A complex task-oriented reconfigurable robot MPMO-SQP double-layer nested configuration optimization method

Abstract

The application discloses a reconfigurable robot MPMO-SQP double-layer nested configuration optimization method for complex tasks, and relates to the technical field of reconfigurable robot configuration optimization. A standardized robot module library is constructed and parameterized representation is completed, a four-dimensional characteristic parameter coding system is established to realize unified expression of a robot topological structure, a kinematic model is automatically generated through sequence expansion and topological recursion, an SQP algorithm is adopted to complete inverse kinematics solving and target point accessibility checking, a multi-dimensional configuration performance evaluation system is constructed, global configuration optimization is realized through an MPMO algorithm, and the optimal configuration is screened out through Pareto optimal solution set processing and comprehensive evaluation. The application can effectively improve the configuration design efficiency and comprehensive performance level of the robot in a complex application environment.

Description

Technical Field

[0001] This invention relates to the field of reconfigurable robot configuration optimization technology, specifically a method for optimizing the MPMO-SQP double-layer nested configuration of reconfigurable robots for complex tasks. Background Technology

[0002] With the increasing demands for on-orbit space services, operations in complex environments, and multi-task collaboration, robotic systems are facing higher requirements for structural reconfiguration and task adaptability. Multi-branch modular reconfigurable robots, through the combination of standardized modules, can dynamically generate different topologies according to task requirements, exhibiting excellent flexibility and scalability in complex environments. This has become an important research direction in the field of space robotics and intelligent equipment.

[0003] Current optimization schemes for the configuration of multi-branch modular reconfigurable robots mainly rely on experience-driven or local heuristic methods, lacking a systematic and computable framework for configuration generation and optimization. Existing research typically models only a single type of module, lacking a unified standardized module library and parametric representation, making it difficult to support the automatic generation of mixed configurations of multiple module types. Furthermore, the complex installation methods and interface relationships between modules lead to inconsistent configuration descriptions, making it difficult to directly map them into the optimization variable space. Descriptions of multi-branch topologies often rely on tree or graph structures for encoding, which, while reflecting connectivity, struggle to account for module type, installation posture, and interface alignment, resulting in incomplete configuration representations that cannot be directly used for kinematic modeling and optimization calculations.

[0004] In kinematic modeling, due to the diverse ways modules can be combined and the different kinematic link structures corresponding to different configurations, traditional methods require the separate establishment of forward kinematic models for specific configurations, lacking a general automatic modeling method, which severely restricts the efficiency of large-scale configuration search and performance evaluation. In inverse kinematics solving, multi-branch robots typically have multiple ends and multiple constraints, making traditional analytical methods difficult to apply, while purely numerical methods suffer from poor convergence and sensitivity to initial values, making it difficult to achieve stable solutions during configuration optimization.

[0005] At the configuration optimization level, robot performance often involves multiple interdependent metrics, including end-effector maneuverability, positioning accuracy, and structural complexity. Existing methods often target a single objective or employ simple weighted strategies, making it difficult to obtain a globally optimal set of configurations.

[0006] In summary, existing technologies lack a unified configuration optimization method, making it difficult to achieve efficient generation and global optimization of multi-branch modular reconfigurable robot configurations under complex task constraints. Therefore, it is necessary to propose a task-oriented configuration optimization method to improve the configuration design efficiency and overall performance of multi-branch modular reconfigurable robots in complex application environments. Summary of the Invention

[0007] To address the shortcomings of the existing technologies, this invention provides a MPMO-SQP double-layer nested configuration optimization method for reconfigurable robots oriented towards complex tasks. This method uses a complete parameterized expression of the robot configuration, solves the reachability verification of the target working point based on the SQP algorithm, constructs a multi-objective optimization system, and employs the MPMO algorithm to achieve global configuration optimization. Finally, the optimal configuration that meets the task requirements is obtained through Pareto optimal solution set selection, thereby improving the configuration design efficiency and overall performance of the robot in complex application environments.

[0008] To achieve the above objectives, the present invention adopts the following technical solution: a method for optimizing the MPMO-SQP double-layer nested configuration of a reconfigurable robot for complex tasks, comprising the following steps:

[0009] Step 1: Construct a standardized robot module library, which includes functional modules such as joint modules, link modules, and integration modules, as well as a torso module that serves as the main structure of the robot base. The assembly and connection between each functional module and the torso module are completed through standard interfaces. The integration module is composed of different joint modules and link modules connected as basic modules. The functional modules in the standardized robot module library are parameterized.

[0010] Step 2: Establish a four-dimensional feature parameter encoding system for functional modules. The four-dimensional feature parameters include module identification feature parameters, module installation feature parameters, standard interface alignment feature parameters, and topology connection feature parameters, thus obtaining the four-dimensional feature parameter encoding of the robot configuration. During the process, the integrated modules are expanded and mapped to describe the module installation method and express the robot topology.

[0011] Step 3: Based on the expansion of integrated module sequences and the recursion of topological relationships, perform kinematic modeling of the multi-branch modular reconfigurable robot;

[0012] Step 4: For the target working point, use the quadratic programming SQP algorithm to solve the inverse kinematics and complete the reachability verification of the target working point;

[0013] Step 5: Construct a multi-dimensional performance evaluation index system for robot configuration. The performance evaluation indexes selected are end-effector operability, maximum end-effector positioning error, and the number of all basic modules.

[0014] Step Six: Employ the multi-objective, multi-population co-evolutionary MPMO algorithm to encode the four-dimensional feature parameters of the robot configuration. A multi-objective optimization vector is constructed using these optimization variables. Multi-objective global optimization is then performed on the configuration space to obtain the Pareto optimal solution set. After normalization of the Pareto optimal solution set, the optimal configuration that meets the task requirements is selected through a comprehensive evaluation function. .

[0015] Furthermore, in step one, the standardized robot module library includes four types of joint modules, three types of link modules, three types of integration modules, a standard interface, and a torso module. The standard DH parameter method is used to model each functional module, and the parameterized representation of the standardized robot module library is defined as follows:

[0016]

[0017] Each functional module is defined as a seven-tuple, represented as:

[0018]

[0019] In the formula, Module number, For module type, This is the rotation matrix from the input end of the joint module to the center of the joint. This is the displacement vector from the input end of the joint module to the center of the joint. This is the rotation matrix from the joint center to the output of the joint module. This represents the displacement vector from the joint center to the output end of the joint module. and These are the rotation matrix and displacement vector from the input to the output of the linkage module, respectively, and when hour Corresponding joint module, , and Take any value; when hour Corresponding link module, , , , and Take any value; when hour Corresponding integrated module, , , , , , and Take any value.

[0020] Furthermore, in step two, for cases where the configuration is determined and the number of functional modules is... The robot, defining its first Each module Its four-dimensional feature parameters are expressed as:

[0021]

[0022] The four-dimensional feature parameter encoding of the robot configuration is represented as follows:

[0023]

[0024] In the formula, The module is identified by characteristic parameters, which indicate the type number of the current module in the standardized robot module library. Module installation feature parameters are used to describe the installation orientation relationship between two adjacent modules. These are standard interface alignment feature parameters used to describe the discrete rotation angle of the input coordinate system of the rear module relative to the output coordinate system of the front module around the z-axis. This is a topology connection characteristic parameter used to describe the position number of the current module in the robot topology preceding the module.

[0025] Furthermore, in step three, the overall four-dimensional feature parameter encoding of the robot is integrated into a module sequence expansion and parameter reordering according to the representation rules of the four-dimensional feature parameters to obtain the expanded overall four-dimensional feature parameter encoding of the robot. Then, the joint angle parameters are input. By combining the expanded encoding, the homogeneous transformation matrix of all modules in the world coordinate system is calculated in one traversal through topological recursion, thereby establishing the robot's forward kinematics model.

[0026] Furthermore, in step four, when using the quadratic programming SQP algorithm to solve the inverse kinematics, the constructed objective function is:

[0027]

[0028] In the formula, For the number of robot end effectors, To activate the flag, , For the first The target working point location corresponding to each end. For the first The actual location of each end The operability of the robot's end effector is calculated based on whether collaborative working conditions exist.

[0029] Furthermore, in step five, the end-effector operability is divided into two types based on the robot's operating conditions: independent operation of each branch and cooperative operation of each branch. The end-effector operability under these two conditions is expressed as follows:

[0030]

[0031] In the formula, Indicates the robot's first Jacobian matrix on each branch This indicates the calculation of the determinant;

[0032]

[0033] In the formula, It stores the number of degrees of freedom for each branch. Indicates the first The first branch of the Jacobian matrix A singular value, , Indicates the first The actual operability ellipsoid at the end of the branch is in the first... Length on the main axis;

[0034] The maximum positioning error of the end effector is the upper bound of the most unfavorable positional deviation that the end effector produces near the target working point, expressed as:

[0035]

[0036] In the formula, It is a coefficient matrix determined by the configuration and joint state. This represents the angular positioning error vector of each joint. This represents the axial displacement error of each joint along the z-axis. This represents the link length error along the x-axis for each link. This indicates the torsional angle error between adjacent links. This indicates the additional angular error term introduced due to assembly errors or structural imperfections. and These represent position error and attitude error, respectively.

[0037] The total number of all basic modules is the total number of joint modules and link modules included in the robot configuration after the integrated modules are unfolded, denoted as . .

[0038] Furthermore, in step six, the constructed multi-objective optimization vector is represented as follows:

[0039]

[0040] In the formula, This represents the target for optimizing end-point operability. This represents the optimization objective for the maximum positioning error at the end point. This represents the optimization target for the number of all basic modules.

[0041] Furthermore, in step six, during multi-objective global optimization, the MPMO algorithm parameters are configured according to task requirements and initialization operations are performed: based on encoding... Particles with several candidate configurations are generated. , Number the particles and initialize each particle. velocity vector Use the zero vector to initialize the individual optimal solution for each particle. Initialize the external file to empty, and generate the corresponding population for each objective in the multi-objective optimization vector;

[0042] Perform a loop search with the maximum number of iterations. Each iteration includes:

[0043] S1: Expand each particle The inverse kinematics are solved using the SQP algorithm from step four. If the target working point is unreachable, the particle is marked as an invalid configuration, and a new configuration is set. If the target point is reachable, calculate the configuration in the target pose. ;

[0044] S2: Update the individual optimal solution for each particle based on the Pareto dominance relation. If the current particle of Dominate it If the target vector is updated, then update If neither of them is dominant, then one of them will be retained as the new one with a 50% probability. ;

[0045] S3: Merge all current... Together with external archives, a candidate solution set is formed;

[0046] S4: Randomly select a non-dominated solution from the candidate solution set as the leader particle. This ensures that the search process balances convergence and solution set diversity.

[0047] S5: Iteratively update the velocity and position of each particle according to the following formula:

[0048]

[0049] In the formula, This represents the velocity vector after iterative updates. This indicates the particle position after iterative update. Indicates the current iteration number. For inertial weights, and As a learning factor, and It is a random variable;

[0050] After the iteration is complete, all non-dominated solutions stored in the external archive constitute the Pareto optimal solution set for the problem.

[0051] Furthermore, in step six, the comprehensive evaluation function is expressed as:

[0052]

[0053] In the formula, These are the optimization objectives in the normalized multi-objective optimization vector, respectively. These are the weight coefficients corresponding to the optimization objective, and they satisfy... By adjusting the weighting coefficients, configurations with different performance focuses can be selected, choosing those that... The smallest configuration is the optimal configuration. .

[0054] Compared with the prior art, the beneficial effects of the present invention are:

[0055] 1. This invention constructs a standardized robot module library that includes joint modules, linkage modules, and integration modules. Through pre-integrated design of the integration modules, the number of connection interfaces can be effectively reduced, the reliability of mechanical and electrical docking during unmanned space operations can be improved, and various typical industrial robotic arm configurations can be quickly constructed with strong adaptability.

[0056] 2. This invention establishes a four-dimensional feature parameter encoding system for modules, realizing a unified parameterized description of the topology of multi-branch modular reconfigurable robots. It also takes into account module type, installation posture, interface alignment, and topological connection relationship, and constructs a mapping relationship from physical structure to optimization variable space, providing core modeling support for automatic kinematic modeling, inverse kinematics solution, and configuration optimization algorithms.

[0057] 3. Based on module sequence expansion and topological relationship recursion, this invention realizes the automatic generation of kinematic models of multi-branch modular reconfigurable robots. The homogeneous transformation matrix calculation of all modules can be completed in one traversal, without the need for separate modeling for specific configurations, which greatly improves the efficiency of large-scale configuration search and performance evaluation.

[0058] 4. This invention adopts an inverse kinematics solution method based on quadratic programming (SQP), which can optimize the end effector operability while ensuring the constraints of each module. It solves the problems of poor convergence and sensitivity to initial values ​​in the inverse kinematics solution of multi-branch modular reconfigurable robots, and can stably complete the reachability determination of the target working point.

[0059] 5. This invention constructs a multi-dimensional configuration performance quantitative evaluation system that includes end-effector operability, end-effector maximum positioning error, and the number of all basic modules. It can be adapted to the independent working conditions of each branch, and can also support the performance evaluation of the working conditions of each branch cooperating with each other, comprehensively reflecting the configuration's operational capability, accuracy performance and structural complexity.

[0060] 6. This invention employs the multi-objective, multi-population co-evolutionary method MPMO to perform a global search of the configuration space, which can obtain a Pareto optimal solution set that takes into account multiple performance indicators. The optimal configuration is selected through normalization and a comprehensive evaluation function. This solves the problem that existing methods with single-objective optimization or simple weighted strategies cannot obtain the globally optimal configuration. The weights can be flexibly adjusted according to engineering needs to adapt to different task focuses. Attached Figure Description

[0061] Figure 1 This is a schematic diagram of the standardized robot module library in this invention;

[0062] Figure 2 This is a schematic diagram of the robot generated based on a standardized robot module library in this invention;

[0063] Figure 3 This is a schematic diagram of the operability space under the robot collaborative working condition in this invention;

[0064] Figure 4 This is a schematic diagram of the operability ellipsoid and its principal axis distribution in this invention;

[0065] Figure 5 This is a flowchart of the MPMO global configuration optimization process in this invention;

[0066] Figure 6 This is a distribution map of the Pareto optimal solution set obtained in the embodiment;

[0067] Figure 7 This is the topology and task pose verification diagram of the optimal configuration in the embodiment. Detailed Implementation

[0068] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the invention, not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0069] like Figures 1-5 As shown, a two-layer nested configuration optimization method for reconfigurable robots (MPMO-SQP) oriented towards complex tasks specifically includes the following steps:

[0070] Step 1: Construct a standardized robot module library and its parameterized representation;

[0071] Build a standardized robot module library, combined with Figure 1 As shown, the module library includes functional modules such as 4 types of joint modules, 3 types of linkage modules, and 3 types of integration modules, as well as a torso module that serves as the main structure of the robot's base. The assembly and connection between the functional modules and the torso module are all completed through standard interfaces. Specifically:

[0072] (1) All joint modules are single-degree-of-freedom rotational joints, including the following 4 types:

[0073] Module 1: Axial coaxial joint module, with its input and output interfaces coaxial;

[0074] Module 2: Axially intersecting joint module, whose input and output axes intersect;

[0075] Module 3: Orthogonal angle joint module, whose input and output axes are orthogonal;

[0076] Module 4: Spatial corner joint module, whose input and output axes form a spatial angle.

[0077] (2) All linkage modules are rigid linkages without degrees of freedom, including the following three forms:

[0078] Module 5: Axial coaxial connecting rod module, with its input and output interfaces coaxial;

[0079] Module 6: Orthogonal corner linkage module, whose input and output axes are orthogonal;

[0080] Module 7: Axially intersecting linkage module, whose input and output axes intersect.

[0081] (3) The integrated module is composed of different joint modules and linkage modules connected as basic modules, including the following three forms:

[0082] Module 8: Composed of Module 1 and Module 2 connected in series;

[0083] Module 9: Composed of Module 1, Module 2, and Module 1 connected in series;

[0084] Module 10: Composed of Module 3, Module 6, Module 1, and Module 6 connected in series with Module 1.

[0085] (4) Standard interface: used to realize the mechanical connection and fixation between connected modules, the transmission of electrical signals and the interconnection of power circuits, to ensure that the modules are easy to disassemble and assemble, neatly connected and interchangeable.

[0086] (5) Torso module: As the main structure of the robot base, it mainly provides stable support for the whole machine, and at the same time undertakes the installation of various functional modules, load bearing and overall configuration constraint.

[0087] In the standardized robot module library, integrated modules, based on pre-integrated designs of different joint and link modules, effectively reduce the number of standard interfaces and improve the reliability of mechanical and electrical connections during unmanned space operations. Based on pre-designed and verified combination methods, multi-branch modular reconfigurable robots can be rapidly constructed by selecting and combining modules from the standardized robot module library as needed. Each branch can adopt typical configuration robotic arms or custom configuration robotic arms as required, combined with… Figure 2 As shown, typical robotic arm configurations include the MAR configuration, SRS configuration, GITAI configuration, and SSRMS configuration. It is important to note that the term "configuration" refers to the structural combination of different modules in the robot, rather than the combination of joint angles.

[0088] The standard DH parameter method is used to model each functional module. The joint module is divided into two parts: the input homogeneous transformation matrix and the output homogeneous matrix transformation. The link module is described by a fixed homogeneous transformation matrix. The integrated module is automatically expanded into a basic module sequence during the subsequent automatic kinematic modeling process.

[0089] The parameterized representation of the standardized robot module library is further defined as follows:

[0090]

[0091] Each functional module Defined as a 7-tuple, it is represented as:

[0092]

[0093] In the formula, The modules are numbered (i.e., the above 4 types of joint modules, 3 types of linkage modules, and 3 types of integrated modules). For module type, This is the rotation matrix from the input end of the joint module to the center of the joint. This is the displacement vector from the input end of the joint module to the center of the joint. This is the rotation matrix from the joint center to the output of the joint module. This represents the displacement vector from the joint center to the output end of the joint module. and These are the rotation matrix and displacement vector from the input to the output of the linkage module, respectively, and when hour Corresponding joint module, , and Take any value; when hour Corresponding link module, , , , and Take any value; when hour Corresponding integrated module, , , , , , and Take any value.

[0094] Step 2: Establish a four-dimensional feature parameter encoding system for functional modules to describe the module installation method and express the robot topology.

[0095] Based on a standardized robot module library, a unified four-dimensional feature parameter encoding system is constructed to characterize the assembly parameters of each functional module and its standard interface, including module identification feature parameters. Module installation characteristic parameters Standard interface alignment feature parameters and topology connection characteristic parameters This coding system realizes a unified parameterized description of the robot's topology, constructs a mapping relationship from physical structure to optimization variable space, and provides core modeling support for automatic kinematic modeling, inverse kinematics solving, and configuration optimization algorithms.

[0096] For a configuration that is already determined and the number of functional modules is The robot, defining its first Each module Its four-dimensional feature parameters are expressed as:

[0097]

[0098] The overall four-dimensional feature parameters of the robot are encoded as follows:

[0099]

[0100] The specific definitions of each feature parameter are as follows:

[0101] (1) Module identifier characteristic parameters: This parameter indicates the type number of the current module in the standardized robot module library, with a value ranging from 1 to 10, corresponding to the 10 functional modules in the library. This parameter is used to complete the module type index and function mapping, as described below:

[0102]

[0103] (2) Module installation characteristic parameters: The following description is used to describe the installation orientation relationship between two adjacent modules:

[0104]

[0105] (3) Standard interface alignment feature parameters: These parameters describe the discrete rotation angle of the input coordinate system of the rear module relative to the output coordinate system of the front module around the z-axis. Based on the mechanical structure characteristics of the standard interface, they are set to three discrete values, as described below:

[0106]

[0107] (4) Topology connection characteristic parameters: These describe the position number of the current module in the robot topology preceding the module, as follows:

[0108]

[0109] Specifically, the integrated module is structurally composed of several joint modules and linkage modules as basic modules, such as the first... Each module is an integrated module. To ensure the consistency and computability of the four-dimensional feature parameter encoding system, it needs to be expanded and mapped. The module identifier feature parameters corresponding to the basic modules within it are represented as follows:

[0110]

[0111] In the formula, The number of basic modules included in the integrated module: When the integrated module uses module 8, , When the integrated module uses module 9, , When the integrated module uses module 10, , .

[0112] In the When a module is an integrated module, its four-dimensional feature parameters are only available in... The corresponding module installation characteristic parameters, standard interface alignment characteristic parameters, and topology connection characteristic parameters in the column are directly taken from the input. , and To ensure consistency of constraints between the integrated module and the front-end module, for For the remaining columns, the corresponding module installation feature parameters and standard interface alignment feature parameters all take fixed values. and Topological connectivity characteristic parameters in Based on this, it is generated sequentially in ascending order, that is, its four-dimensional feature parameters are represented as: .

[0113] Step 3: Perform automatic kinematic modeling based on the sequence expansion of integrated modules and the recursive deduction of topological relationships;

[0114] The establishment of the forward kinematics model mainly involves calculating the rotation matrix and displacement vector of the joint coordinate system relative to the world coordinate system. Considering that the integrated module may contain both joint modules and link modules, although the forward kinematics solution is mainly driven by joint angle parameters, the link modules still have a significant impact on the robot configuration. Therefore, during the modeling process, the structural parameters of the link modules are equivalently integrated into the joint module parameters, without affecting the forward kinematics solution results based on joint angles under the automatic modeling framework.

[0115] For the integrated module, the four-dimensional feature parameters of the robot as a whole are encoded according to the representation rules of its four-dimensional feature parameters. After performing sequence expansion and reordering all parameters, we obtain:

[0116]

[0117] In the formula, This represents the encoding of the four-dimensional feature parameters of the unfolded robot. This indicates the total number of modules contained in the robot after the integrated modules are deployed.

[0118] Input joint angle parameters , combined To establish the robot's forward kinematics model, the rotation matrix of each joint coordinate system relative to the world coordinate system is first calculated. Since most modules are symmetrical in both forward and reverse installation, the characteristic parameters of module installation are not distinguished here. The resulting computational differences are addressed by adjusting the rotation matrix of each module based on the type of the preceding and current modules. The calculation is divided into six cases:

[0119]

[0120] In the formula, This represents the rotation matrix of the preceding module relative to the world coordinate system. This represents the rotation matrix of the current module relative to the preceding module. This represents the rotation matrix of the torso module interface position relative to the world coordinate system. This represents a rotation matrix that rotates the object by a specified angle around the z-axis of the current coordinate system. .

[0121] Next, calculate the displacement vectors of each joint coordinate system relative to the world coordinate system. Similarly, the displacement vector of each module The calculation is divided into six cases:

[0122]

[0123] In the formula, This represents the displacement vector of the preceding module relative to the world coordinate system. This represents the displacement vector of the current module relative to the preceding module. This represents the displacement vector of the torso module interface position relative to the world coordinate system.

[0124] Through the above recursive process, the homogeneous transformation matrix of all modules in the world coordinate system can be obtained in one traversal. Based on this result, forward kinematics calculations can be performed directly, and inverse kinematics solutions, Jacobian matrix construction, operability calculation, and maximum positioning error analysis can be supported.

[0125] Step 4: Solve the inverse kinematics using the quadratic programming (SQP) algorithm for the target working point;

[0126] To enable the robot to accurately reach the designated target working point under multi-branch and multi-degree-of-freedom conditions, the quadratic programming (SQP) algorithm is used to solve the inverse kinematics, while verifying whether the target working point is reachable.

[0127] First, give a set of target working points Calculate the actual position of the robot's end effector ,in The number of robot end effectors, each end effector corresponds to one target working point, and each target working point corresponds to one activation flag. This is used to indicate whether the target working point is involved in optimization.

[0128] Using the Spatial Quadratic Programming (SQP) algorithm, combining the end-point location error and operability index, the objective function is constructed as follows:

[0129]

[0130] In the formula, This indicates the robot's end effector operability, and is calculated based on whether collaborative working conditions exist.

[0131] Generally, provided the target operating point is reachable, this method can search for flags that enable each activation flag. The corresponding combination of joint angles that maximizes the maneuverability of the robot's end effector. This ensures that the robot has good motion performance and stability while reaching the target working point.

[0132] Step 5: Construction of Robot Configuration Performance Indicators and Quantitative Evaluation System;

[0133] To compare and analyze different configurations To select the optimal configuration, it is necessary to establish a configuration performance evaluation index system. The performance evaluation indexes selected in this invention include end-effector maneuverability, maximum end-effector positioning error, and the total number of all basic modules (the sum of the number of basic modules included in the integrated modules of the robot, plus the original number of joint modules and link modules). Specifically:

[0134] (1) End-point operability:

[0135] Traditional maneuverability, proposed by Yoshikawa in 1985, is applicable to calculating the end-effector maneuverability of a robot under independent operating conditions, and is expressed as:

[0136]

[0137] In the formula, Indicates the robot's first Jacobian matrix on each branch This indicates the calculation of the determinant.

[0138] Combination Figure 3 As shown, in the process of robot collaborative operation, the base coordinate system is first used as a unified reference to establish the coordinate systems of each branch's end effector, and then mapped to the coordinate system of the corresponding task, thereby achieving a unified expression of each end effector to the task space. Based on this, the motion capability of each branch is represented in the task space as an operability ellipsoid using the Jacobian matrix. Due to the collaborative constraints between multiple branches, the operability ellipsoids of each branch need to undergo coordinate transformation and find their intersection in the same task coordinate system. The volume of this intersection reflects the system's motion capability under the condition of satisfying the collaborative constraints. Therefore, the operability of the end effector under the condition of mutual cooperation among the robot's branches is expressed as:

[0139]

[0140] In the formula, It stores the number of degrees of freedom for each branch. Indicates the first The first branch of the Jacobian matrix A singular value, , Indicates the first The actual operability ellipsoid at the end of the branch is in the first... The length on the principal axis, the operability ellipsoid and its principal axis distribution combined Figure 4 As shown.

[0141] (2) Maximum positioning error at the end point:

[0142] Unlike the end-position error in step four, under a given configuration and their corresponding joint angle combinations Based on the combined effects of joint motion errors and structural parameter errors, the upper limit of the most unfavorable positional deviation of the end effector near the target working point is called the maximum positioning error of the end effector. , and Let these represent the position error and attitude error, respectively. This maximum end-effector positioning error reflects the limiting characteristics of the error distribution, rather than the instantaneous position deviation obtained from a single inverse kinematics solution. A first-order maximum end-effector positioning error model is established based on the DH parameter deviation, expressed as:

[0143]

[0144] In the formula, It is a coefficient matrix determined by the configuration and joint state. This represents the angular positioning error vector of each joint. This represents the axial displacement error of each joint along the z-axis. This represents the link length error along the x-axis for each link. This indicates the torsional angle error between adjacent links. This indicates additional angular error terms introduced due to assembly errors or structural imperfections.

[0145] (3) Number of all basic modules:

[0146] To reflect configurational complexity and system reliability, the number of all basic modules is introduced as an evaluation metric. Considering that integrated modules are structurally derived from several basic modules, the number of basic modules is based on the module sequence expansion result in step three, for a given configuration. Perform a unified count and record the number of basic modules included in the overall robot configuration. .

[0147] Step Six: Multi-objective global configuration optimization based on multi-objective multi-population co-evolution (MPMO);

[0148] The standardized robot module library is initialized, and the target working point is input. To achieve global optimization of robot configuration among multiple performance indicators, a multi-objective, multi-population cooperative evolution (MPMO) algorithm is used to search the configuration space. The execution process is combined with... Figure 5 As shown, the coding of the robot configuration As optimization variables, construct a multi-objective optimization vector:

[0149]

[0150] In the formula, This represents the target for optimizing end-point operability. This represents the optimization objective for the maximum positioning error at the end point. This represents the optimization target for the number of all basic modules.

[0151] Configure MPMO algorithm parameters and perform initialization operations according to task requirements: based on encoding Particles with several candidate configurations are generated. , Number the particles and initialize each particle. velocity vector Use the zero vector to initialize the individual optimal solution for each particle. The external file is initialized to empty and used to store all non-dominated solutions found during the iteration process. A corresponding population is generated for each objective in the multi-objective optimization vector.

[0152] Perform a loop search with the maximum number of iterations, executing the following 5 core steps in each iteration:

[0153] S1: Expand each particle The inverse kinematics are solved using the SQP algorithm from step four. If the target working point is unreachable, the particle is marked as an invalid configuration, and a new configuration is set. If the target point is reachable, calculate the configuration in the target pose. .

[0154] S2: Update the individual optimal solution for each particle based on the Pareto dominance relation. If the current particle of Dominate it If the target vector is updated, then update If neither of them is dominant, then one of them will be retained as the new one with a 50% probability. .

[0155] S3: Merge all current... Together with external archives, a candidate solution set is formed.

[0156] S4: Randomly select a non-dominated solution from the candidate solution set as the leader particle. This ensures that the search process balances convergence and solution set diversity.

[0157] S5: Iteratively update the velocity and position of each particle according to the following formula:

[0158]

[0159] In the formula, This represents the velocity vector after iterative updates. This indicates the particle position after iterative update. Indicates the current iteration number. For inertial weights, and As a learning factor, and It is a random variable.

[0160] After iteration, all non-dominated solutions stored in the external archive constitute the Pareto optimal solution set for the problem, with each solution achieving varying degrees of trade-offs among the three performance evaluation metrics. To select the optimal configuration that best meets engineering requirements and eliminate differences in the dimensions and orders of magnitude of different performance evaluation metrics, the performance evaluation metrics corresponding to each configuration in the Pareto optimal solution set are normalized, as follows:

[0161]

[0162] In the formula, These are the maximum values ​​of the corresponding optimization objectives in the Pareto optimal solution set. These are the minimum values ​​of the corresponding optimization objectives in the Pareto optimal solution set.

[0163] Based on the importance of each optimization objective in engineering applications, weighting coefficients are introduced to construct a comprehensive evaluation function, expressed as:

[0164]

[0165] In the formula, These are the weight coefficients corresponding to the optimization objective, and they satisfy... By adjusting the weighting coefficients, configurations with different performance focuses can be selected, choosing the configuration that best suits the desired performance. The smallest configuration is the optimal configuration. .

[0166] For the optimal configuration obtained through screening The physical structure is decoded, and the final output is a robot configuration description that can be directly used for engineering implementation. This includes a sequence of module types, topological connections, spatial installation posture, and a complete set of kinematic parameters. Based on the decoded physical configuration, the kinematic model is called for forward kinematic verification and performance review to ensure that it meets the target workspace requirements, operability constraints, and error index requirements, thereby guaranteeing the feasibility and reliability of the configuration result in actual engineering.

[0167] Example

[0168] This embodiment conducts configuration optimization experiments for two sets of given target points. After obtaining the Pareto optimal solution set for configuration optimization, the optimal configuration is selected from the Pareto optimal solution set based on the pre-set weight coefficients of the comprehensive evaluation function. .

[0169] To improve search efficiency and ensure configuration effectiveness, the following constraints are imposed on the configuration optimization process:

[0170] (1) Module number constraint: The total number of modules in the robot configuration is limited to a minimum of 2 and an maximum of 13, of which the number of joint modules is limited to a minimum of 6 and an maximum of 7. Under the premise of ensuring the dexterity of the end effector, a certain degree of redundancy is allowed to be retained in the configuration for some complex target points to improve the task adaptability.

[0171] (2) Invalid configuration pre-screening: Before entering the configuration optimization process, the particles of the configuration are pre-screened. Perform preliminary screening. If particles If two joint modules are located at opposite ends of a straight line, the configuration is considered invalid and discarded. An invalid configuration is defined as follows: The determination criteria can be expressed in configuration coding form as follows:

[0172]

[0173] In the formula, / represents any value for particles containing integrated module configurations. First, it needs to be topologically expanded, and then filtered according to the above rules.

[0174] (3) Module Connection Rules Constraints: Joint modules can be directly connected to other joint modules or link modules, but direct connection between link modules is prohibited; furthermore, link modules cannot be located at the beginning or end of any branch. This is because direct connection between link modules would result in passive ends connecting to passive ends in the standard interface, thus forming an invalid configuration. Similarly, for particles containing integrated module configurations... First, topology expansion needs to be performed, and then constraint determination should be completed according to the above rules.

[0175] The robot's working mode is set to single-arm operation. A target working point is defined, and this point is used as the objective for solving the inverse kinematics. The homogeneous transformation matrix of the target working point relative to the base coordinate system is:

[0176]

[0177] Set the range of module numbers and the upper and lower bounds of variables:

[0178]

[0179] Initialize the parameters of the quadratic programming (SQP) algorithm as shown in Table 1:

[0180] Table 1 SQP Parameter Settings

[0181]

[0182] The parameters for the Multi-Objective Multi-Population Co-evolution (MPMO) algorithm are initialized as shown in Table 2:

[0183] Table 2 MPMO Parameter Settings

[0184]

[0185] Set the multi-objective optimization vector for the multi-objective multi-population co-evolution (MPMO) algorithm:

[0186]

[0187] Begin iterating, for each particle The position and velocity are updated using the following formula:

[0188]

[0189] Obtaining the Pareto optimal solution set Figure 6 As shown, to eliminate differences in the dimensions and orders of magnitude of different performance indicators, the performance evaluation indicators corresponding to each configuration in the Pareto optimal solution set are normalized. Furthermore, based on engineering application requirements, weighting coefficients are introduced to construct a comprehensive evaluation function. In this embodiment, considering the need for highly maneuverable configurations in engineering applications, the optimization objective is set to prioritize searching for robot configurations with the highest possible maneuverability. Therefore, the weighting coefficient is set to... .

[0190] The optimal configuration is obtained by filtering from the Pareto optimal solution set. and their joint angle combinations:

[0191]

[0192] For the optimal configuration Kinematic verification was performed, and the corresponding robot topology was combined with it. Figure 7 As shown, it can be seen that this configuration is similar to... The encoding results are strictly one-to-one and satisfy all constraints. Figure 7 The red nodes represent joint modules, totaling 7; the cyan nodes represent link modules, which, together with the joint modules, form a complete series-parallel hybrid topology, totaling 9 modules; the black nodes represent the interface positions of the torso modules and the positions of the end effectors, describing the connection between the robot and the environment and the task execution endpoints. Specifically, the homogeneous transformation matrix that enables the robot's end effector to stably and accurately reach the target point is... The solution satisfies the task space constraints and verifies the optimal configuration. Effectiveness and accessibility in a kinematic sense.

[0193] In addition, for the optimal configuration Performance verification was performed at the target location, based on the optimal configuration. The optimization objectives for this configuration at the target pose are calculated as follows:

[0194]

[0195] The calculation results show that this optimal configuration... It not only accurately and stably reaches the designated target working point, satisfying the kinematic constraints of all task spaces, but also exhibits high positioning accuracy and high maneuverability under the target point pose, demonstrating good motion flexibility and end-effector control capabilities. This fully proves that the configuration optimization strategy, under complex multi-objective constraints, can not only ensure the feasibility of the structural topology, but also effectively achieve a balance and improvement in robot performance indicators.

[0196] Simulation results show that the proposed configuration optimization method, which combines the multi-objective multi-population co-evolution (MPMO) algorithm with inverse kinematics solution of quadratic programming (SQP), can efficiently avoid invalid configurations in a large search space while strictly adhering to module connection rules and multiple constraints on the number of modules. By introducing a comprehensive evaluation function and setting specific weight coefficients, the optimal configuration that meets the requirements is selected from the Pareto optimal solution set. .

[0197] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of the equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0198] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A method for optimizing the MPMO-SQP two-layer nested configuration of a reconfigurable robot for complex tasks, characterized in that: Includes the following steps: Step 1: Construct a standardized robot module library, which includes functional modules such as joint modules, link modules, and integration modules, as well as a torso module that serves as the main structure of the robot base. The assembly and connection between each functional module and the torso module are completed through standard interfaces. The integration module is composed of different joint modules and link modules connected as basic modules. The functional modules in the standardized robot module library are parameterized. Step 2: Establish a four-dimensional feature parameter encoding system for functional modules. The four-dimensional feature parameters include module identification feature parameters, module installation feature parameters, standard interface alignment feature parameters, and topology connection feature parameters, thus obtaining the four-dimensional feature parameter encoding of the robot configuration. During the process, the integrated modules are expanded and mapped to describe the module installation method and express the robot topology. Step 3: Based on the expansion of integrated module sequences and the recursion of topological relationships, perform kinematic modeling of the multi-branch modular reconfigurable robot; Step 4: For the target working point, use the quadratic programming SQP algorithm to solve the inverse kinematics and complete the reachability verification of the target working point; Step 5: Construct a multi-dimensional performance evaluation index system for robot configuration. The performance evaluation indexes selected are end-effector operability, maximum end-effector positioning error, and the number of all basic modules. Step Six: Employ the multi-objective, multi-population co-evolutionary MPMO algorithm to encode the four-dimensional feature parameters of the robot configuration. A multi-objective optimization vector is constructed using these optimization variables. Multi-objective global optimization is then performed on the configuration space to obtain the Pareto optimal solution set. After normalization of the Pareto optimal solution set, the optimal configuration that meets the task requirements is selected through a comprehensive evaluation function. .

2. The MPMO-SQP double-layer nested configuration optimization method for reconfigurable robots oriented towards complex tasks according to claim 1, characterized in that: In step one, the standardized robot module library includes four types of joint modules, three types of link modules, three types of integrated modules, a standard interface, and a torso module. The standard DH parameter method is used to model each functional module, and the parameterized representation of the standardized robot module library is defined as follows: Each functional module is defined as a seven-tuple, represented as: In the formula, Module number, For module type, This is the rotation matrix from the input end of the joint module to the center of the joint. This is the displacement vector from the input end of the joint module to the center of the joint. This is the rotation matrix from the joint center to the output of the joint module. This represents the displacement vector from the joint center to the output end of the joint module. and These are the rotation matrix and displacement vector from the input to the output of the linkage module, respectively, and when hour Corresponding joint module, , and Take any value; when hour Corresponding link module, , , , and Take any value; when hour Corresponding integrated module, , , , , , and Take any value.

3. The MPMO-SQP double-layer nested configuration optimization method for reconfigurable robots oriented towards complex tasks according to claim 2, characterized in that: In step two, for cases where the configuration is determined and the number of functional modules is [number missing], [details missing]. The robot, defining its first Each module Its four-dimensional feature parameters are expressed as: The four-dimensional feature parameter encoding of the robot configuration is represented as follows: In the formula, The module is identified by characteristic parameters, which indicate the type number of the current module in the standardized robot module library. Module installation feature parameters are used to describe the installation orientation relationship between two adjacent modules. These are standard interface alignment feature parameters used to describe the discrete rotation angle of the input coordinate system of the rear module relative to the output coordinate system of the front module around the z-axis. This is a topology connection characteristic parameter used to describe the position number of the current module in the robot topology preceding the module.

4. The MPMO-SQP double-layer nested configuration optimization method for reconfigurable robots oriented towards complex tasks according to claim 3, characterized in that: In step three, the robot's overall four-dimensional feature parameter encoding is integrated into a module sequence expansion and parameter reordering according to the representation rules of the four-dimensional feature parameters to obtain the expanded robot's overall four-dimensional feature parameter encoding. Then, the joint angle parameters are input. By combining the expanded encoding, the homogeneous transformation matrix of all modules in the world coordinate system is calculated in one traversal through topological recursion, thereby establishing the robot's forward kinematics model.

5. The MPMO-SQP double-layer nested configuration optimization method for reconfigurable robots oriented towards complex tasks according to claim 4, characterized in that: In step four, when using the quadratic programming SQP algorithm to solve the inverse kinematics, the objective function constructed is: In the formula, For the number of robot end effectors, To activate the flag, , For the first The target working point location corresponding to each end. For the first The actual location of each end The operability of the robot's end effector is calculated based on whether collaborative working conditions exist.

6. The MPMO-SQP double-layer nested configuration optimization method for reconfigurable robots oriented towards complex tasks according to claim 5, characterized in that: In step five, the end-effector operability is divided into two types based on the robot's operating conditions: independent operation of each branch and cooperative operation of each branch. The end-effector operability under the two conditions is expressed as follows: In the formula, Indicates the robot's first Jacobian matrix on each branch This indicates the calculation of the determinant; In the formula, It stores the number of degrees of freedom for each branch. Indicates the first The first branch of the Jacobian matrix A singular value, , Indicates the first The actual operability ellipsoid at the end of the branch is in the first... Length on the main axis; The maximum positioning error of the end effector is the upper bound of the most unfavorable positional deviation that the end effector produces near the target working point, expressed as: In the formula, It is a coefficient matrix determined by the configuration and joint state. This represents the angular positioning error vector of each joint. This represents the axial displacement error of each joint along the z-axis. This represents the link length error along the x-axis for each link. This indicates the torsional angle error between adjacent links. This indicates the additional angular error term introduced due to assembly errors or structural imperfections. and These represent position error and attitude error, respectively. The total number of all basic modules is the total number of joint modules and link modules included in the robot configuration after the integrated modules are unfolded, denoted as . .

7. The MPMO-SQP double-layer nested configuration optimization method for reconfigurable robots oriented towards complex tasks according to claim 6, characterized in that: In step six, the constructed multi-objective optimization vector is represented as follows: In the formula, This represents the target for optimizing end-point operability. This represents the optimization objective for the maximum positioning error at the end point. This represents the optimization target for the number of all basic modules.

8. The MPMO-SQP double-layer nested configuration optimization method for reconfigurable robots oriented towards complex tasks according to claim 7, characterized in that: In step six, when performing multi-objective global optimization, the MPMO algorithm parameters are configured according to task requirements and initialization operations are performed: based on encoding. Particles with several candidate configurations are generated. , Number the particles and initialize each particle. velocity vector Use the zero vector to initialize the individual optimal solution for each particle. Initialize the external file to empty, and generate the corresponding population for each objective in the multi-objective optimization vector; Perform a loop search with the maximum number of iterations. Each iteration includes: S1: Expand each particle The inverse kinematics are solved using the SQP algorithm from step four. If the target working point is unreachable, the particle is marked as an invalid configuration, and a new configuration is set. If the target point is reachable, calculate the configuration in the target pose. ; S2: Update the individual optimal solution for each particle based on the Pareto dominance relation. If the current particle of Dominate it If the target vector is updated, then update If neither of them is dominant, then one of them will be retained as the new one with a 50% probability. ; S3: Merge all current... Together with external archives, a candidate solution set is formed; S4: Randomly select a non-dominated solution from the candidate solution set as the leader particle. This ensures that the search process balances convergence and solution set diversity. S5: Iteratively update the velocity and position of each particle according to the following formula: In the formula, This represents the velocity vector after iterative updates. This indicates the particle position after iterative update. Indicates the current iteration number. For inertial weights, and As a learning factor, and It is a random variable; After the iteration is complete, all non-dominated solutions stored in the external archive constitute the Pareto optimal solution set for the problem.

9. The MPMO-SQP double-layer nested configuration optimization method for reconfigurable robots oriented towards complex tasks according to claim 8, characterized in that: In step six, the comprehensive evaluation function is expressed as follows: In the formula, These are the optimization objectives in the normalized multi-objective optimization vector, respectively. These are the weight coefficients corresponding to the optimization objective, and they satisfy... By adjusting the weighting coefficients, configurations with different performance focuses can be selected, choosing those that... The smallest configuration is the optimal configuration. .

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