An autonomous obstacle avoidance trajectory planning method for a humanoid robot mechanical arm

Abstract

This invention relates to the field of robotics and discloses an autonomous obstacle avoidance trajectory planning method for a humanoid robot arm. By sensing the environment and pose, an initial virtual three-dimensional lattice network is generated in the workspace. The robot arm's operability matrix is ​​calculated and eigenvalues ​​are extracted, establishing a mapping relationship with negative Poisson's ratio, and updating the anisotropic compliance tensor of the lattice network. Obstacles are represented as rigid indenters intruding into the lattice network. Based on the negative Poisson's ratio same-sign strain effect, the comprehensive strain tensor of the compressed region is solved, and the coordinate system of the continuous low-potential energy channel formed by tangential contraction is extracted. The robot arm is fitted as a continuous elastic spline curve, and the internal smooth strain energy and external constraint energy are superimposed to generate a total strain energy functional. The obstacle avoidance spline trajectory corresponding to the minimum value of the functional is solved using the variational method and converted into driving commands for execution. This invention eliminates stationary points at minimum values, ensuring the continuity and mechanical stability of obstacle avoidance.

Description

Technical Field

[0001] This invention relates to the field of robotics, specifically to a method for autonomous obstacle avoidance trajectory planning for a humanoid robot arm. Background Technology

[0002] Autonomous obstacle avoidance trajectory planning for humanoid robotic arms refers to the process by which a system calculates a collision-free, continuous trajectory that satisfies specific constraints in real time, based on obstacle spatial pose information acquired by sensors and the robotic arm's own kinematic model, in a known or unknown dynamic working environment. This technology is a fundamental module ensuring the safety of humanoid robots performing complex interactive tasks, physical grasping operations, and human-robot collaboration. The reliability of its planning algorithm directly determines the robotic arm's operational efficiency and control stability in a three-dimensional Cartesian workspace.

[0003] In current applications of autonomous obstacle avoidance trajectory planning for robotic arms, control logic based on the artificial potential field method is widely adopted. This method constructs a virtual force field within the robotic arm's workspace, setting the target position as the gravitational source generating global attraction and physical obstacles in the environment as repulsive sources generating repulsive forces. Within the control cycle, the system calculates the gravitational and repulsive vectors acting on each control point on the robotic arm's links, generates a combined force direction through vector superposition, and then uses the gradient descent path of this combined force direction to guide the robotic arm towards the target point in space while avoiding obstacle boundaries.

[0004] This traditional trajectory planning mechanism, which relies on scalar distance calculations and the superposition of repulsive force vectors, has an inherent limitation of local minima. When a physical obstacle is located near the line connecting the robot's control point and the target point, or within a complex and confined space, the repulsive force vector generated by the obstacle and the attractive force vector generated by the target point are very likely to be collinear and equal in magnitude at a specific spatial location, causing the combined force vectors to cancel each other out. This mutual cancellation of force vectors can cause the robot to fall into a mathematically zero-gradient state in front of the obstacle, leading to stagnation or high-frequency motion oscillations in the robot's underlying control system within the local minimum region. This makes it impossible to guarantee the determinism of the path search and the continuity of the obstacle avoidance physical process. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides an autonomous obstacle avoidance trajectory planning method for a humanoid robot arm, solving the problems mentioned in the background section.

[0006] To achieve the above objectives, the present invention provides an autonomous obstacle avoidance trajectory planning method for a humanoid robot arm.

[0007] The method includes state initialization and environmental geometry representation steps. The environment and body perception module obtains the initial joint configuration vector of the humanoid robot arm, solves the reference pose of each link of the robot arm in the three-dimensional Cartesian workspace through the forward kinematic equation, and synchronously drives the three-dimensional environment perception device to scan the robot arm workspace to obtain obstacle geometric envelope data.

[0008] In the anisotropic reconstruction step of the virtual lattice based on the operability ellipsoid, the tensor field dynamics reconstruction module maps and generates an initial virtual three-dimensional lattice network within the robot arm's workspace. The tensor field dynamics reconstruction module calculates the robot arm's operability matrix under the initial joint configuration vector and performs eigenvalue decomposition to extract the spatial principal axis directions of the operability ellipsoid. The tensor field dynamics reconstruction module establishes a physical mapping relationship between the negative Poisson's ratio parameter and eigenvalues, updating the anisotropic compliance tensor of the virtual three-dimensional lattice network. Specifically, the reconstruction principle involves substituting the resolved current joint configuration vector into the kinematic model to update the homogeneous transformation matrix, extracting the position and direction vectors, and generating the robot arm Jacobian matrix using a vector cross product algorithm. The robot arm Jacobian matrix is ​​multiplied by its transpose to construct a symmetric positive definite operability matrix. Matrix eigenvalue decomposition is performed on the operability matrix to extract real eigenvalues ​​on the main diagonal and orthogonal column vectors in the orthogonal eigenvector matrix. The orthogonal column vectors are directly assigned the rotation transformation matrix from the local coordinate system of the discrete mesh nodes to the spatial base coordinate system, aligning the local orthogonal basis with the spatial principal axis direction of the operand ellipsoid. When calculating the mechanical constitutive parameters, the principal axis direction of the operand ellipsoid is used as the local orthogonal coordinate system. The ratio of the real eigenvalue corresponding to the principal axis direction to the largest eigenvalue is multiplied by a preset proportional gain constant to obtain a negative Poisson's ratio parameter with a negative sign. This calculation logic assigns a negative Poisson's ratio value with a larger absolute value to the principal axis direction with a larger real eigenvalue. Subsequently, preset basic Young's modulus and basic shear modulus are extracted, and combined with the negative Poisson's ratio value, an anisotropic compliance tensor matrix is ​​constructed according to the generalized Hooke's law and written into the corresponding discrete mesh nodes.

[0009] In the obstacle intrusion and cohesive topology channel spontaneous generation step, the deformation mapping and topology processing module equates the obstacle geometric envelope data to a rigid indenter entity intruding into the virtual three-dimensional lattice network. Based on the mapping relationship between the obstacle's normal intrusion depth and the preset virtual penalty stiffness, it calculates the normal compressive stress tensor distribution applied by the rigid indenter entity. The deformation mapping and topology processing module solves for the comprehensive strain tensor of the compressed region of the virtual three-dimensional lattice network, extracting the coordinate system of the three-dimensional continuous low-potential energy channel formed by the tangential inward contraction strain of the mesh nodes. Specifically, the deformation and extraction principle is as follows: the normal projection distance from the initial spatial coordinates of the contact boundary nodes to the surface of the rigid indenter entity is calculated, and the normal projection distance is multiplied by the virtual penalty stiffness coefficient to obtain the normal compressive stress tensor. The normal compressive stress tensor is substituted into the anisotropic compliance tensor matrix containing the negative Poisson's ratio parameter to solve for the comprehensive strain tensor. According to the theory of the same-sign strain effect in solid mechanics, the negative normal compressive strain component, after being converted by a negative Poisson's ratio, generates a negative tangential contraction strain component, causing the virtual three-dimensional lattice network to undergo physical inward contraction deformation in the tangential direction perpendicular to the normal of the external obstacle. The stress tensor borne by the discrete mesh nodes is multiplied by the resulting combined strain tensor to obtain the scalar form of the lattice deformation potential energy value. Based on the tangential strain release induced by the inward contraction deformation, a minimum distribution of strain energy density spontaneously forms in space, lower than that of the surrounding compressed region. A spatial gradient search algorithm is used to search along the negative direction of the lattice deformation potential energy gradient, selecting the mesh node sequence with the minimum potential energy value and fitting it to generate a continuous three-dimensional low-potential-energy channel coordinate system.

[0010] In the elastic spline mapping and comprehensive strain energy functional construction steps, the functional optimization and trajectory planning module fits and maps the discrete link structure of the robotic arm in the Cartesian workspace into a parameterized continuous elastic spline curve traversing a deformed virtual three-dimensional lattice network. It then superimposes the first-order tensile strain energy and second-order bending strain energy constraining the geometric smoothness of the robotic arm body, along with the external constraint energy generated by the deformation of the virtual three-dimensional lattice network, to generate the total strain energy functional of the system. Specifically, the functional construction principle involves using the three-dimensional spatial coordinates of each joint of the robotic arm as control vertices to generate a spatial coordinate vector function for the spline curve. The first and second partial derivatives of the spatial coordinate vector function with respect to the curve arc length parameter are calculated. The product of the squared L2 norm of the first partial derivative and the first-order tensile weight coefficient, and the product of the squared L2 norm of the second partial derivative and the second-order bending weight coefficient are also calculated. These products are then integrated over the total arc length of the curve to obtain the internal kinematic strain energy. The external constraint energy is obtained by extracting the lattice deformation form energy values ​​on the spline curve integration path and performing integration calculations. The internal kinematic strain energy and the external constraint energy are algebraically summed to generate the total strain energy functional.

[0011] In the variational trajectory solving and low-level control command issuance steps, the functional optimization and trajectory planning module iteratively updates the spatial coordinate sequence of the parameterized continuous elastic spline curve based on the variational method, extracting the Cartesian space obstacle avoidance spline trajectory corresponding to the minimum state of the total strain energy functional. The low-level control and mapping execution module calls the inverse kinematics algorithm to transform the Cartesian space obstacle avoidance spline trajectory into a joint configuration space control drive flow, and sends drive signals to the servo motor driver network to complete the obstacle avoidance action of the robotic arm. Specifically, the execution principle is as follows: the discrete functional gradient descent algorithm is called to calculate the negative gradient direction of the discrete spline waypoints under the total strain energy functional, and the spatial coordinate sequence is updated until the L2 norm of the difference between the spatial coordinate vectors of adjacent iteration steps is less than the preset convergence threshold. The difference between adjacent coordinates of the extracted Cartesian space obstacle avoidance spline trajectory is extracted and divided by the low-level control cycle step size to calculate the Cartesian space velocity vector. The Moore-Penrose generalized inverse operation is performed on the Jacobian matrix of the robotic arm to generate the Jacobian pseudo-inverse matrix. A penalty potential energy function is constructed, with the difference between the current joint angle and the maximum physical limit angle of the joint as the variable. The partial derivative of the penalty potential energy function with respect to the current joint angle is calculated to generate the joint limit avoidance gradient function. Combining the Jacobian pseudo-inverse matrix, the Cartesian space velocity vector, and the null space optimization constraint term containing the joint limit avoidance gradient function, the output joint angular velocity command flow is calculated.

[0012] The second aspect of this invention provides an autonomous obstacle avoidance trajectory planning system for a humanoid robot arm.

[0013] The system includes an environment and ontology perception module, a tensor field dynamics reconstruction module, a deformation mapping and topology processing module, a functional optimization and trajectory planning module, and a low-level control and mapping execution module.

[0014] The environment and body perception module is used to obtain the initial joint configuration vector of the humanoid robot arm, solve the reference pose of each link of the robot arm in the three-dimensional Cartesian workspace through the forward kinematic equation, and synchronously drive the three-dimensional environment perception device to scan the robot arm workspace to obtain obstacle geometric envelope data.

[0015] The tensor field dynamics reconstruction module is used to map and generate an initial virtual three-dimensional lattice network in the workspace of the robotic arm, calculate the operability matrix of the robotic arm under the initial joint configuration vector and perform eigenvalue decomposition, extract the spatial principal axis direction of the operability ellipsoid, establish the physical mapping relationship between the negative Poisson's ratio parameter and the eigenvalue, and update the anisotropic compliance tensor of the virtual three-dimensional lattice network.

[0016] The deformation mapping and topology processing module is used to convert the geometric envelope data of obstacles into rigid indenter entities that intrude into the virtual three-dimensional lattice network. Based on the mapping relationship between the normal intrusion depth of the obstacle and the preset virtual penalty stiffness, the normal compressive stress tensor distribution applied by the rigid indenter entity is calculated, the comprehensive strain tensor of the compressed region of the virtual three-dimensional lattice network is solved, and the coordinate system of the three-dimensional continuous low potential energy channel formed by the tangential inward contraction strain of the mesh nodes is extracted.

[0017] The functional optimization and trajectory planning module is used to fit and map the discrete link structure of the robotic arm in the Cartesian workspace into a parameterized continuous elastic spline curve that shuttles through the deformed virtual three-dimensional lattice network. The module superimposes the first-order tensile strain energy and second-order bending strain energy that constrain the geometric smoothness of the robotic arm body, as well as the external constraint energy generated by the deformation of the virtual three-dimensional lattice network, to generate the total strain energy functional of the system. Based on the variational method, the spatial coordinate sequence of the parameterized continuous elastic spline curve is iteratively updated, and the Cartesian space obstacle avoidance spline trajectory corresponding to the minimum state of the total strain energy functional is extracted.

[0018] The underlying control and mapping execution module is used to call the inverse kinematics algorithm to transform the Cartesian space obstacle avoidance spline trajectory into a joint configuration space control drive flow, and send the drive signal to the servo motor driver network to complete the obstacle avoidance action of the robotic arm.

[0019] This invention provides an autonomous obstacle avoidance trajectory planning method for a humanoid robot arm. It has the following beneficial effects:

[0020] 1. This invention constructs a virtual tensor field with negative Poisson's ratio mechanical properties, thus changing the logic of obstacle avoidance in traditional potential field methods that rely solely on repulsive force vectors. When an obstacle intrudes into the virtual space, the tensor response with negative Poisson's ratio properties causes the mesh to contract inward in the tangential direction, thereby spontaneously forming low-potential topological channels around the obstacle's envelope. This mechanism effectively eliminates local minima caused by the mutual opposition of attraction and repulsion at specific locations, guiding the robotic arm smoothly into the obstacle avoidance path and ensuring the determinism of path search and the continuity of the obstacle avoidance process in complex confined spaces.

[0021] 2. This invention achieves deep coupling between environmental topological constraints and the physical motion capabilities of the robotic arm by introducing a kinematic maneuverability ellipsoid to dynamically reconstruct a virtual three-dimensional lattice network. The system extracts the maneuverability eigenvalues ​​of the robotic arm's Jacobian matrix in real time and maps them to the stiffness tensor of the virtual lattice's anisotropy, causing the geometric manifold of the obstacle avoidance channel to spontaneously deflect towards the principal axis direction where the robotic arm's motion flexibility is highest. This method avoids the robotic arm entering singular configurations or triggering joint limitations during obstacle avoidance, improves the rationality of redundant degree-of-freedom allocation, and ensures that the generated trajectory, while meeting obstacle avoidance requirements, always remains within the optimal dynamic response range of the robotic arm itself.

[0022] 3. This invention establishes a total strain energy functional that includes internal kinematically smooth strain energy and external topologically guided potential energy, and transforms obstacle avoidance planning into a variational extremum optimization process, thus ensuring the physical feasibility of the generated trajectory from the underlying mathematical framework. The energy minimization evolution process of the elastic spline in the tensor field gives the generated Cartesian space trajectory a natural second-order continuity, effectively suppressing the acceleration abrupt changes in the joint space of the robotic arm during obstacle avoidance transients. This globally optimized trajectory generation mechanism significantly reduces the tracking pressure on the underlying servo system and enhances the motion smoothness and mechanical structural stability of the humanoid robot arm when performing high-dynamic obstacle avoidance tasks. Attached Figure Description

[0023] Figure 1 A flowchart of the autonomous obstacle avoidance trajectory planning method for a humanoid robotic arm;

[0024] Figure 2 This is a flowchart of the S404 variational trajectory solution of the present invention. Detailed Implementation

[0025] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0026] Please see the appendix Figure 1 -Appendix Figure 2 This invention provides an autonomous obstacle avoidance trajectory planning method for a humanoid robot arm, including an environment and body perception module, a tensor field dynamics reconstruction module, a deformation mapping and topology processing module, a functional optimization and trajectory planning module, and a low-level control and mapping execution module.

[0027] The hardware execution carriers of the environment and body perception module include RGB-D depth vision sensors, LiDAR devices, and absolute encoders distributed across various joints of the humanoid robot arm. The environment and body perception module is responsible for acquiring 3D environmental point cloud data within the robot arm's workspace, simultaneously reading the angle parameters of each joint, and constructing a real-time environment and pose dataset reflecting the physical characteristics of the robot arm's workspace.

[0028] The hardware execution platform for the tensor field dynamics reconstruction module is an industrial control computer equipped with a graphics processing unit (GPU). The tensor field dynamics reconstruction module receives body pose data from the real-time environment and pose dataset transmitted by the environment and body perception modules. It then extracts the maneuverability feature data of the robotic arm through the GPU and sends this data to a virtual 3D lattice network constructed in the industrial control computer's memory. The module dynamically updates the anisotropic stiffness parameters and negative Poisson's ratio tensor parameters of the virtual 3D lattice network.

[0029] The deformation mapping and topology processing module runs within the central processing unit of the industrial control computer. This module converts obstacle point cloud data from the 3D environment point cloud data input from the environment and body perception module into intrusion stress data. It then substitutes this intrusion stress data into the dynamically updated constitutive model from the tensor field dynamics reconstruction module to perform discrete mesh strain calculations, outputting deformed spatial potential energy topology map data.

[0030] The functional optimization and trajectory planning module runs within the algorithm acceleration unit of the industrial control computer. It uses virtual continuous elastic splines to equivalently replace the geometric skeleton of the robotic arm. In the deformation space defined by the spatial potential energy topology map data output by the deformation mapping and topology processing module, it constructs a total strain energy functional that includes internal bending energy calculation terms and external constraint energy calculation terms. It then calls an optimization algorithm to solve for the Cartesian space safe trajectory point sequence corresponding to the minimum state of the total strain energy functional.

[0031] The hardware execution carriers of the underlying control and mapping execution module are the servo motor driver network and the robotic arm joint motors. The underlying control and mapping execution module converts the Cartesian space safe trajectory point sequence obtained by the functional optimization and trajectory planning module into a joint angular velocity command sequence or joint position command sequence recognized by the servo motor driver network through inverse kinematics algorithm, and sends it to the robotic arm joint motors to execute obstacle avoidance actions.

[0032] The macroscopic logical method for autonomous obstacle avoidance trajectory planning in a robotic arm autonomous obstacle avoidance trajectory planning system based on an anisotropic negative Poisson's ratio tensor field includes the following steps:

[0033] Step S100: State initialization and environmental geometry representation. The environment and body perception module acquires the initial joint configuration vector of the humanoid robot arm, solves the reference pose of each link of the robot arm in the three-dimensional Cartesian workspace through forward kinematic equations, and synchronously drives the three-dimensional environment perception device to scan the robot arm's workspace to acquire obstacle geometric envelope data.

[0034] Step S200: Anisotropic reconstruction of the virtual lattice based on the operability ellipsoid. The tensor field dynamics reconstruction module maps and generates an initial virtual three-dimensional lattice network within the robot arm's workspace, calculates the operability matrix of the robot arm under the initial joint configuration vector, performs eigenvalue decomposition, and extracts the spatial principal axis directions of the operability ellipsoid. The tensor field dynamics reconstruction module establishes a physical mapping relationship between the negative Poisson's ratio parameter and the eigenvalues, and updates the anisotropic compliance tensor of the virtual three-dimensional lattice network.

[0035] Step S300: Obstacle intrusion and cohesive topology channel spontaneously generated. The deformation mapping and topology processing module equates the obstacle geometric envelope data to a rigid indenter entity intruding into the virtual three-dimensional lattice network. Based on the mapping relationship between the obstacle's normal intrusion depth and the preset virtual penalty stiffness, it calculates the normal compressive stress tensor distribution applied by the rigid indenter entity, solves the comprehensive strain tensor of the compressed region of the virtual three-dimensional lattice network, and extracts the coordinate system of the three-dimensional continuous low-potential energy channel formed by the tangential inward contraction strain of the mesh nodes.

[0036] Step S400: Elastic spline mapping and construction of the comprehensive strain energy functional. The functional optimization and trajectory planning module fits and maps the discrete link structure of the robotic arm in the Cartesian workspace into a parameterized continuous elastic spline curve that travels through the deformed virtual three-dimensional lattice network. The first-order tensile strain energy and second-order bending strain energy constraining the geometric smoothness of the robotic arm body, as well as the external constraint energy generated by the deformation of the virtual three-dimensional lattice network, are superimposed to generate the total strain energy functional of the system.

[0037] Step S500: Variational trajectory solving and low-level control command issuance. The functional optimization and trajectory planning module iteratively updates the spatial coordinate sequence of the parameterized continuous elastic spline curve based on the variational method, extracting the Cartesian space obstacle avoidance spline trajectory corresponding to the minimum state of the total strain energy functional. The low-level control and mapping execution module calls the inverse kinematics algorithm to transform the Cartesian space obstacle avoidance spline trajectory into a joint configuration space control drive flow, and sends the drive signal to the servo motor driver network to complete the obstacle avoidance action of the robotic arm.

[0038] When the system executes step S200, which involves the virtual lattice anisotropy reconstruction based on the operability ellipsoid, the tensor field dynamics reconstruction module needs to extract operability feature data of the humanoid robot arm based on the real-time environment and pose dataset. The process of extracting operability feature data mainly includes obtaining joint configuration vectors, calculating the robot arm Jacobian matrix, and constructing the operability matrix. The specific implementation process for calculating the robot arm Jacobian matrix and the operability matrix is ​​detailed in sub-steps S201 to S203.

[0039] In step S201, the tensor field dynamics reconstruction module reads the absolute encoder data collected by the environment and body perception modules via a fieldbus. The fieldbus includes an EtherCAT bus or a CAN bus. The tensor field dynamics reconstruction module parses the absolute encoder data into a current-moment joint configuration vector containing the angle values ​​of each joint of the humanoid robot arm, and retrieves a preset standard link parameter table for the robot arm from the industrial control computer's memory. Specifically, the standard DH parameter table or an improved DH parameter table for the robot arm is used. Based on the current-moment joint configuration vector and the standard link parameter table, the tensor field dynamics reconstruction module updates the homogeneous transformation matrix of each link coordinate system of the robot arm in the spatial base coordinate system.

[0040] In step S202, the tensor field dynamics reconstruction module calculates the Jacobian matrix of the robotic arm corresponding to the joint configuration vector at the current moment based on the homogeneous transformation matrix. The robotic arm Jacobian matrix represents the linear transformation relationship between the joint space velocity of the humanoid robot arm and the velocity in the three-dimensional Cartesian workspace. The tensor field dynamics reconstruction module uses the vector cross product algorithm to extract the column vectors of the robotic arm Jacobian matrix. Specifically, the tensor field dynamics reconstruction module extracts the position vector and Z-axis direction vector of the origin of each link coordinate system from the updated homogeneous transformation matrix. For a robotic arm configuration composed of rotary joints, the formula for calculating the column vectors of the robotic arm Jacobian matrix is:

[0041] ;

[0042] In the formula, The first Jacobian matrix representing the robotic arm column vectors, Representing the The unit direction vector of the Z-axis of the link coordinate system in the spatial base coordinate system. This represents the three-dimensional position coordinate vector of the robotic arm's end effector in the spatial base coordinate system. Representing the The three-dimensional position coordinate vector of the origin of the link coordinate system in the spatial base coordinate system. The cross product operator represents a vector in three-dimensional space. The tensor field dynamics reconstruction module traverses all the degrees of freedom of the humanoid robot arm, sequentially concatenating all the calculated column vectors to generate the complete Jacobian matrix of the robot arm. The specific derivation process for solving the Jacobian matrix of the robot arm using differential kinematics can be obtained by those skilled in the art using conventional function derivative operations based on the specific kinematic configuration of the humanoid robot arm; this is well-known technology in the field and will not be elaborated upon here.

[0043] In step S203, the tensor field dynamics reconstruction module constructs the operability matrix based on the spliced ​​robotic arm Jacobian matrix. The module performs a matrix transpose operation on the robotic arm Jacobian matrix to generate its transpose matrix. Then, it performs matrix multiplication between the robotic arm Jacobian matrix and the transpose matrix to calculate and output the operability matrix. The formula for calculating the operability matrix is:

[0044] ;

[0045] In the formula, Represents the operability matrix. Represents the joint configuration vector at the current moment. The corresponding Jacobian matrix for the robotic arm, This represents the transpose of the Jacobian matrix of the robotic arm. The operability matrix is ​​a symmetric positive definite matrix, and the distribution of its matrix elements reflects the differences in the magnitude of translational and rotational displacements produced by the robotic arm's end effector in various directions of the three-dimensional Cartesian workspace. The tensor field dynamics reconstruction module stores the calculated operability matrix in the cache of the industrial control computer, providing it for subsequent operability ellipsoidal space eigenvalue decomposition steps.

[0046] After the system completes sub-step S203, the tensor field dynamics reconstruction module retrieves the operability matrix stored in the cache and performs eigenvalue decomposition on the operability matrix to extract the geometric feature parameters of the operability ellipsoid, thereby completing the physical mapping between the principal axis direction of the operability ellipsoid and the local coordinate system of the virtual three-dimensional lattice network. The specific implementation process of operability eigenvalue decomposition and spatial ellipsoid principal axis mapping is divided into sub-steps S204 to S206 for detailed explanation.

[0047] Step S204: The tensor field dynamics reconstruction module reads the symmetric positive definite form of the operand matrix and calls the underlying linear algebra function library to perform matrix eigenvalue decomposition on the operand matrix. For the specific algorithmic processing logic of the eigenvalue decomposition performed by the linear algebra function library, those skilled in the art can use the standard QR algorithm or the Jacobi iteration method to solve for the eigenvalues ​​and eigenvectors of the symmetric matrix. Eigenvalue decomposition of symmetric matrices is a well-known technique in this field and will not be elaborated further here. The algebraic formula for eigenvalue decomposition is:

[0048] ;

[0049] In the formula, Represents the operability matrix. Represents an orthogonal eigenvector matrix. Represents a diagonal matrix of eigenvalues. This represents the transpose of the orthogonal eigenvector matrix.

[0050] In step S205, the tensor field dynamics reconstruction module analyzes the orthogonal eigenvector matrix and the eigenvalue diagonal matrix to extract the three-dimensional spatial parameters of the operance ellipsoid. Specifically, the tensor field dynamics reconstruction module extracts three real eigenvalues ​​on the main diagonal of the eigenvalue diagonal matrix. These three real eigenvalues ​​represent the scalar magnitudes of the semi-axis lengths of the operance ellipsoid in the three orthogonal directions of the three-dimensional Cartesian workspace. The positive correlation between the magnitudes of these three real eigenvalues ​​reflects the amplitude of the motion flexibility of the humanoid robot arm's end effector in the corresponding orthogonal directions. Simultaneously, the tensor field dynamics reconstruction module extracts three orthogonal column vectors contained in the orthogonal eigenvector matrix. These three orthogonal column vectors correspond to the spatial pointing vectors of the three principal axes of the operance ellipsoid in the spatial base coordinate system.

[0051] In step S206, the tensor field dynamics reconstruction module maps the extracted three-dimensional spatial parameters to a virtual three-dimensional lattice network. The module traverses all discrete mesh nodes within the virtual three-dimensional lattice network, directly assigning the orthogonal eigenvector matrix as the rotation transformation matrix from the local coordinate system to the spatial basis coordinate system of each discrete mesh node, ensuring that the three orthogonal column vectors align with the local orthogonal basis of each discrete mesh node. Through this rotation transformation matrix mapping, the tensor field dynamics reconstruction module ensures that the local force analysis coordinate system of each mesh element within the virtual three-dimensional lattice network coincides with the direction of maximum motion flexibility of the humanoid robot arm in its current pose. This coincidence of the local force analysis coordinate system provides an anisotropic direction reference that aligns with the robot arm's kinematic capabilities for subsequent constitutive equation calculations when external obstacles intrude.

[0052] After the system completes sub-step S206 to coincide the coordinate system for local force analysis, the tensor field dynamics reconstruction module constructs a virtual three-dimensional lattice network in the industrial control computer's memory and assigns corresponding mechanical constitutive parameters. The specific implementation process of constructing the virtual lattice network and assigning the anisotropic negative Poisson's ratio constitutive equation is detailed in sub-steps S207 to S209.

[0053] In step S207, the tensor field dynamics reconstruction module, based on the physical arm span limit of the humanoid robot arm, divides the spatial bounding box within the three-dimensional Cartesian workspace and, according to a preset spatial discretization resolution, divides the spatial bounding box into a finite number of discrete mesh nodes. To improve the efficiency of computer retrieval of spatial positions, the system uses an octree data structure or a three-dimensional voxel matrix to organize all discrete mesh nodes, and then establishes a virtual spring connection topology between adjacent discrete mesh nodes, ultimately generating a spatially complete virtual three-dimensional lattice network.

[0054] In step S208, the tensor field dynamics reconstruction module reads the three real eigenvalues ​​extracted in sub-step S205. Using the three principal axes of the operand ellipsoid as a local orthogonal coordinate system, it constructs a formula for calculating the negative Poisson's ratio parameter in this local orthogonal coordinate system, thus establishing a mathematical mapping relationship between the negative Poisson's ratio parameter and the three real eigenvalues. Poisson's ratio characterizes the ratio of transverse strain to axial strain of a material under stress. The formula for calculating the negative Poisson's ratio parameter is:

[0055] ;

[0056] In the formula, Represents the local orthogonal coordinate system Directional normal stress caused Negative Poisson's ratio parameter for lateral strain in the direction of the strain. This represents the preset proportional gain constant. The ellipsoid representing the degree of operation is Real eigenvalues ​​in the direction, This represents the largest of the three real eigenvalues. The tensor field dynamics reconstruction module calculates the negative Poisson's ratio values ​​that couple between the three principal axes based on this formula. A principal axis with a larger real eigenvalue indicates higher mobility of the humanoid robot arm. Therefore, the system assigns a larger absolute value of the negative Poisson's ratio to this direction, resulting in a more significant tangential inward contraction mechanical property in the corresponding spatial principal axis direction of the virtual three-dimensional lattice network.

[0057] Step S209: The tensor field dynamics reconstruction module constructs the anisotropic constitutive equation of the virtual three-dimensional lattice network based on the negative Poisson's ratio value. Specifically, the tensor field dynamics reconstruction module extracts the system's preset basic Young's elastic modulus and basic shear modulus, combines them with the calculated negative Poisson's ratio value, and constructs a constitutive equation based on the generalized Hooke's law. An anisotropic compliance tensor matrix of dimension 1. In this matrix, the main diagonal elements are composed of the reciprocals of the fundamental Young's modulus and the fundamental shear modulus, and the specific off-diagonal elements are the ratios of the negative Poisson's ratio to the fundamental Young's modulus (i.e., ...). The anisotropic constitutive equation is composed of the following tensor:

[0058] ;

[0059] In the formula, The strain tensor represents the strain tensor generated by external forces on a virtual three-dimensional lattice network. This represents the anisotropic compliance tensor matrix containing negative Poisson's ratio values. This represents the stress tensor borne by the virtual 3D lattice network. The tensor field dynamics reconstruction module writes the anisotropic compliance tensor matrix into the data structure attributes corresponding to each discrete mesh node within the virtual 3D lattice network, completing the reconstruction of the dynamic parameters of the virtual 3D lattice network. This writing operation of the compliance tensor matrix provides the underlying mechanical computational foundation for the subsequent deformation mapping and topology processing modules to perform discrete mesh strain calculations.

[0060] After the system completes sub-step S209 to reconstruct the dynamic parameters of the virtual three-dimensional lattice network, the deformation mapping and topology processing module initiates the calculation and processing of the interference forces of external obstacles. The specific implementation process of obstacle envelope detection, virtual rigid indenter model equivalence, interface normal compressive stress calculation, and tensor network forced solution is divided into sub-steps S301 to S304 for detailed explanation.

[0061] In step S301, the deformation mapping and topology processing module receives the 3D environment point cloud data from the environment and ontology perception module, calls the point cloud clustering and segmentation algorithm to extract obstacle point cloud data from the 3D environment point cloud data, and performs envelope geometry modeling on the obstacle point cloud data to generate an obstacle geometric envelope surface model. For the specific processing logic of performing envelope geometry modeling on the obstacle point cloud data, those skilled in the art can use the fast convex hull algorithm to generate a 3D convex hull polyhedron model of the obstacle, or use principal component analysis to construct an obstacle orientation bounding box model. Obstacle point cloud envelope geometry modeling is a well-known technology in this field and will not be elaborated further here.

[0062] In step S302, the deformation mapping and topology processing module maps the obstacle's geometric envelope surface model to the Cartesian space where the virtual three-dimensional lattice network constructed by the tensor field dynamics reconstruction module resides, and defines the obstacle's geometric envelope surface model as an equivalent virtual rigid indenter entity. Simultaneously, combined with a collision detection algorithm, the deformation mapping and topology processing module filters out discrete mesh nodes located inside the virtual rigid indenter entity and discrete mesh nodes intersecting with the surface of the virtual rigid indenter entity within the virtual three-dimensional lattice network, marking the filtered discrete mesh nodes as contact boundary nodes. To quantify the degree of external intrusion, the deformation mapping and topology processing module calculates the normal projection distance from the initial spatial coordinates of the contact boundary nodes to the surface of the virtual rigid indenter entity, defining the normal intrusion depth distribution data.

[0063] Step S303: Based on the normal intrusion depth distribution data, the deformation mapping and topology processing module calculates the virtual external interference force exerted by the virtual rigid indenter entity on the virtual three-dimensional lattice network. The deformation mapping and topology processing module retrieves the preset virtual penalty stiffness coefficient from system memory, multiplies the virtual penalty stiffness coefficient by the normal intrusion depth distribution data, and calculates the normal compressive stress tensor distribution borne by the contact boundary nodes. The formula for calculating the components of the normal compressive stress tensor is:

[0064] ;

[0065] In the formula, Represents the virtual rigid indenter entity in the local coordinate system of the virtual three-dimensional lattice network. The normal compressive stress tensor component applied in the direction, This represents the preset virtual penalty stiffness coefficient. Represents the virtual rigid indenter entity in the local coordinate system The numerical value of the normal intrusion depth in the direction. The deformation mapping and topology processing module summarizes the normal compressive stress tensor components of all contact boundary nodes and constructs the external interference stress tensor input to the contact interface of the virtual three-dimensional lattice network.

[0066] In step S304, the deformation mapping and topology processing module substitutes the external interference stress tensor into the anisotropic constitutive equation of the virtual three-dimensional lattice network to solve for the comprehensive strain tensor generated in the compressed region of the virtual three-dimensional lattice network. The deformation mapping and topology processing module reads the anisotropic compliance tensor matrix of each discrete mesh node written by the tensor field dynamics reconstruction module in sub-step S209 and performs the forced solution operation for the strain of the discrete mesh nodes. The calculation formula for the comprehensive strain tensor components is:

[0067] ;

[0068] In the formula, Represents a virtual three-dimensional lattice network in a local coordinate system The combined strain tensor components generated in the direction The compliance elements represent the arrangement within the anisotropic compliance tensor matrix. Represents the external interference stress tensor in the local coordinate system The normal compressive stress tensor components in the direction. The deformation mapping and topology processing module calculates the comprehensive strain tensor data, including principal strain and transverse strain, generated by the normal compressive stress transmission to the contact boundary nodes and adjacent meshes around the contact boundary nodes through matrix multiplication and summation operations. The deformation mapping and topology processing module stores the comprehensive strain tensor data in the memory space of the industrial control computer, providing it to subsequent steps as optimization judgment data for extracting the coordinate system of the continuous low potential energy channel in three-dimensional space.

[0069] After the system completes sub-step S304 to calculate the comprehensive strain tensor data including principal strain and transverse strain, the deformation mapping and topology processing module determines the geometric topological evolution trend of the virtual three-dimensional lattice network based on the comprehensive strain tensor data. The principle of spontaneous channel generation and coordinate extraction process under the negative Poisson's ratio strain effect is explained in detail in sub-steps S305 to S307.

[0070] Step S305: The deformation mapping and topology processing module analyzes the same-sign strain effect within the comprehensive strain tensor data based on solid mechanics strain theory. When a conventional isotropic material is subjected to normal compressive stress, the tangential surface perpendicular to the normal compressive direction will generate expansion strain. For the anisotropic negative Poisson's ratio values ​​embedded within the virtual three-dimensional lattice network, the deformation mapping and topology processing module substitutes them into the same-sign strain effect rule to calculate the tangential contraction strain component. The formula for calculating the tangential contraction strain component is:

[0071] ;

[0072] In the formula, This represents the tangential contraction strain component generated in the tangential direction by the virtual three-dimensional lattice network. The negative Poisson's ratio represents the tangential deformation caused by normal force. This represents the normal compressive strain component borne by the contact boundary node. Since the normal compressive strain component is negative, and the negative Poisson's ratio assigned by the system is also negative, according to the above formula, the calculated tangential strain component must also be negative. The negative tangential strain component characterizes the inward contraction physical deformation of the virtual three-dimensional lattice network in the tangential direction perpendicular to the normal of the external obstacle, thus eliminating the outward expansion and repulsion tendency of the grid nodes in the traditional artificial potential field method from the physical level.

[0073] Step S306: The deformation mapping and topology processing module constructs the topological potential energy field of the workspace based on the aforementioned inward contraction physical deformation. Specifically, the deformation mapping and topology processing module traverses all discrete mesh nodes contained in the virtual three-dimensional lattice network, converting the comprehensive strain tensor of each discrete mesh node into a scalar form of the lattice deformation potential energy value. The formula for calculating the lattice deformation potential energy value is:

[0074] ;

[0075] In the formula, The numerical value of the lattice deformation state energy representing discrete grid nodes. The stress tensor element representing the stress experienced by the discrete mesh nodes. This represents the combined strain tensor element generated by the discrete mesh nodes. The inward contraction physical deformation causes the material nodes of the virtual three-dimensional lattice network to converge and contract towards the obstacle's normal surroundings, resulting in strain release in the tangential peripheral space far from the intrusion center. This spontaneously forms a local potential energy minimum region with a lower strain energy density compared to the surrounding compressed area. This local potential energy minimum region appears as a low-potential-energy spatial envelope layer surrounding the obstacle surface in the three-dimensional workspace.

[0076] In step S307, the deformation mapping and topology processing module calls the spatial gradient search algorithm to extract a three-dimensional continuous low-potential energy channel coordinate system from the topological potential energy field. Starting from the contact boundary nodes, the module calculates the lattice deformation potential energy gradient vector between adjacent discrete grid nodes and performs a discrete grid step-by-step search along the negative direction of the lattice deformation potential energy gradient vector, filtering layer by layer to find the grid node sequence with the smallest lattice deformation potential energy value within the local spatial range. Since the absolute value distribution of negative Poisson's ratio values ​​is proportional to the real eigenvalue of the manipulator's operability ellipsoid, the inward contraction geometric amplitude reaches its maximum value in the principal axis direction where the humanoid robot arm has the highest motion flexibility. The direction with the largest contraction amplitude directly corresponds to the deepest part of the local potential energy minimum region, causing the geometric connection of the grid node sequence in three-dimensional space to naturally bias towards the direction of the humanoid robot arm's maximum motion flexibility. Finally, the deformation mapping and topology processing module records the spatial curve coordinate system formed by fitting and connecting the grid node sequences as a three-dimensional continuous low-potential energy channel coordinate system. The three-dimensional continuous low-potential channel coordinate system provides a safe detour topological constraint boundary for the subsequent functional optimization and trajectory planning modules to perform elastic spline variational iterations, avoiding singular configurations.

[0077] After the system completes sub-step S307 to extract the coordinate system of the continuous low-potential energy channel in three-dimensional space, the functional optimization and trajectory planning module performs trajectory mapping and evolution calculation for the humanoid robot arm entity. The specific implementation process of elastic spline mapping, comprehensive strain energy functional construction, and variational trajectory solution is divided into sub-steps S401 to S404 for detailed explanation.

[0078] In step S401, the functional optimization and trajectory planning module fits and maps the discrete link structure of the humanoid robot arm in the three-dimensional Cartesian workspace into a continuous elastic spline curve. Specifically, the functional optimization and trajectory planning module extracts the three-dimensional spatial coordinates of each joint of the humanoid robot arm, uses these extracted three-dimensional spatial coordinates as control vertices, and calls a spline interpolation algorithm to generate a parameterized continuous elastic spline curve. For the specific processing logic of calling the spline interpolation algorithm to generate the parameterized continuous elastic spline curve, those skilled in the art can use cubic B-spline interpolation or Bézier curve interpolation algorithms. Spline curve interpolation fitting is a well-known technique in this field and will not be elaborated further here. The functional optimization and trajectory planning module establishes the spatial coordinate vector function of the parameterized continuous elastic spline curve by introducing the curve arc length parameter.

[0079] Step S402: The functional optimization and trajectory planning module constructs an internal kinematic strain energy calculation term to constrain the geometric smoothness of the humanoid robot arm. The module calculates the first and second partial derivatives of the spatial coordinate vector function of the parameterized continuous elastic spline curve with respect to the arc length parameter. The first partial derivative corresponds mechanically to the tensile deformation of the parameterized continuous elastic spline curve, and the second partial derivative corresponds mechanically to the bending deformation. Combining the preset first-order tensile weighting coefficient and second-order bending weighting coefficient, the module constructs the internal kinematic strain energy calculation formula:

[0080] ;

[0081] In the formula, This represents the calculated result of internal kinematic strain energy. The total arc length represents the parameterized continuous elastic spline curve. Represents the arc length parameter of the curve. The spatial coordinate vector representing the position of the parameterized continuous elastic spline curve at the curve's arc length parameter. Represents the first-order stretching weight coefficient. This represents the second-order bending weighting coefficient. The internal kinematic strain energy calculation term is used to suppress high-frequency oscillations in the joint space of the humanoid robot arm during trajectory optimization iterations.

[0082] In step S403, the functional optimization and trajectory planning module constructs the external constraint energy calculation term generated by the deformation of the virtual three-dimensional lattice network. The functional optimization and trajectory planning module reads the topological potential energy field data calculated in sub-step S306 by the deformation mapping and topology processing module, maps the spatial coordinate vector of the parameterized continuous elastic spline curve to the topological potential energy field, and extracts the corresponding lattice deformation potential energy value along the integration path of the parameterized continuous elastic spline curve. The formula for calculating the external constraint energy is:

[0083] ;

[0084] In the formula, The result represents the calculation of external constraint energy. Represents the topological potential field in spatial coordinate vectors The lattice deformation state energy value is calculated at a given location. The functional optimization and trajectory planning module algebraically sums the calculated results of the internal kinematic strain energy and the external constraint energy to generate the total strain energy functional of the system. The total strain energy functional characterizes the comprehensive cost of the motion evolution of the parameterized continuous elastic spline curve in the workspace.

[0085] Step S404: The functional optimization and trajectory planning module iteratively updates the spatial coordinate sequence of the parameterized continuous elastic spline curve based on the variational method. The module discretizes the parameterized continuous elastic spline curve into a finite number of discrete spline waypoints and uses the discrete functional gradient descent algorithm to calculate the negative gradient direction of each discrete spline waypoint under the total strain energy functional. The iterative update formula for the discrete spline waypoints is:

[0086] ;

[0087] In the formula, Representing the The discrete spline waypoint space coordinate vector generated in the next iteration step. Representing the The current discrete spline waypoint space coordinate vector in the next iteration step. This represents the preset iterative evolution step size. This represents the variational gradient operator of the total strain energy functional with respect to the spatial coordinate vectors of discrete spline waypoints. The functional optimization and trajectory planning module iteratively updates the formula until the L2 norm of the difference between the spatial coordinate vectors between two adjacent iterations is less than a preset convergence threshold. The parameterized continuous elastic spline curves that satisfy the convergence threshold condition converge spatially to the interior of the three-dimensional continuous low-potential channel coordinate system. The functional optimization and trajectory planning module extracts the spatial coordinate sequence of the parameterized continuous elastic spline curves that have reached the minimum state of the total strain energy functional, and records the extracted spatial coordinate sequence as a Cartesian space obstacle avoidance spline trajectory.

[0088] After the system completes sub-step S404 to extract the Cartesian space obstacle avoidance spline trajectory, the underlying control and mapping execution module converts the Cartesian space obstacle avoidance spline trajectory into physical instructions executable by the humanoid robot arm hardware. The specific implementation process of inverse kinematics mapping and underlying control instruction issuance is divided into sub-steps S501 to S503 for detailed explanation.

[0089] In step S501, the low-level control and mapping execution module retrieves the preset system low-level control cycle step size and performs time-dimensional numerical difference processing on the Cartesian space obstacle avoidance spline trajectory. Specifically, the low-level control and mapping execution module extracts the spatial coordinate difference between two adjacent discrete spline waypoints, divides the spatial coordinate difference by the system low-level control cycle step size, and calculates the Cartesian space velocity vector of the Cartesian space obstacle avoidance spline trajectory at continuous time nodes. The Cartesian space velocity vector represents the three-dimensional linear velocity and three-dimensional angular velocity of the humanoid robot arm end effector moving in the workspace.

[0090] In step S502, the low-level control and mapping execution module calls the inverse kinematics mapping algorithm based on the Jacobian pseudo-inverse operation to transform the Cartesian space velocity vector into the joint configuration space control drive flow. The low-level control and mapping execution module reads the robotic arm Jacobian matrix calculated by the tensor field dynamics reconstruction module, performs the Moore-Ponros generalized inverse operation on the robotic arm Jacobian matrix to generate the corresponding Jacobian pseudo-inverse matrix, and then constructs the inverse kinematics mapping execution formula with superimposed null space optimization constraints. The inverse kinematics mapping execution formula is as follows:

[0091] ;

[0092] In the formula, The joint angular velocity command stream output at the set time node. The pseudo-inverse matrix representing the Jacobian matrix of the robotic arm. The Cartesian space velocity vector calculated in step S501 represents the velocity vector in the Cartesian space. This represents a unit diagonal matrix with the same number of degrees of freedom as the robotic arm. The Jacobian matrix represents the robotic arm. This represents the null space optimization constraint. The underlying control and mapping execution module sets the joint limit avoidance gradient function within the null space optimization constraint. To achieve physical executability of the underlying control, the module constructs a penalty potential energy function with the difference between the current joint angle and the maximum physical limit angle as the variable. The partial derivative of the penalty potential energy function with respect to the current joint angle is calculated to generate the joint limit avoidance gradient function. This gradient function utilizes the redundant degrees of freedom of the humanoid robot arm to drive the internal joints of the arm away from the physical limit angle of the mechanical structure without changing the pose of the end effector.

[0093] In step S503, the low-level control and mapping execution module sends the joint angular velocity command stream to the servo motor driver network to execute the physical action. The low-level control and mapping execution module synchronously sends the joint angular velocity command stream to the servo motor drivers distributed at each joint of the humanoid robot arm via a field industrial communication bus at a set control cycle frequency. For the closed-loop tracking control logic after the servo motor receives the command, those skilled in the art can use a conventional three-loop cascade proportional-integral-derivative control algorithm (current loop, velocity loop, and position loop). The closed-loop tracking control of the servo motor is a well-known technology in the field and will not be elaborated further here. After receiving the drive information, the servo motor driver outputs the corresponding drive current to the robot arm joint motors according to the received joint angular velocity command stream, driving the humanoid robot arm to complete the obstacle avoidance physical action along the extracted Cartesian space obstacle avoidance spline trajectory.

[0094] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for autonomous obstacle avoidance trajectory planning of a humanoid robot arm, characterized in that, Includes the following steps: S100, State Initialization and Environmental Geometric Representation: The environment and body perception module obtains the initial joint configuration vector of the humanoid robot arm, solves the reference pose of each link of the robot arm in the three-dimensional Cartesian workspace through the forward kinematic equation, and synchronously drives the three-dimensional environment perception device to scan the robot arm workspace to obtain obstacle geometric envelope data. S200, Virtual Lattice Anisotropic Reconstruction Based on Manipulation Ellipsoid: The tensor field dynamics reconstruction module maps and generates an initial virtual three-dimensional lattice network in the workspace of the robotic arm, calculates the manipulation matrix of the robotic arm under the initial joint configuration vector and performs eigenvalue decomposition, extracts the spatial principal axis direction of the manipulation ellipsoid, establishes the physical mapping relationship between the negative Poisson's ratio parameter and the eigenvalue, and updates the anisotropic compliance tensor of the virtual three-dimensional lattice network; S300, obstacle intrusion and cohesive topology channel spontaneous generation: the deformation mapping and topology processing module equates the obstacle geometric envelope data to a rigid indenter entity intruding into the virtual three-dimensional lattice network. Based on the mapping relationship between the obstacle normal intrusion depth and the preset virtual penalty stiffness, it calculates the normal compressive stress tensor distribution applied by the rigid indenter entity, solves the comprehensive strain tensor of the compressed region of the virtual three-dimensional lattice network, and extracts the coordinate system of the three-dimensional continuous low potential energy channel formed by the tangential inward contraction strain of the mesh nodes. S400, Elastic Spline Mapping and Comprehensive Strain Energy Functional Construction: The functional optimization and trajectory planning module fits and maps the discrete link structure of the robotic arm in the Cartesian workspace into a parameterized continuous elastic spline curve that shuttles through the deformed virtual three-dimensional lattice network. The first-order tensile strain energy and second-order bending strain energy constraining the geometric smoothness of the robotic arm body, as well as the external constraint energy generated by the deformation of the virtual three-dimensional lattice network, are superimposed to generate the total strain energy functional of the system. S500, variational trajectory solving and low-level control command issuance: The functional optimization and trajectory planning module iteratively updates the spatial coordinate sequence of the parameterized continuous elastic spline curve based on the variational method, extracts the Cartesian space obstacle avoidance spline trajectory corresponding to the minimum state of the total strain energy functional, and the low-level control and mapping execution module calls the inverse kinematics algorithm to transform the Cartesian space obstacle avoidance spline trajectory into the joint configuration space control drive flow, and sends the drive signal to the servo motor driver network to complete the obstacle avoidance action of the robotic arm.

2. The autonomous obstacle avoidance trajectory planning method for a humanoid robot arm according to claim 1, characterized in that the tensor field dynamics reconstruction module calculates the maneuverability matrix of the robot arm under the initial joint configuration vector, including: The tensor field dynamics reconstruction module reads the absolute encoder data collected by the environment and body perception modules through the fieldbus, parses the absolute encoder data into the current moment joint configuration vector containing the angle values ​​of each joint of the humanoid robot arm, retrieves the preset standard link parameter table of the robot arm in the memory of the industrial control computer, and updates the homogeneous transformation matrix of each link coordinate system of the robot arm in the spatial base coordinate system according to the current moment joint configuration vector and the standard link parameter table of the robot arm. The tensor field dynamics reconstruction module extracts the position vector and Z-axis direction vector of the origin of each link coordinate system from the updated homogeneous transformation matrix, and uses the vector cross product algorithm to extract each column vector of the robotic arm Jacobian matrix. All the calculated column vectors are then concatenated in sequence to generate the complete robotic arm Jacobian matrix. The tensor field dynamics reconstruction module performs a matrix transpose operation on the Jacobian matrix of the robotic arm to generate the transpose matrix of the corresponding robotic arm Jacobian matrix. It then performs matrix multiplication on the robotic arm Jacobian matrix and the transpose matrix to calculate and output the operability matrix, which is a symmetric positive definite matrix.

3. The autonomous obstacle avoidance trajectory planning method for a humanoid robot arm according to claim 2, characterized in that the tensor field dynamics reconstruction module extracts the spatial principal axis directions of the operability ellipsoid, including: The tensor field dynamics reconstruction module calls the underlying linear algebra operation function library to perform matrix eigenvalue decomposition on the operability matrix, extracting three real eigenvalues ​​on the main diagonal of the eigenvalue diagonal matrix. Simultaneously, the tensor field dynamics reconstruction module extracts three orthogonal column vectors contained in the orthogonal eigenvector matrix. The three orthogonal column vectors correspond to the spatial pointing vectors of the three principal axes of the operability ellipsoid in the spatial base coordinate system. The tensor field dynamics reconstruction module traverses all discrete mesh nodes contained in the virtual three-dimensional lattice network and directly assigns the orthogonal eigenvector matrix to the rotation transformation matrix from the local coordinate system to the spatial basis coordinate system of each discrete mesh node. This ensures that the three orthogonal column vectors are aligned with the local orthogonal basis of the discrete mesh nodes, so that the local force analysis coordinate system of each mesh unit inside the virtual three-dimensional lattice network coincides with the direction of maximum motion flexibility of the humanoid robot arm under its current pose.

4. The autonomous obstacle avoidance trajectory planning method for a humanoid robot arm according to claim 3, characterized in that the tensor field dynamics reconstruction module establishes a physical mapping relationship between the negative Poisson's ratio parameter and the eigenvalue, and updates the anisotropic compliance tensor of the virtual three-dimensional lattice network including: The tensor field dynamics reconstruction module uses the three principal axes of the operand ellipsoid as a local orthogonal coordinate system to construct a formula for calculating the negative Poisson's ratio parameter under the local orthogonal coordinate system. Based on the formula for calculating the negative Poisson's ratio parameter, the negative Poisson's ratio values ​​that are coupled between the three principal axes are calculated. The system then assigns a negative Poisson's ratio value with a larger absolute value to the principal axis direction with a larger real eigenvalue. The tensor field dynamics reconstruction module extracts the system's preset basic Young's elastic modulus and basic shear modulus, and combines them with the calculated negative Poisson's ratio. Based on the generalized Hooke's law, it constructs an anisotropic compliance tensor matrix. The tensor field dynamics reconstruction module writes the anisotropic compliance tensor matrix into the data structure attributes corresponding to each discrete grid node in the virtual three-dimensional lattice network, thus completing the reconstruction of the dynamic parameters of the virtual three-dimensional lattice network.

5. The autonomous obstacle avoidance trajectory planning method for a humanoid robot arm according to claim 1, characterized in that the calculation of the normal compressive stress tensor distribution applied by the rigid indenter entity based on the mapping relationship between the obstacle's normal intrusion depth and the preset virtual penalty stiffness includes: The deformation mapping and topology processing module calls the point cloud clustering and segmentation algorithm to extract obstacle point cloud data from the 3D environment point cloud data, performs envelope geometry modeling on the obstacle point cloud data, generates obstacle geometric envelope surface model, and defines the obstacle geometric envelope surface model as an equivalent virtual rigid indenter entity. The deformation mapping and topology processing module, combined with the collision detection algorithm, filters out discrete mesh nodes located inside the virtual rigid indenter entity and discrete mesh nodes intersecting with the surface of the virtual rigid indenter entity in the virtual three-dimensional lattice network, and marks the filtered discrete mesh nodes as contact boundary nodes. The deformation mapping and topology processing module calculates the normal projection distance from the initial spatial coordinates of the contact boundary node to the surface of the virtual rigid indenter entity. The normal projection distance is defined as the normal intrusion depth distribution data. The virtual penalty stiffness coefficient is multiplied by the normal intrusion depth distribution data to calculate the normal compressive stress tensor distribution borne by the contact boundary node. The normal compressive stress tensor components of all contact boundary nodes are summarized to construct the external interference stress tensor input to the contact interface of the virtual three-dimensional lattice network.

6. The autonomous obstacle avoidance trajectory planning method for a humanoid robot arm according to claim 5, characterized in that the three-dimensional continuous low-potential energy channel coordinate system formed by the tangential inward contraction strain of the extracted mesh nodes includes: The deformation mapping and topology processing module substitutes the external interference stress tensor into the anisotropic constitutive equation of the virtual three-dimensional lattice network to solve the comprehensive strain tensor generated in the compressed region of the virtual three-dimensional lattice network. Based on the strain theory of solid mechanics, it analyzes the same-sign strain effect inside the comprehensive strain tensor data. Substituting the anisotropic negative Poisson's ratio value into the same-sign strain effect rule, it is calculated that the tangential contraction strain component must be negative. The deformation mapping and topology processing module traverses all discrete grid nodes contained in the virtual three-dimensional lattice network, converts the comprehensive strain tensor of each discrete grid node into a scalar form of lattice deformation potential energy value, and the material nodes of the virtual three-dimensional lattice network gather and shrink towards the obstacle normal surroundings, thereby generating strain release in the tangential peripheral space far away from the invasion center, spontaneously forming a local potential energy minimum region with a lower strain energy density than the surrounding pressure region. The deformation mapping and topology processing module calls the spatial gradient search algorithm to calculate the lattice deformation potential energy gradient vector between adjacent discrete grid nodes in the topological potential energy field, starting from the contact boundary node. It then performs discrete grid step search along the negative direction of the lattice deformation potential energy gradient vector, and filters out the grid node sequence with the smallest lattice deformation potential energy value in the local space layer by layer. The spatial curve coordinate system formed by fitting and connecting the grid node sequence is recorded as a three-dimensional continuous low potential energy channel coordinate system.

7. The autonomous obstacle avoidance trajectory planning method for a humanoid robot arm according to claim 1, characterized in that, the step of fitting and mapping the discrete link structure of the robot arm in the Cartesian workspace to a parameterized continuous elastic spline curve traversing a deformed virtual three-dimensional lattice network, and superimposing the first-order tensile strain energy and the second-order bending strain energy constraining the geometric smoothness of the robot arm body, includes: The functional optimization and trajectory planning module extracts the three-dimensional spatial coordinates of each joint of the humanoid robot arm, uses the extracted three-dimensional spatial coordinates as control vertices, and calls the spline interpolation algorithm to generate parameterized continuous elastic spline curves. The functional optimization and trajectory planning module calculates the first and second partial derivatives of the spatial coordinate vector function of the parameterized continuous elastic spline curve with respect to the curve arc length parameter. Combined with the preset first-order tension weight coefficient and second-order bending weight coefficient, the functional optimization and trajectory planning module constructs the internal kinematic strain energy calculation formula.

8. The autonomous obstacle avoidance trajectory planning method for a humanoid robot arm according to claim 7, characterized in that, The generation of the total strain energy functional of the system, based on the variational method, iteratively updates the spatial coordinate sequence of the parameterized continuous elastic spline curve, including: The functional optimization and trajectory planning module maps the spatial coordinate vector of the parameterized continuous elastic spline curve to the topological potential energy field, extracts the corresponding lattice deformation potential energy value along the integral path of the parameterized continuous elastic spline curve, and performs algebraic summation of the internal kinematic strain energy calculation results and the external constraint energy calculation results to generate the total strain energy functional of the system. The functional optimization and trajectory planning module discretizes the parameterized continuous elastic spline curve into a finite number of discrete spline waypoints. It calls the discrete functional gradient descent algorithm to calculate the negative gradient direction of each discrete spline waypoint under the total strain energy functional. It iteratively updates the formula until the L2 norm of the difference between the spatial coordinate vectors between two adjacent iterations is less than the preset convergence threshold. The functional optimization and trajectory planning module extracts the spatial coordinate sequence of the parameterized continuous elastic spline curve that reaches the functional minimum state of total strain energy, and records the extracted spatial coordinate sequence as a Cartesian space obstacle avoidance spline trajectory.

9. The autonomous obstacle avoidance trajectory planning method for a humanoid robot arm according to claim 1, characterized in that the step of calling the inverse kinematics algorithm to transform the Cartesian space obstacle avoidance spline trajectory into a joint configuration space control drive flow includes: The underlying control and mapping execution module retrieves the preset system underlying control cycle step size, performs time dimension numerical difference processing on the Cartesian space obstacle avoidance spline trajectory, extracts the spatial coordinate difference between two adjacent discrete spline waypoints, divides the spatial coordinate difference by the system underlying control cycle step size, and calculates the Cartesian space velocity vector of the Cartesian space obstacle avoidance spline trajectory at continuous time nodes. The underlying control and mapping execution module reads the robotic arm Jacobian matrix calculated by the tensor field dynamics reconstruction module, performs the Moore-Penrose generalized inverse operation on the robotic arm Jacobian matrix to generate the corresponding Jacobian pseudo-inverse matrix, constructs the inverse kinematic mapping execution formula with superimposed null space optimization constraints, and constructs a penalty potential energy function with the difference between the current joint angle and the maximum physical limit angle of the joint as the variable. The module calculates the partial derivative of the penalty potential energy function with respect to the current joint angle and generates the joint limit avoidance gradient function.

10. An autonomous obstacle avoidance trajectory planning system for a humanoid robot arm, used to execute the autonomous obstacle avoidance trajectory planning method for a humanoid robot arm as described in any one of claims 1 to 9, characterized in that the system comprises: The environment and body perception module is used to obtain the initial joint configuration vector of the humanoid robot arm, solve the reference pose of each link of the robot arm in the three-dimensional Cartesian workspace through the forward kinematic equation, and synchronously drive the three-dimensional environment perception device to scan the robot arm workspace to obtain obstacle geometric envelope data. The tensor field dynamics reconstruction module is used to map and generate an initial virtual three-dimensional lattice network in the workspace of the robotic arm, calculate the operability matrix of the robotic arm under the initial joint configuration vector and perform eigenvalue decomposition, extract the spatial principal axis direction of the operability ellipsoid, establish the physical mapping relationship between the negative Poisson's ratio parameter and the eigenvalue, and update the anisotropic compliance tensor of the virtual three-dimensional lattice network. The deformation mapping and topology processing module is used to convert the geometric envelope data of obstacles into rigid indenter entities that intrude into the virtual three-dimensional lattice network. Based on the mapping relationship between the normal intrusion depth of the obstacle and the preset virtual penalty stiffness, the module calculates the normal compressive stress tensor distribution applied by the rigid indenter entity, solves the comprehensive strain tensor of the compressed region of the virtual three-dimensional lattice network, and extracts the coordinate system of the three-dimensional continuous low potential energy channel formed by the tangential inward contraction strain of the mesh nodes. The functional optimization and trajectory planning module is used to fit and map the discrete link structure of the robotic arm in the Cartesian workspace to a parameterized continuous elastic spline curve that shuttles through the deformed virtual three-dimensional lattice network. The module superimposes the first-order tensile strain energy and second-order bending strain energy that constrain the geometric smoothness of the robotic arm body, as well as the external constraint energy generated by the deformation of the virtual three-dimensional lattice network, to generate the total strain energy functional of the system. Based on the variational method, the spatial coordinate sequence of the parameterized continuous elastic spline curve is iteratively updated, and the Cartesian space obstacle avoidance spline trajectory corresponding to the minimum state of the total strain energy functional is extracted. The underlying control and mapping execution module is used to call the inverse kinematics algorithm to transform the Cartesian space obstacle avoidance spline trajectory into the joint configuration space control drive flow, and send the drive signal to the servo motor driver network to complete the obstacle avoidance action of the robotic arm.

Images