result of optimization at the k-th time step dt. k,x Let f be the x-direction component of the linear force f at the k-th time step. k,y Let f be the y-direction component of the linear force f at the k-th time step. k,z Let f be the z-direction component of the linear force f at the k-th time step. μ is the coefficient of sliding friction. k,z,swing In the middle, "swing" represents the legs dangling in the air. k,z,stance In the middle, "stance" represents the leg touching the ground.

[0071] The nonlinear optimization problem is solved using a planning solver, and the torso trajectory x, the robotic arm and foot trajectory p, and the corresponding foot force f satisfy the single rigid body dynamics are finally obtained.

[0072] It should be noted that the single rigid body model is established using the following two formulas as the starting point:

[0073] (1) Force analysis of robot torso (translational dynamics): Vertical upward support force provided by the supporting leg: z-axis component of f z The force of gravity acting on the torso; using Newton's second law f=ma, we obtain the torso acceleration.

[0074] (2) Rotational Dynamics: According to the angular momentum theorem, the differential of the angular momentum of a rigid body at its center of mass with respect to time is equal to the vector sum of the torques produced at the center of mass by all external forces acting on the rigid body, i.e. ω is the torso attitude angular velocity vector: dr, dp, dyaw, f i Represents the three-dimensional linear force of the i-th contact leg.

[0075] (3) Analysis: It simply means that the two formulas above are written in matrix form.

[0076] Step 3: Robot kinematic tree modeling and kinematics.

[0077] To ensure the accuracy of the model, a URDF file of the legged collaborative robot was exported using the 3D CAD software SolidWorks. The robot's kinematics tree was then built using the URDF file. Figure 4 In the kinematic tree, a single index represents a rigid body of the robot, and the connecting lines between rigid bodies represent joints between them.

[0078] To achieve control of the floating-base quadruped robot, a virtual 6-DOF (degrees of freedom) for the torso is introduced. To meet programming requirements, the rigid body of the leg-arm collaborative robot's torso is numbered 5 in the kinematic tree. The entire kinematic tree contains 18 rigid bodies and 18 joints. Number 5 represents the robot's torso. The right foreleg contains three rigid body components numbered 6-7-8, where 6 represents the hip, 7 the thigh, and 8 the lower leg. The left foreleg is numbered 9-10-11, the right hind leg is numbered 12-13-14, the left hind leg is numbered 15-16-17, and 18-23 represent the rigid body components of the robotic arm. The relative positions, masses, and inertia tensors of each rigid body, as well as the joint types and rotation axis positions between rigid bodies, can all be directly obtained from the robot's own configuration.

[0079] To facilitate the subsequent derivation of dynamic parameters, rigid body relation notation is introduced. Let λ(i) represent the parent rigid body of rigid body i. Let μ(i) represent the child rigid body of rigid body i. Let v(i) represent all subtrees starting from rigid body i and ending at the branch, including rigid body i. Let κ(i) represent the subtree starting from the root and ending at rigid body i, excluding rigid body i. Based on... Figure 4 A simple example of rigid body relation notation is as follows:

[0080] λ(6)=λ(9)=λ(12)=λ(15)=λ(18)=5

[0081] λ(19)=18,λ(23)=22

[0082] μ(5) = {6, 9, 12, 15, 18}

[0083] μ(18)=19, μ(20)=21

[0084] ν(5)={5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23}

[0085] ν(18)={18,19,20,21,22,23}

[0086] κ(11)={5,9,10}

[0087] κ(22)={5,18,19,20,21}

[0088] Based on the kinematic tree, the kinematic relationships of the legged-arm collaborative robot are derived, and the coordinate systems of each rigid body of the legged-arm collaborative robot are established, such as... Figure 5 and Figure 6 As shown, w represents the world coordinate system, B represents the fixed coordinate system of the torso's center of mass, and each other rigid body exists in two coordinate systems: T λ(i) With T λ(i)，i (Unless otherwise stated, the rigid body coordinate system mentioned below refers to T) λ(i) ). T λ(i) With T λ(i)，i The positional relationship is determined based on the configuration of the leg-arm collaborative robot. The change in joint angle between the parent rigid body λ(i) and the child rigid body i is defined as q. i When q i When T = 0, λ(i)，i With T i Overlap. T λ(i) With T λ(i)，i Both are coordinate systems established on the rigid body λ(i), while T i This is a coordinate system established on rigid body i. Let λ(i) denote the parent rigid body of rigid body i, and T λ(i)T represents the first coordinate system on the rigid body λ(i). λ(i)，i This represents the second coordinate system on the rigid body λ(i). Establishing two coordinate systems on a rigid body is to integrate two sets of dynamics (rigid body translational dynamics and rotational dynamics) calculations into a single set of formulas, reducing the number of formulas and improving computational efficiency. The condition for integrating translational and rotational dynamics is that there is no relative displacement between the two rigid body coordinate systems. If a single coordinate system is established for a single rigid body, the integration condition cannot be met; therefore, two coordinate systems T are established on each rigid body. λ(i) With T λ(i)，i T λ(i) With T λ(i)，i The relationship between them represents the lengths of rigid bodies, and there will be no relative displacement or rotation; while T λ(i)，i With the next rigid body i, T i This can be understood as the length relationship of the joint connecting two rigid bodies λ(i) and i, which involves relative rotation but no relative displacement. The first parameter in the subscript represents the coordinate system established on the rigid body λ(i), and the second parameter i represents the sub-rigid body i connected to it.

[0089] To address the issue of low computational efficiency in traditional kinematics and dynamics algorithms due to the complex structure of legged collaborative robots, this paper proposes a method based on spatial vectors to simplify formula derivations and improve modeling efficiency. This method utilizes a 6-dimensional vector [ω...] x ,ω y ,ω z ,v x ,v y ,v z T [] represents the spatial velocity of a rigid body, where ω represents angular velocity and v represents linear velocity. Using a 6-dimensional vector [n] ox ,n oy ,n oz ,f x ,f y ,f z ] T This represents the spatial force of a rigid body, where n represents torque and f represents force.

[0090] The transformation relationship for spatial velocity from rigid body coordinate system A to rigid body coordinate system B is as follows:

[0091]

[0092] From B to A:

[0093]

[0094] Where E = B R ALet r be the three-dimensional rotation matrix from coordinate system A to coordinate system B, and let r be the three-dimensional vector pointing from the origin of coordinate system A to the origin of coordinate system B. Let r× represent the cross product operator of the three-dimensional vector, which is a 3-dimensional matrix.

[0095] The transformation relationship of spatial forces from rigid body coordinate system A to rigid body coordinate system B is as follows:

[0096]

[0097] From B to A:

[0098]

[0099] Space velocity transformation matrix B X A With spatial force transformation matrix The following transformation relationship exists:

[0100]

[0101] The kinematics of the leg-arm collaborative robot are derived using a constructed kinematic tree and spatial vectors. The torso pose angles are calculated from the robot's torso IMU. 5 E w The position r of the robot's center of mass relative to the world coordinate system is obtained from the state estimation. w5 This leads to the spatial velocity transformation matrix from the world coordinate system w to the torso center of mass coordinate system B. 5 X w ,5 represents the index of the torso in the kinematics tree (hereinafter referred to as torso 5). After obtaining the relationship between the rigid body coordinate system of torso 5 and the world system, the kinematic relationship of the leg-arm collaborative robot is derived by traversing the kinematics tree through the rigid body relationship, as shown in the following formula:

[0102] i X λ(i) =X J (i)X T (i)

[0103]

[0104] in, i X λ(i) This represents the transformation relationship of spatial velocity from the parent rigid body λ(i) of rigid body i to the coordinate system of rigid body i. J (i) represents the coordinate system T at joint i. λ(i)，i With T i The transformation relationship (of the first coordinate system on rigid body i) is such that, since all joints of the leg-arm collaborative robot are rotary joints, X... J (i) Based on the different forms of the joint rotation axis and the rotation angle value q fed back by each joint iIt can be represented as:

[0105]

[0106] X T (i) represents the two coordinate systems T on the rigid body i. i With T i,μ(i) The fixed positional relationship, without angle changes, can be directly determined based on the actual situation of the leg-arm collaborative robot. i v i This represents the spatial velocity of rigid body i in the rigid body coordinate system i. i S i Let the joint subspace mapping matrix of rigid body i be represented in the coordinate system of rigid body i. If the joint corresponding to rigid body i has a single degree of freedom and rotates about the x-axis, then i S i =[1,0,0,0,0,0] T The torso has 6 degrees of freedom in space, so its position in the torso's 5-coordinate system... 5 S5 is a six-dimensional identity matrix, representing the matrix of all joints of the robot. i S i It can be determined directly based on the type of each joint of the robot. The rate of change of the joint angle of joint i can be obtained directly through the joint sensor.

[0107] For the kinematics tree branch of a 6-DOF robot, the transformation matrix for spatial velocity from the world frame to the robot's 23-coordinate system can be expressed as:

[0108]

[0109] Among them, S i It is the joint subspace mapping matrix, because It is the rate of change of joint angle, which is one-dimensional, while the spatial velocity... 18 v 18 It is 6-dimensional, so it needs S. i Map it to 6 dimensions.

[0110] Based on the block matrix, through 23 X w get w X 23 The spatial velocity of the robotic arm's end effector is obtained. w v 23 By combining the relationship between the robotic arm's end effector and the 23 coordinate system, the position of the robotic arm's end effector in the world coordinate system can be obtained. w p arm .

[0111] For the kinematic tree branches of the four 3-DOF legs, taking the right foreleg as an example, the spatial velocity transformation matrix can be expressed as:

[0112] 8 X w = 8 X7 7 X6 6 X5 5 X w

[0113]

[0114]

[0115]

[0116] w v8= w X8 8 v8

[0117] w v RF = w v8

[0118] The positions of the remaining leg end rigid bodies relative to the world coordinate system are obtained using the same method as for the robotic arm. w p RF , w p LF , w p RH , w p LH With space velocity w v RF , w v LF , w v RH , w v LH .

[0119] At this point, the mapping from the joint space of the leg-arm collaborative robot to Cartesian space has been completed, and the forward kinematics solution has been finished.

[0120] By applying the principle of virtual work, the mapping relationship between the Cartesian space and the joint space of the leg-arm collaborative robot is derived, the task Jacobian matrix corresponding to the multi-task end is obtained, and the inverse kinematics of the robot is solved.

[0121] When the robot is in static equilibrium, for the robot as a whole, the work done by the set of spatial force vectors F acting on each end (Cartesian space) to produce a set of relative displacements δx is the same as the work done by the set of joint angle changes δq caused by the set of joint torques τ at each joint (joint space), which is the principle of virtual work.

[0122] F T δx=τ Tδq

[0123] (F) T =[F RF T ,F LF T ,F RH T ,F LH T ,F Arm T ] 1×30

[0124] δx=[δx RF ,δθ RF ,...,δx LH ,δθ LH ,δx Arm ,δθ Arm ] T 30×1

[0125] τ T =[τ0,...,τ6,...,τ 23 ] 1×24

[0126] δq=[δq0,...,δq6,...,δq 23 ] T 24×1

[0127] Among them, F RF δx RF δθ RF These represent the spatial force vector, displacement, and attitude change of the right foreleg foot, respectively. LF δx LF δθ LF These represent the spatial force vector, displacement, and attitude change of the left foreleg foot, respectively. LH δx LH δθ LH These represent the spatial force vector, displacement, and attitude change of the left hind leg foot, respectively. RH δx RH δθ RH These represent the spatial force vector, displacement, and attitude change of the right hind leg foot, respectively. Arm δx Arm δθ Arm These represent the spatial force vector, displacement, and attitude change of the robotic arm, respectively, τ. i δq i These represent the torque and angle changes at the joints corresponding to rigid body i of robot i, respectively.

[0128] Since δx = Jδq, the following relationship exists for the entire robot:

[0129] τ=J T F

[0130] For a single rigid body and its corresponding joints, τ i = i S i T F i F i Let i be the spatial force acting on rigid body i. The spatial force vector acting on the corresponding rigid body is mapped to its joint space torque by transposing the joint subspace mapping matrix.

[0131] Combining the above formulas, we traverse the kinematic tree to derive the Jacobian matrix corresponding to the task space and the generalized joint space:

[0132]

[0133]

[0134] like Figure 4 As shown in the kinematic tree, with For example, RF in the upper left corner represents the right foreleg, 5 in the lower right corner represents the torso, its rigid body index in the kinematic tree is 5, T in the upper right corner represents matrix transpose, and X represents the velocity space rotation matrix. i X λ(i) This represents the transformation relationship of spatial velocity from the parent rigid body λ(i) of rigid body i to the coordinate system of rigid body i. * The asterisk (*) in the upper right corner represents spatial force rotation. This represents the spatial force rotation matrix.

[0135] This can be obtained through forward kinematics. RF The X5 motion space transformation matrix is ​​used to obtain the corresponding joint subspace mapping matrix based on the joint type. i S i At this point, the Jacobian matrix J corresponding to the task space and the generalized joint space has been solved. The task Jacobian matrix corresponding to the multi-task end can be obtained by dividing J into blocks, and the robot inverse kinematics solution is complete. Taking a 3-DOF robotic arm as an example, the task space represents the end-effector position [x, y, z]. The generalized joint space represents the angle changes of each joint of the robotic arm [q1, q2, q3]. When the end-effector reaches a certain position, its joint angles also match that position. The task space corresponds to the end-effector position, and the joint space corresponds to the joint angles of the robotic arm. The reason for writing the generalized joint space in this embodiment is that it not only considers the angles of the robotic arm, but also the angles of each leg and the virtual 6-DOF of the torso.

[0136] Step 4: Model the overall dynamics of the robot.

[0137] Leg-arm collaborative robots dancing is a method of... Calculate the corresponding joint torque τ 24×1 Inverse dynamics solution process. While the joint angle changes can be obtained by second-differentiating the changes when exporting the trajectory from animation software, the error is too large. Therefore, in this step of overall dynamic modeling, we first... Treating it as a known quantity, it will be determined by q in step 5 below. Obtained through zero-space iteration method

[0138] The dynamic equations of the legged-arm collaborative robot are in the form of:

[0139]

[0140] Among them, M 24×24 Let C be the robot mass distribution matrix. 24×1 G is the generalized Coriolis force matrix. 24×1 These three matrices are generalized gravity matrices, and they are all related to the robot configuration q. related, Let τ be the generalized joint space vector of the robot. 24×1 J is the joint torque. c,RF Let f be the contact force at the right foreleg foot. Since torque has little effect on the contact between the foot and the ground, only the three-dimensional linear force at the foot is considered (f). RF ) 3×1 、(f LF ) 3×1 、(f RH ) 3×1 、(f LH ) 3×1 , and (f RF ) 3×1 、(f LF ) 3×1 、(f RH ) 3×1 、(f LH ) 3×1 The contact Jacobian matrix (J) can be obtained through trajectory optimization in step 2, which is the plantar force f. c,RF ) 3×24 、(J c,LF ) 3×24 、(J c,RH ) 3×24 、(J c,LH ) 3×24 This can be obtained by dividing the Jacobian matrix J of the task space and generalized joint space obtained in step 3 into blocks. In summary, besides the joint torque τ... 24×1The unknown quantity in the dynamic equations of the legged-arm collaborative robot is currently M. 24×24 C 24×1 G 24×1 .

[0141] First, the robot mass distribution matrix M is obtained by combining rigid bodies. 24×24 .

[0142] The total kinetic energy of the robot's kinematic tree is equal to the sum of the kinetic energies of the rigid bodies in the tree; therefore, we have...

[0143]

[0144] Among them, v k Let k be the rigid body space velocity. κ(k) is the rigid body relation symbol mentioned in step 3, representing the subtree starting from the root and ending at rigid body k, excluding rigid body k. k The spatial inertia matrix, m k Let k be the mass of the rigid body, and r be the mass of the rigid body. × The cross product operator, I, represents the position of the center of mass in a rigid body coordinate system. i Let I be the rigid body inertia tensor. 3×3 It is a third-order identity matrix.

[0145] The rigid body velocity v k Substituting the formula into the kinetic energy equation, we get:

[0146]

[0147] This formula traverses the entire kinematics tree, and since rigid bodies i and j jointly support rigid body k, this formula can be reformulated as:

[0148]

[0149] The total kinetic energy of the robot's kinematic tree can also be obtained through the mass distribution matrix M. 24×24 Representation of joint space state quantities:

[0150]

[0151] By comparing the two robot kinetic energy expressions, we can obtain M. ij The corresponding expression is:

[0152]

[0153] I i c Represents the combined rigid body i. i X j *This represents the spatial force rotation matrix. Thus, the robot's mass distribution matrix M... 24×24 Calculation complete.

[0154] Secondly, obtain the robot mass distribution matrix C. 24×1 With G 24×1 Observe the robot's dynamic equations, when and the contact force F at the foot end foot When the value is 0, the dynamic equation is expressed as: C 24×1 +G 24×1 =τ 24×1 Therefore, τ can be obtained using the recursive Newton-Euler method. 24×1 Get C 24×1 With G 24×1 The recursive Newton-Euler method is as follows:

[0155]

[0156]

[0157]

[0158] τ i = i S i Ti F i

[0159] in, i a i Let the spatial acceleration of rigid body i in coordinate system T be... i The representation in the text. λ(i) a λ(i) Let λ(i) be the spatial acceleration of the rigid body in coordinate system T. λ(i) The representation in the text. i v i Let the spatial velocity of rigid body i in coordinate system T be... i The representation in [the text]. i Represents the spatial inertia of rigid body i, × * It is the cross-star multiplication of spatial vectors. i I represents the spatial acceleration of rigid body i. i v represents the spatial inertia of rigid body i. i This represents the spatial velocity of rigid body i. i X w * This represents the spatial force rotation matrix that transforms the world system w to the rigid body coordinate system i. i X j * Represented by the rigid body coordinate system T j Transform to rigid body coordinate system T i The spatial force rotation matrix.j F j The spatial force F acting on rigid body j in the rigid body coordinate system T represents the force F acting on rigid body j in the rigid body coordinate system T. j The representation in the text.

[0160] Let the above formula F foot τ calculated as 0 i Combining them into a column vector gives C 24×1 +G 24×1 .

[0161] Step 5: Task-based hierarchical control and relaxation optimization. After prioritizing the tasks of the torso, robotic arm, and robotic leg, the position, velocity, and acceleration of each task are calculated through null space mapping, combining the torso trajectory, robotic arm trajectory, robotic leg foot trajectory, and robotic leg foot force. Based on the acceleration of each task and the robotic leg foot force, the joint torque is obtained through relaxation optimization of the torso dynamics equation of the leg-arm collaborative robot and then through the robot's whole-body dynamics equation. Using the joint torque as a feedforward, combined with the position and velocity of each task, proportional-derivative control is performed on the robot's joints to obtain the control rate of the joint torque, thus completing the reproduction of the dance movement.

[0162] Prioritize tasks for the robot's torso, legs, and arms, and use a zero-space mapping method to achieve full-body control of the leg-arm collaborative robot, reproducing dance movements while ensuring robot stability.

[0163] The tasks are prioritized as follows: supporting leg, torso pose, robotic arm pose, and swinging leg (the supporting leg's foot always touches the ground, while the swinging leg's foot swings in the air; the leg's ground contact information is obtained during animation model export). The supporting leg task provides the robot with the foot force needed to perform actions and is the foundation for robot dance. The torso pose task is a prerequisite for maintaining robot stability, so it is ranked second or third in priority. Precise control of the robotic arm pose enables the leg-arm collaborative robot to present better dance effects, such as the "chicken head mode." The robot's swinging leg has a relatively low impact on both robot stability and dance effects, so the swinging leg's foot task is ranked as the lowest priority.

[0164] The torso trajectory x represents the torso pose task. The corresponding plantar force f represents the supporting leg task. The foot trajectory represents the swing leg task. The robotic arm trajectory represents the robotic arm pose task.

[0165] For the two tasks of the leg-arm collaborative robot, the Jacobian matrices J1 and J2 of Task 1 and Task 2 respectively completed the inverse kinematics solutions of their respective tasks and the generalized joint state variables (generalized joint space, representing the angle values ​​of each joint of the robotic arm, the leg joints, and the virtual 6-DOF joints of the torso). In general, J1 is not a square matrix. The pseudo-inverse matrix of J1 is: therefore It can be converted into N1 is the null projection matrix. Its function is to make any Map it to the null space of J1 so that it does not interfere with the task of task 1. To cause any impact. Substitution middle: Therefore, the generalized space vectors of both Task 1 and Task 2 can be implemented simultaneously. Since N1 is an idempotent Hermitian matrix, we have Let the generalized space state quantity of Task 1 be denoted as... Simultaneously implement the generalized spatial state variables of Task 1 and Task 2 as follows: make Then there is And so on, mapping the third task. Within the null space of the second task, there is in When the number of tasks is expanded to n, there is a task-level null space mapping. in

[0166]

[0167] Depend on (Velocity is obtained by the differential of position) (The angular velocity is obtained by differentiating the angle) to obtain the iterative formula for the position-level null space mapping: Will Differentiation yields the iterative formula for the null space mapping of the acceleration level: By using null space mapping, priority control of multiple tasks in a legged-arm collaborative robot can be achieved. The iterative formulas for the position, velocity, and acceleration levels of the nth-level task are integrated as follows:

[0168] Position-level iterative formula:

[0169]

[0170] Differentiation yields the velocity level iterative formula:

[0171]

[0172] Differentiating again yields the iterative formula for the acceleration level:

[0173]

[0174] After the iteration is complete, [(J c,RF T ) 24×3 (fRF ) 3×1 +...+(J c,LH T ) 24×3 (f LH ) 3×1 ] is denoted as J out T f out The torso dynamics equations of the leg-arm collaborative robot are as follows:

[0175]

[0176] Among them, J c,RF Let be the contact Jacobian matrix for the right forefoot, where 'c' represents contact, since contact force only occurs when the foot tip contacts the ground. RF represents the right front foot. This matrix is ​​obtained by dividing the Jacobian matrix J corresponding to the task space and generalized joint space, as calculated in step 3, into blocks. J out f represents the total contact Jacobian matrix obtained by combining the contact Jacobian matrices of each supporting leg. out S represents the total contact force vector, which is a combination of contact forces. base This represents a 6-dimensional selection matrix for the torso. (Without adding S) base Time is the dynamic equation of the whole body.

[0177] The two sides of the equation are not equal because the left side... The force on the right foot is obtained through zero-space iteration, while the force on the right foot is obtained through optimization of the robot's simplified single rigid body model (step 2). Therefore, relaxation optimization is performed on the robot's torso dynamics equations to obtain a suitable result. The contact external force satisfies the torso dynamics equation.

[0178] The relaxation optimization process is as follows:

[0179]

[0180] in, δf is the plantar force f obtained by optimizing the trajectory. out Joint space acceleration obtained by iteration with null space The relaxation optimization solution quantity that satisfies the torso dynamics equations, -μf k,z ≤f k,x ≤μf k,z With -μf k,z ≤f k,y ≤μf k,z This represents the constraint on the plantar force during trajectory optimization in step 2.

[0181] In obtaining with f out,changedThen, the corresponding joint torque τ can be obtained through the robot's whole-body dynamics equations. 24×1 :

[0182]

[0183] The obtained torque τ is used as the feedforward quantity, combined with the position and velocity of each task after zero-space iteration. With Δq n The robot's physical joints are controlled by joint PD (proportional-derivative) control, with a control rate of:

[0184]

[0185] Where, τ joint The torque of the robot's physical joint motors is the vector formed by removing the torques of the first six virtual joints of the torso from the torque τ mentioned earlier. p : Proportional coefficient in proportional-derivative control. q: Current joint angle value. Current angular velocity of the joint.

[0186] Calculate the control rate τ of the torque of each joint of the robot. cmd After that, the dance movements of the leg-arm collaborative robot can be reproduced.

[0187] Example 2

[0188] This embodiment provides a trajectory generation and tracking control system for a legged-arm collaborative robot dancing, which specifically includes:

[0189] The data acquisition module is configured to acquire the dance movements of the leg-arm collaborative robot animation model in the animation software.

[0190] The trajectory extraction module is configured to: extract and optimize the trajectory of the dance movement to obtain the torso trajectory, robotic arm trajectory, robotic leg foot end trajectory, and robotic leg foot end force that conform to robot dynamics.

[0191] The null space mapping module is configured to: prioritize the tasks of the torso, robotic arm, and robotic leg, and then calculate the position, velocity, and acceleration of each task level by combining the torso trajectory, robotic arm trajectory, robotic leg foot trajectory, and robotic leg foot force through null space mapping.

[0192] The relaxation optimization module is configured to: based on the acceleration and plantar force at the end of the mechanical leg at each level of task, obtain the joint torque through the robot's whole-body dynamics equation after relaxation optimization of the torso dynamics equation of the leg-arm collaborative robot;

[0193] The control module is configured to use joint torque as a feedforward quantity, combine it with the position and speed of each task, perform proportional-derivative control on the robot's joints to obtain the control rate of the joint torque, and complete the reproduction of the dance movement.

[0194] It should be noted that each module in this embodiment corresponds one-to-one with each step in Embodiment 1, and their specific implementation processes are the same, so they will not be repeated here.

[0195] Example 3

[0196] This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps in the trajectory generation and tracking control method for a leg-arm collaborative robot dancing as described in Embodiment 1 above.

[0197] Example 4

[0198] This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the trajectory generation and tracking control method for a leg-arm collaborative robot dancing as described in Embodiment 1 above.

[0199] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0200] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

Claims

1. A method for trajectory generation and tracking control of a legged-arm collaborative robot dancing, characterized in that, include: To obtain the dance movements of the leg-arm collaborative robot animation model in the animation software; The dance movements are extracted and optimized to obtain the torso trajectory, robotic arm trajectory, robotic leg foot trajectory, and robotic leg foot force that conform to robot dynamics. The constraints for trajectory optimization include: rigid body dynamics model, force constraints when the foot is supported, force constraints when the foot is suspended, friction cone constraints at the foot, position constraints when the foot is supported, and position constraints at the end of the robotic arm. After prioritizing the tasks of the torso, robotic arm, and robotic leg, and combining the torso trajectory, robotic arm trajectory, robotic leg foot trajectory, and robotic leg foot force, the priority ranking is in the following order: supporting leg, torso, robotic arm, and swinging leg. Through null space mapping, which includes task-level null space mapping, position-level null space mapping, and acceleration-level null space mapping, the position, velocity, and acceleration of each task are calculated. Based on the acceleration at each task level and the plantar force at the end of the mechanical leg, after relaxation optimization of the trunk dynamics equation of the leg-arm collaborative robot, the joint torque is obtained through the robot's whole-body dynamics equation. The robot's whole-body dynamics equation is as follows: in, The mass distribution matrix of the robot. For the generalized Coriolis force matrix, For the generalized gravity matrix, , , Obtained through zero-space iteration For the robot's generalized joint space vectors For the mechanical leg foot end plantar force, and All of these are relaxation optimization solutions that satisfy the trunk dynamics equations. Represents the Jacobian matrix. Indicates joint torque; Using joint torque as a feedforward quantity, combined with the position and speed of each task, the robot's joints are subjected to proportional-derivative control to obtain the control rate of the joint torque, thereby completing the reproduction of the dance movement.

2. The trajectory generation and tracking control method for a legged-arm collaborative robot dancing as described in claim 1, characterized in that, The torso, robotic arm, and robotic leg are each composed of several rigid bodies, which are connected by joints.

3. The trajectory generation and tracking control method for a legged-arm collaborative robot dancing as described in claim 1, characterized in that, The null space mapping is based on the Jacobian matrix of each task; The Jacobian matrix is ​​obtained by deriving the mapping relationship from Cartesian space to joint space of the leg-arm collaborative robot through the principle of virtual work.

4. A trajectory generation and tracking control system for a legged-arm collaborative robot dancing, characterized in that, include: The data acquisition module is configured to acquire the dance movements of the leg-arm collaborative robot animation model in the animation software. The trajectory extraction module is configured to: extract and optimize the trajectory of the dance movements to obtain the torso trajectory, robotic arm trajectory, robotic leg foot trajectory, and robotic leg foot force conforming to robot dynamics. The constraints for trajectory optimization include: rigid body dynamics model, force constraints when the foot is supported, force constraints when the foot is suspended, friction cone constraints at the foot, position constraints when the foot is supported, and position constraints at the end of the robotic arm. The zero-space mapping module is configured to: prioritize the tasks of the torso, robotic arm, and robotic leg, and then combine the torso trajectory, robotic arm trajectory, robotic leg foot trajectory, and robotic leg foot force, wherein the priority ranking is in the order of: supporting leg, torso, robotic arm, and swinging leg, and calculate the position, velocity, and acceleration of each task level through zero-space mapping, which includes: task-level zero-space mapping, position-level zero-space mapping, and acceleration-level zero-space mapping; The relaxation optimization module is configured to: based on the acceleration and plantar force at the end of the mechanical leg at each task level, after relaxation optimization of the trunk dynamics equation of the leg-arm collaborative robot, obtain the joint torque through the robot's whole-body dynamics equation, which is: in, The mass distribution matrix of the robot. For the generalized Coriolis force matrix, For the generalized gravity matrix, , , Obtained through zero-space iteration For the robot's generalized joint space vectors For the mechanical leg foot end plantar force, and All of these are relaxation optimization solutions that satisfy the trunk dynamics equations. Represents the Jacobian matrix. Indicates joint torque; The control module is configured to use joint torque as a feedforward quantity, combine it with the position and speed of each task, perform proportional-derivative control on the robot's joints to obtain the control rate of the joint torque, and complete the reproduction of the dance movement.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps in the trajectory generation and tracking control method for a leg-arm collaborative robot dancing as described in any one of claims 1-3.

6. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the trajectory generation and tracking control method for a leg-arm collaborative robot dancing as described in any one of claims 1-3.

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