Method, device and medium for motion planning of a rigid-flexible coupled cable-driven parallel robot

Abstract

The application discloses a rigid-flexible coupling rope traction parallel robot motion planning method, equipment and medium, and belongs to the field of rope motion planning. The method comprises the following steps: step 1, a kinematics model and a statics model of the robot are established; step 2, a performance index is constructed based on the established model; step 3, under the known target pose of an end effector, the optimal target pose is obtained by optimizing and solving the target pose through a particle swarm algorithm using the performance index; step 4, a low-dimensional proxy model is constructed based on the established model and the performance index; step 5, the optimal target pose is used as a whole body motion planning target, a path in a mobile platform space and a matching path in a mechanical arm joint space are generated by using the low-dimensional proxy model and a hierarchical planning algorithm, and a whole body motion path is obtained; and step 6, the whole body motion path is processed by using a minimum impact trajectory optimization algorithm, and a whole body motion trajectory for driving the robot is generated. The application can consider obstacle avoidance safety and mechanical stability, and improve quality and execution reliability.

Description

Technical Field

[0001] This invention relates to the field of planning for rigid-flexible coupled rope-traction parallel robots, and more particularly to a two-stage whole-body motion planning method for rigid-flexible coupled rope-traction parallel robots. Background Technology

[0002] The rigid-flexible coupling rope-driven parallel robot is a composite robot system that combines a rope-driven parallel robot with a robotic arm. Its mobile platform is driven by multiple flexible ropes, and a robotic arm is integrated into the platform as the operation execution unit. This system combines the advantages of rope-driven parallel robots—large workspace, high load capacity, and low system inertia—with the characteristics of a robotic arm—flexible attitude adjustment and high operational precision within a local area. It can perform delicate operations while moving over a wide range of areas, making it suitable for applications such as material handling, assembly, and mobile operations.

[0003] However, the aforementioned rigid-flexible coupling structure also introduces significant kinematic and mechanical coupling characteristics, making the system face more complex constraints when performing full-body motion planning from the initial configuration to the target configuration. On the one hand, the system involves multiple variables, such as the pose of the mobile platform and the joint states of the robotic arm, significantly increasing the dimensionality of its configuration space. Full-body motion planning requires coordinating multiple degrees of freedom variables in a high-dimensional space, leading to a significant increase in planning complexity and computational burden. On the other hand, the rope can only provide tension and cannot apply thrust, and the robotic arm, as the load on the mobile platform, causes changes in the force state of the mobile platform due to its joint movements, requiring the system to continuously satisfy the rope's mechanical feasibility constraints during motion. Therefore, the system's full-body motion planning not only needs to ensure that the motion trajectory is geometrically collision-free but also must ensure that the system remains in a mechanically feasible state throughout the entire motion process.

[0004] Furthermore, in such whole-body motion planning problems, the selection of the target configuration directly affects the feasibility of the system's overall motion and operation. As the final state of whole-body motion, the target configuration not only determines the pose of the end effector during the operation phase and whether it is in a singular or near-singular state, but also directly affects the cable tension distribution in that state. If the target configuration is not selected reasonably, even if there is a motion path that simultaneously satisfies geometric and mechanical constraints, the system may still be in the boundary region of the mechanically feasible domain or in an unfavorable working state after reaching the target configuration, making it difficult to support the stable execution of subsequent operational tasks.

[0005] Existing whole-body motion planning methods still have certain limitations when applied to rigid-flexible coupled rope-traction parallel robots. On the one hand, they typically lack systematic optimization of the system's target configuration, making it difficult to fully consider the impact of the target configuration on subsequent operational performance during the planning phase. On the other hand, while some high-dimensional space planning methods based on hierarchical thinking effectively reduce computational burden, they do not fully consider the mechanical effects introduced by the robotic arm as a load during the motion planning process of the mobile platform, which can easily lead to insufficient mechanical stability of the planned path. Therefore, under high-dimensional and multi-constraint conditions, how to reasonably select the target configuration and plan a safe and stable whole-body motion trajectory based on it has become a key problem that urgently needs to be solved for rigid-flexible coupled rope-traction parallel robots.

[0006] In view of this, the present invention is hereby proposed. Summary of the Invention

[0007] The purpose of this invention is to provide a motion planning method, device, and medium for a rigid-flexible coupled rope-traction parallel robot, which can realize whole-body motion planning for the rigid-flexible coupled rope-traction parallel robot, thereby improving the overall planning efficiency and path stability, and solving the above-mentioned problems existing in the prior art.

[0008] The objective of this invention is achieved through the following technical solution:

[0009] A motion planning method for a rigid-flexible coupled rope-driven parallel robot includes:

[0010] Step 1: Establish the kinematic and static models of the rigid-flexible coupled rope-driven parallel robot;

[0011] Step 2: Using the kinematic and static models from Step 1, construct performance indicators to evaluate the robot;

[0012] Step 3: Given the target pose of the robot's end effector, use the performance metrics from Step 2 to optimize the target configuration using the particle swarm optimization algorithm to obtain the optimal target configuration.

[0013] Step 4: Using the kinematic and static models from Step 1 and the performance indicators from Step 2, construct a low-dimensional proxy model based on the statistical characteristics of capacity margin that can establish a mapping relationship between the pose and mechanical stability of the mobile platform.

[0014] Step 5: Take the optimal target configuration from Step 3 as the target state for whole-body motion planning. Using the low-dimensional surrogate model from Step 4 and a stability-guided hierarchical planning algorithm, generate a mobile platform path that satisfies obstacle avoidance and mechanical stability in the mobile platform space, and generate a robotic arm joint path that matches the mobile platform path in the robotic arm joint space, thereby obtaining a collision-free and mechanically stable whole-body motion path.

[0015] Step 6: The whole-body motion path from Step 5 is parameterized and smoothed using the minimum impact trajectory optimization algorithm to generate the whole-body motion trajectory of the mobile platform and robotic arm that drive the rigid-flexible coupled rope-traction parallel robot to move in coordination.

[0016] A processing apparatus, comprising:

[0017] At least one memory for storing one or more programs;

[0018] At least one processor is capable of executing one or more programs stored in the memory, such that when the processor executes one or more programs, the processor can implement the method of the present invention.

[0019] A readable storage medium storing a computer program that, when executed by a processor, enables the implementation of the methods described in this invention.

[0020] Compared with existing technologies, the rigid-flexible coupling rope-driven parallel robot motion planning method, equipment, and medium provided by this invention have the following advantages:

[0021] By dividing the whole-body motion planning process into two stages—target configuration optimization and whole-body path generation—the performance requirements of the movement and manipulation stages can be addressed and balanced separately, thereby reducing interference caused by performance coupling in the overall framework. In the whole-body path generation stage, a hierarchical stability-guided path planning algorithm is employed. This algorithm decomposes the high-dimensional planning problem into a low-dimensional subspace for solution. During the search process, not only are rope mechanics feasibility constraints integrated to ensure path mechanics feasibility, but system mechanical stability indices are also introduced to guide the planning process. This reduces computational complexity while obtaining a mechanically stable planning path. Therefore, this invention can simultaneously ensure geometric obstacle avoidance safety and mechanical stability in complex environments, making it suitable for rigid-flexible coupled rope-traction parallel robots performing tasks such as handling, assembly, and movement. Attached Figure Description

[0022] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 A flowchart of a motion planning method for a rigid-flexible coupled rope-traction parallel robot provided for an embodiment of the present invention.

[0024] Figure 2A schematic diagram of the structure of a rigid-flexible coupled rope-traction parallel robot provided for an embodiment of the present invention.

[0025] Figure 3 A block diagram of a two-stage whole-body motion planning framework for a rigid-flexible coupled rope-traction parallel robot provided for an embodiment of the present invention. Detailed Implementation

[0026] The technical solutions of 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 a part of the embodiments of the present invention, and not all of them, and do not constitute a limitation on the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the protection scope of the present invention.

[0027] First, the following explanations are provided for the terms that may be used in this article:

[0028] The term "and / or" means that either or both can be achieved simultaneously. For example, X and / or Y means that it includes both "X" or "Y" as well as the three cases of "X and Y".

[0029] The terms "comprising," "including," "containing," "having," or other similar semantic descriptions should be interpreted as non-exclusive inclusion. For example, including a technical feature element (such as raw material, component, ingredient, carrier, dosage form, material, size, part, component, mechanism, device, step, process, method, reaction conditions, processing conditions, parameter, algorithm, signal, data, product or article of manufacture, etc.) should be interpreted as including not only the expressly listed technical feature element, but also other technical feature elements that are not expressly listed and are well-known in the art.

[0030] The term "composed of" excludes any technical features not expressly listed. When used in a claim, it closes the claim to exclude all technical features other than those expressly listed, except for associated conventional impurities. If the term appears only in a clause of a claim, it limits the claim to the elements expressly listed in that clause; elements recited in other clauses are not excluded from the overall claim.

[0031] Unless otherwise explicitly specified or limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to the internal connection between two components. Those skilled in the art can understand the specific meaning of the above terms in this document according to the specific circumstances.

[0032] The terms “center,” “longitudinal,” “lateral,” “length,” “width,” “thickness,” “up,” “down,” “front,” “back,” “left,” “right,” “vertical,” “horizontal,” “top,” “bottom,” “inner,” “outer,” “clockwise,” and “counterclockwise” indicate the current orientation or positional relationship, and are only for the convenience and simplification of description, and do not explicitly or implicitly suggest that the device or component referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this document.

[0033] The technical solution provided by this invention will be described in detail below. Contents not described in detail in the embodiments of this invention are prior art known to those skilled in the art. Where specific conditions are not specified in the embodiments of this invention, they shall be performed according to conventional conditions in the art or conditions recommended by the manufacturer. Reagents or instruments used in the embodiments of this invention whose manufacturers are not specified are all conventional products that can be purchased commercially.

[0034] like Figure 1 As shown, an embodiment of the present invention provides a motion planning method for a rigid-flexible coupled rope-driven parallel robot, comprising:

[0035] Step 1: Establish the kinematic and static models of the rigid-flexible coupled rope-driven parallel robot;

[0036] Step 2: Using the kinematic and static models from Step 1, construct performance indicators to evaluate the robot;

[0037] Step 3: Given the target pose of the robot's end effector, use the performance metrics from Step 2 to optimize the target configuration using the particle swarm optimization algorithm to obtain the optimal target configuration.

[0038] Step 4: Using the kinematic and static models from Step 1 and the performance indicators from Step 2, construct a low-dimensional proxy model based on the statistical characteristics of capacity margin that can establish a mapping relationship between the pose and mechanical stability of the mobile platform.

[0039] Step 5: Take the optimal target configuration from Step 3 as the target state for whole-body motion planning. Using the low-dimensional surrogate model from Step 4 and a stability-guided hierarchical planning algorithm, generate a mobile platform path that satisfies obstacle avoidance and mechanical stability in the mobile platform space, and generate a robotic arm joint path that matches the mobile platform path in the robotic arm joint space, thereby obtaining a collision-free and mechanically stable whole-body motion path.

[0040] Step 6: The whole-body motion path from Step 5 is parameterized and smoothed using the minimum impact trajectory optimization algorithm to generate a continuous and executable whole-body motion trajectory that drives the mobile platform and robotic arm of the rigid-flexible coupled rope-traction parallel robot to move in coordination.

[0041] See Figure 2 Preferably, in the above method, the rigid-flexible coupled rope-driven parallel robot includes: root rope driven Freedom of movement platform, installed below the movement platform by Composed of joints A robotic arm with degrees of freedom; among which,

[0042] One end of each rope is connected to the lead-out point on the drum of the fixed frame. The other end is connected to the connection point on the mobile platform. Number of ropes Greater than the freedom of mobile platforms ;

[0043] Each rope is connected to a drum that is connected to the power shaft of a motor, which can change the tension and release of the corresponding rope by the winch of each motor.

[0044] Preferably, in step 1 of the above method, the kinematic and static models of the rigid-flexible coupled rope-driven parallel robot are established in the following manner, including:

[0045] The kinematic model of the rigid-flexible coupled rope-traction parallel robot is constructed using four coordinate systems:

[0046] A global coordinate system fixed on the frame of a parallel robot pulled by a rigid-flexible coupling cable. The mobile platform coordinate system with its origin at the geometric center of the mobile platform. The coordinate system of the robotic arm base attached to the robotic arm base coordinate system with the end effector attached to the end of the robotic arm ;

[0047] pose of mobile platform Defined as: ;

[0048] in, This indicates the position of the mobile platform origin in the global coordinate system; Let XYZ be the Euler angles of the attitude, and its corresponding rotation matrix be... ; superscript Represents the transpose of a matrix; It represents the set of real numbers; 6 represents 6 degrees of freedom;

[0049] Joint vectors of the robotic arm Defined as , Indicates the number of joints in the robotic arm;

[0050] pose of the end effector of the robotic arm Defined as , Indicates the position of the end effector; The XYZ Euler angles represent the attitude of the end effector;

[0051] Generalized configuration of a rigid-flexible coupled rope-driven parallel robot writing ; Indicates the pose of the mobile platform. Indicates that there is Degrees of freedom Equal to the number of joints in the robotic arm;

[0052] In the geometric model of a rope, a point and points In the global coordinate system and the moving platform coordinate system, respectively, they are represented as follows: and Thus, the kinematic model was established, namely the first... Vector of the root rope Written as:

[0053] (1);

[0054] Given the pose of the mobile platform The rope length can be directly calculated. This corresponds to the inverse kinematics problem of a rigid-flexible coupled rope-traction parallel robot; while the forward kinematics problem of a rigid-flexible coupled rope-traction parallel robot requires solving the pose of the moving platform through numerical iteration under the condition of known rope length.

[0055] The robot arm's base coordinate system is fixedly connected to the mobile platform coordinate system. The robot arm's kinematics is modeled using the DH parameter method: forward kinematics is derived from the robot arm's joint vectors. Homogeneous transformation recursively calculates the pose of the robotic arm's end effector. Inverse kinematics, on the other hand, is based on analytical or numerical methods to solve the joint vectors corresponding to the pose of the end effector of the robotic arm.

[0056] Based on the constructed kinematic model, a static model of the rigid-flexible coupled rope-traction parallel robot is established. Since the static equilibrium of the rigid-flexible coupled rope-traction parallel robot is determined by both the rope tension and the generalized force applied to the moving platform, let the rope tension vector be... At the same time The unit direction vector of the root rope is used This indicates the static model of a parallel robot with rigid-flexible coupling and rope traction. for:

[0057] (2);

[0058] in, (·) represents the structural matrix of a rigid-flexible coupled rope-driven parallel robot; For generalized forces applied to the mobile platform, including the mobile platform's gravity. Generalized force generated by the end effector load and the generalized force generated by the robotic arm linkage ,Should for:

[0059] (3);

[0060] Each of these general forces Written as:

[0061] (4);

[0062] in, For the first The mass of a rigid body; For the first The rigid body relative to the coordinate system of the moving platform The centroid position vector; Represents the unit direction vector of the z-axis in the global coordinate system;

[0063] Given the generalized configuration of a rigid-flexible coupled rope-driven parallel robot Below, the rope tension is physically constrained. Physical constraints define the feasible set of rope tensions. And through the structure matrix Mapped into the generalized force space, forming a set of feasible generalized forces. for:

[0064] (5);

[0065] in, Represents the set of feasible generalized forces Elements in;

[0066] When the generalized force required by the task Belongs to set When a rigid-flexible coupled rope-traction parallel robot can maintain equilibrium in a static sense, the set of configurations that satisfy the static feasibility conditions is defined as the force feasible space of the rigid-flexible coupled rope-traction parallel robot.

[0067] Preferably, in the above method, the performance indicators constructed in step 2 include: an operability indicator reflecting the manipulator's operational capability, a capacity margin indicator reflecting the mechanical stability of the rigid-flexible coupled rope-traction parallel robot, and a collision distance indicator reflecting the geometric safety of the rigid-flexible coupled rope-traction parallel robot; wherein,

[0068] Operability index, reflecting the manipulator's operational capability Yoshikawa Index:

[0069] (6);

[0070] in, The Jacobian matrix of the robotic arm; superscript Represents the transpose of a matrix; (·) represents the determinant of a matrix;

[0071] Capacity margin index reflecting the mechanical stability of a rigid-flexible coupled rope-traction parallel robot Defined as:

[0072] (7);

[0073] in, and Denote the sets of feasible generalized forces respectively. The The boundary distance and the first One normal vector; (·) denotes the set of feasible generalized forces that can be traversed. All boundary constraint surfaces, and take the minimum value of the capacity margin corresponding to each constraint surface;

[0074] The mobile platform and rope of the rigid-flexible coupled rope-driven parallel robot are approximated as directed bounding boxes, and the robotic arm links are modeled as discrete collision spheres. These together form a box-sphere combination. The Gilbert-Johnson-Keerthi algorithm is used to calculate the collision detection and minimum distance between the box and the sphere. The Gilbert-Johnson-Keerthi algorithm utilizes support functions on two convex bodies... , Minkowski difference convex set Iterative search, Indicates origin from convex body set A point, Indicates origin from convex body set A point: if the origin is located at If the two convex bodies intersect, then the minimum distance from the origin to the convex set is the minimum distance between the two convex bodies. This is the collision distance index, which reflects the geometric safety of the rigid-flexible coupled rope-traction parallel robot. The collision distance index is defined as the minimum distance between the element z in the convex set and the origin. :

[0075] (8);

[0076] in, Describing the Minkowski difference convex set One of the vectors.

[0077] Preferably, in step 3 of the above method, the optimal target configuration is obtained by optimizing the target configuration using the performance indicators from step 2 and the particle swarm optimization algorithm, under the known target pose of the robot's end effector, in the following manner:

[0078] Based on the target pose of the end effector of the robotic arm The target pose of the mobile platform is obtained analytically using the following equation (9). Kinematic mapping function The input is the joint vector of the robotic arm. The output is the position of the moving platform in the global coordinate system. Rotation matrix with attitude Target pose of the mobile platform The mapping relationship is defined as follows:

[0079] (9);

[0080] in, Represents the joint vectors of the robotic arm. Represents the target joint vector of the robotic arm; Indicates the position of the moving platform in the global coordinate system; This represents the rotation matrix corresponding to the attitude of the mobile platform in the global coordinate system. This indicates the position of the end effector of the robotic arm in the global coordinate system; The rotation matrix represents the orientation of the end effector of the robotic arm in the global coordinate system. The rotation matrix represents the orientation of the end effector of the robotic arm in the coordinate system of the moving platform. This indicates the position of the end effector of the robotic arm in the coordinate system of the moving platform;

[0081] The objective function for the robot's target configuration is obtained by solving the target pose of the end effector of the given robotic arm using the particle swarm optimization algorithm. Constraints are then embedded into the objective function using a penalty term to obtain a constrained optimization problem. Finally, the constrained optimization problem is transformed into an unconstrained weighted multi-objective problem. for:

[0082] (10);

[0083] in, and These respectively measure the operability of the robotic arm and the capacity margin of the robot; Weighting parameters for measuring the operability of a robotic arm; The two weighting parameters are the robot's capacity margin. , The two performance metrics are normalized to a unified scale for value selection. Weighting parameters representing the number of collisions; The weight parameter represents the penalty for violating the minimum gap penalty; The weight parameters represent the penalties for exceeding the workspace; the above three penalty weight parameters , , All values ​​are maximized to make the corresponding soft constraints approximately equivalent to hard constraints in the optimization process, ensuring that the constraints are strictly satisfied. Indicates the penalty for the number of collisions; Minimum gap penalty, used to apply a penalty when the safe distance between critical geometries is below a threshold; This is a penalty used to describe a mobile platform's position or orientation that exceeds the feasible workspace; Let represent the target joint vector of the robotic arm; where, and The specific forms of the two penalty items are as follows:

[0084] (11);

[0085] In the above formula, and For the upper and lower bounds of the mobile platform pose; For the element-wise positive operator, penalties are only incurred when constraints are violated; Indicates the index of the key geometry detection pair; Indicates the first The minimum safe distance threshold for each detection pair; Indicates the first position under the current configuration The actual distance between each detection pair; This represents the upper bound of each dimension of the mobile platform pose; Represents the lower bound of each dimension of the mobile platform pose; ||·|| 2 The 2-norm squared of a vector is used to aggregate multi-dimensional out-of-bounds penalties into a scalar for optimizing the objective.

[0086] Preferably, in step 4 of the above method, based on the kinematic and static models of step 1 and the performance indicators of step 2, a low-dimensional proxy model that establishes a mapping relationship between the pose and mechanical stability of the mobile platform based on the statistical characteristics of capacity margin is constructed in the following manner:

[0087] During the offline phase, the robot's workspace is sampled. Mobile platform pose And sample the pose of each mobile platform. The joint angle of the robotic arm The capacity margin value is calculated by sampling the pose of the mobile platform and the corresponding joint angles of the robotic arm. The average capacity margin is obtained by robustly aggregating the capacity margin values ​​using the upper tail mean. Defined as:

[0088] (12);

[0089] in, This represents the upper tail mean function; (·) denotes the conditional expectation operator, which represents the mathematical expectation under given conditions; For quantile operators; The ratio of the upper and lower tails; Indicates the first A capacity margin sample set of all sampling points under the pose of a mobile platform;

[0090] A training dataset was constructed using the obtained poses and average capacity margins of each mobile platform. Multilayer perceptron is used based on the training dataset By fitting the mapping relationship between the mobile platform pose and the average capacity margin, a low-dimensional surrogate model based on the statistical characteristics of the capacity margin is obtained, which can establish the mapping relationship between the mobile platform pose and mechanical stability. for:

[0091] (13);

[0092] in, Indicates pose from mobile platform The mapping from the 6-dimensional real space to the 1-dimensional real space of the mechanical stability index; This represents a low-dimensional proxy model.

[0093] Preferably, in step 5 of the above method, the optimal target configuration of step 3 is used as the target state for whole-body motion planning. Using the low-dimensional surrogate model from step 4 and a stability-guided hierarchical planning algorithm, a path satisfying obstacle avoidance and mechanical stability is first generated in the mobile platform space, and then a matching path is generated in the robotic arm joint space to obtain a collision-free and mechanically stable whole-body motion path, including:

[0094] A stability-guided hierarchical planning algorithm is used to construct search trees sequentially at the robot's mobile platform layer and robotic arm layer to obtain the corresponding bit sequence. First, a dual expansion decision is applied at both the mobile platform layer and the robotic arm layer to sample and check candidate path segments during the expansion process, and then a path is selected from the candidate path segments. sampling points And ensure that each sampling point simultaneously satisfies the collision distance constraint. With capacity margin constraints ,Right now:

[0095] (14);

[0096] Among them, collision distance constraint To simultaneously calculate the collision distances between the mobile platform, ropes, robotic arm links, and external obstacles using the collision distance index in step 2; the capacity margin of the mobile platform layer is predicted by a low-dimensional proxy model, and the capacity margin of the robotic arm layer is directly calculated using the capacity margin function of the real static model;

[0097] If any sampling point does not meet the above constraints, the expansion will be considered infeasible and rejected.

[0098] Both the mobile platform layer and the robotic arm layer adopt a unified form of capacity margin weighted cost function. :

[0099] (15);

[0100] in, Represents the geometric distance of a path segment; An indicator representing the average capacity margin of a path segment;

[0101] The Stability-Guided Multilayer Bi-RRT* algorithm, a hierarchical planning algorithm with stability guidance, is employed at the robotic arm level, based on the already obtained mobile platform path. Afterwards, the root nodes of the two search trees of the robotic arm layer are bound to the start and end points of the mobile platform path, respectively. The search trees are organized into a multi-layer structure arranged along the mobile platform path, where the h-th layer corresponds to the h-th discrete pose in the mobile platform path. The two search trees are expanded alternately between adjacent layers in the forward or reverse direction, and the reconnection process is restricted to the adjacent layers.

[0102] The following heuristic mechanism is introduced into the layer selection step and failure count update step of the stability-guided hierarchical programming algorithm:

[0103] Step 5.1) Failure-aware dynamic difficulty estimation: A stability-guided hierarchical programming algorithm maintains the failure count for each layer. When a layer is not selected, its failure count will decrease according to a predetermined schedule; if the current expansion fails, the count will increase; if the expansion succeeds, it will remain unchanged. The update rule for the failure count is as follows:

[0104] (16);

[0105] in, Indicates the first The layer maintenance failure count is incremented by 1; This indicates taking the maximum value;

[0106] Step 5.2) Difficulty-Driven Initial Expansion: During the search process, when there are still layers without nodes, the stability-guided hierarchical programming algorithm enters the initial expansion phase. In this phase, the expanded layers are only selected from the set of layers with already generated nodes. Choose from the layers that can be selected. Its selection probability and failure count Reciprocal correlation:

[0107] (17);

[0108] in, For the first Layer expansion weights; For the first Layer selection probability; For the first The number of nodes contained in a layer; This is the set of layers for which nodes have already been generated; This refers to the set of layers that have already generated nodes. elements, It refers to the first layer;

[0109] Step 5.3) Sparseness-driven balanced expansion: Once all layers have nodes, the stability-guided hierarchical planning algorithm expands based on the number of nodes in each layer. The expansion probability is allocated according to the following sparsity method:

[0110] (18);

[0111] in, For the first Layer expansion weights; For the first Layer selection probability; For the first The number of nodes in the layer; N is the number of nodes in the mobile platform path; This refers to layers 2 to 3. The layer.

[0112] Preferably, the minimum impact trajectory optimization algorithm in step 6 of the above method includes:

[0113] First, the discrete sequence of whole-body motion paths obtained in step 5 is used to generate a continuous trajectory through 7th-order polynomial interpolation. Then, the minimum impact optimization method is used for continuous trajectories. After performing time parameterization and smoothing, the problem is solved separately for each degree of freedom, and the optimization problem takes the form of:

[0114] (19);

[0115] in, is the coefficient vector of the polynomial locus; The weight matrix is ​​a symmetric positive semidefinite weight matrix derived from minimizing the impact target; equality constraints. These are parameters used to ensure the continuity of the trajectory in the dimensions of position, velocity, and acceleration, where and Let these represent the coefficient matrix and vector respectively for equality constraints; inequality constraints. Used to satisfy dynamic constraints, where and Let represent the coefficient matrix and vector respectively, which are used to write the inequality constraints. Describes the coefficient vector of the polynomial locus Perform a minimal optimization.

[0116] This invention also provides a processing apparatus, comprising:

[0117] At least one memory for storing one or more programs;

[0118] At least one processor is capable of executing one or more programs stored in the memory, such that when the processor executes one or more programs, the processor can implement the method of the present invention.

[0119] The present invention further provides a readable storage medium storing a computer program that, when executed by a processor, can implement the method described in the present invention.

[0120] To more clearly demonstrate the technical solution and its effects provided by the present invention, the following detailed description of the solution provided by the embodiments of the present invention is provided with reference to specific examples.

[0121] Example 1

[0122] like Figure 1 As shown, this embodiment provides a motion planning method for a rigid-flexible coupled rope-traction parallel robot, which is a two-stage whole-body motion planning method for a rigid-flexible coupled rope-traction parallel robot, including:

[0123] Step 1: Establish the kinematic and static models of the rigid-flexible coupled rope-traction parallel robot to describe the geometric and mechanical relationships between the mobile platform, the robotic arm, and the rope.

[0124] Step 2: Based on the kinematic and static models established in Step 1, construct multiple performance indicators for evaluating the system's motion and operational performance. These performance indicators include: operability indicators reflecting the robotic arm's operational capabilities, capacity margin indicators reflecting the system's mechanical stability, and collision distance indicators reflecting the system's geometric safety.

[0125] Step 3: Given the target pose of the robot's end effector, use the performance metrics constructed in Step 2 and employ the particle swarm optimization algorithm to optimize the robot's target configuration, thereby obtaining the optimal target configuration that meets the collision-free requirement, has high operability, and possesses good mechanical stability.

[0126] Step 4: Based on the kinematic and static models established in Step 1 and the collision distance index established in Step 2, construct a low-dimensional proxy model based on the statistical characteristics of capacity margin, establish the mapping relationship between the pose and mechanical stability of the mobile platform, thereby replacing the performance evaluation that originally needed to be calculated in the high-dimensional configuration space.

[0127] Step 5: Take the optimal target configuration obtained in Step 3 as the target state for whole-body motion planning. Using the low-dimensional surrogate model obtained in Step 4 and a stability-guided hierarchical planning algorithm, first generate the mobile platform path, and then generate the robotic arm joint path that matches the mobile platform path, thereby obtaining a collision-free whole-body motion path with better mechanical stability.

[0128] Step 6: Based on the whole-body motion path generated in Step 5, the minimum impact trajectory optimization algorithm is used to perform time parameterization and smoothing on the whole-body motion path to obtain a continuous and executable whole-body motion trajectory, which is used to drive the mobile platform and the robotic arm of the rigid-flexible coupled rope traction parallel robot to complete the motion in coordination.

[0129] like Figure 2 As shown, the rigid-flexible coupled rope-traction parallel robot of this embodiment consists of... Root ropes (i.e., S1, S2, ..., S) i S m ) driven Freedom of movement platform M ( > (redundant drive) and the component installed under the mobile platform There are several joints (i.e., joint q1, joint q2, ..., joint q...). k Composed of The robotic arm Q has three degrees of freedom. The movement of the mobile platform is achieved through a cable-driven unit, with one end of the cable connected to a drum (C1, C2, ..., C...) on the fixed frame. i C m Lead-out points on (each roll) There are A1, A2, ..., A i A m One end is a lead-out point, and the other end is connected to a connection point on the mobile platform. There are a total of B1, B2, ..., B i B m There are several connection points. The tension and release of the rope are changed by the winch of the motor, and the number of ropes... Greater than the degrees of freedom of the moving platform This enables redundant drive of the rope-traction parallel robot, allowing tension distribution to be implemented while the moving platform is in motion.

[0130] Preferably, in step 1 of the above method, the kinematic and static models of the rigid-flexible coupled rope-driven parallel robot are established in the following manner, including:

[0131] like Figure 2 As shown, four coordinate systems were used in the kinematic analysis of the rigid-flexible coupled rope-driven parallel robot, including the global coordinate system. Fixed to the frame; moving platform coordinate system The origin is located at the geometric center of the mobile platform; the coordinate system of the robotic arm base. Attached to the base of the robotic arm; end effector coordinate system Attached to the end effector of the robotic arm. The pose of the mobile platform is defined as follows: ,in, This indicates the position of the mobile platform origin in the global coordinate system. Let XYZ be the Euler angles of the attitude, and its corresponding rotation matrix be... The joint vectors of the robotic arm are defined as follows: ,in, The pose of the end effector of the robotic arm, representing each joint, is defined as follows: Therefore, the generalized configuration of a rigid-flexible coupled rope-driven parallel robot can be written as... .

[0132] In the geometric model of a rope, a point and points In the coordinate system respectively and coordinate system The following is represented as and Thus, the kinematic model was established, namely the first... The vector of the root rope can be written as:

[0133] (1);

[0134] Given the pose of the mobile platform The rope length can be directly calculated. This corresponds to the inverse kinematics problem of a rigid-flexible coupled rope-traction parallel robot; while its forward kinematics requires solving the pose of the mobile platform through numerical iteration (such as the Levenberg–Marquardt algorithm) under the condition of known rope length.

[0135] Base coordinate system of the robotic arm With the mobile platform coordinate system For fixed connections, the kinematics of the robotic arm is modeled using the DH parameter method: forward kinematics is achieved through the joint vectors of the robotic arm. Homogeneous transformation recursively calculates the pose of the robotic arm's end effector. Inverse kinematics, on the other hand, is based on analytical or numerical methods to solve for the joint vectors corresponding to the pose of the end effector of the robotic arm.

[0136] Based on this, a static model of a rigid-flexible coupled rope-driven parallel robot can be further established. The static equilibrium of the rigid-flexible coupled rope-driven parallel robot is determined by the rope tension and the generalized force applied to the moving platform. Let... Let be the rope tension vector, and simultaneously use Indicates the first The unit direction vector of the rope. The static equilibrium equation of the rigid-flexible coupled rope-traction parallel robot is:

[0137] (2);

[0138] in, (·) represents the structural matrix of a rigid-flexible coupled rope-driven parallel robot; For generalized forces applied to the mobile platform, including the mobile platform's gravity. Generalized force generated by the end effector load and the generalized force generated by the robotic arm linkage It can be written as:

[0139] (3);

[0140] Each generalized force can be written as:

[0141] (4);

[0142] in, For the first The mass of a rigid body For the first The rigid body relative to the coordinate system of the moving platform The centroid position vector.

[0143] Given the generalized configuration of a rigid-flexible coupled rope-driven parallel robot Below, the rope tension is physically constrained. These constraints define the feasible set of rope tensions. And through the structure matrix Mapped into the generalized force space, this forms a feasible set of generalized forces for a rigid-flexible coupled rope-driven parallel robot. :

[0144] (4);

[0145] When the generalized force required by the task Belongs to set When a rigid-flexible coupled rope-driven parallel robot is in static equilibrium, the set of configurations that satisfy the static feasibility conditions is defined as the force feasible space of the rigid-flexible coupled rope-driven parallel robot.

[0146] Based on the kinematic and static models established in step 1, a variety of performance indicators are constructed to evaluate the motion and operation performance of the rigid-flexible coupled rope-traction parallel robot. These indicators are: the operability indicator, which reflects the manipulator's operational capability; the capacity margin indicator, which reflects the mechanical stability of the rigid-flexible coupled rope-traction parallel robot; and the collision distance indicator, which reflects the geometric safety of the rigid-flexible coupled rope-traction parallel robot.

[0147] First, to reflect the maneuverability of a robotic arm, a maneuverability index is introduced. Maneuverability reflects the robotic arm's ability to apply force and move its end effector within a given positioning configuration, and is an important indicator for evaluating the kinematic performance of rigid-flexible coupled rope-driven parallel robots. Commonly used maneuverability... The Yoshikawa exponent is defined as follows:

[0148] (6);

[0149] in, The Jacobian matrix of the robotic arm, with superscript... To represent the transpose of a matrix, (·) represents the determinant of the matrix. The larger the operability value, the stronger the robotic arm's motion capability in the current configuration, and the more balanced the end effector's speed and force output capability in multiple directions.

[0150] Then, to measure the mechanical stability of a rigid-flexible coupled rope-traction parallel robot, a capacity margin index is introduced. The capacity margin index measures the ability of a rope-traction parallel robot to resist external loads and maintain force balance under a given positioning posture; it is an important indicator reflecting the robot system's load-bearing capacity and disturbance resistance performance. This is based on a defined set of feasible generalized forces. The capacity margin index can be expressed as the task generalized force. The minimum distance to the boundary of this set can be calculated using the hyperplane method. For a machine composed of... Driven by a rope, possessing For a rigid-flexible coupled rope-driven parallel robot with one degree of freedom, the arbitrary - The generalized force tension generated by a rope -1-dimensional hyperplane, while the remaining - The additional rope determines the boundary of the feasible generalized force set in the normal direction of the hyperplane. Therefore, considering the overall static model of the rigid-flexible coupled rope-traction parallel robot system, the capacity margin index of this rigid-flexible coupled rope-traction parallel robot is... It can be defined as:

[0151] (7);

[0152] in, and Denote the sets of feasible generalized forces respectively. The The boundary distance and the first One normal vector; (·) denotes the set of feasible generalized forces that can be traversed. All boundary constraint surfaces are calculated, and the minimum capacity margin corresponding to each constraint surface is taken. By calculating the capacity margin index under a given rigid-flexible coupled rope-traction parallel robot configuration, it is possible to quickly determine whether the configuration is statically feasible and obtain the safety margin in force space.

[0153] Finally, a collision distance metric is introduced to measure the geometric safety of a rigid-flexible coupled rope-driven parallel robot. In the motion planning of a rigid-flexible coupled rope-driven parallel robot, the geometric constraints between the robot and its environment, as well as between the robot's internal components, directly determine the feasibility of the motion. To ensure modeling accuracy while controlling computational overhead, this invention employs a hybrid convex body modeling strategy: the moving platform and ropes are approximated as directed bounding boxes (OBBs), while the robotic arm links are modeled as discrete collision spheres. This "box-sphere" combination covers the main collision risks and significantly improves the efficiency of collision detection and distance calculation. Collision detection and minimum distance calculation are based on the Gilbert-Johnson-Keerthi (GJK) algorithm. GJK uses support functions on two convex bodies... , Minkowski difference convex set Iterative search, Indicates origin from convex body set A point, Indicates origin from convex body set A point: if the origin is located at If the two convex bodies intersect, then the minimum distance from the origin to the convex set is the minimum distance between the two convex bodies. This is the collision distance index, which reflects the geometric safety of the rigid-flexible coupled rope-traction parallel robot. The collision distance index is defined as the minimum distance between the element z in the convex set and the origin. It can be defined as:

[0154] (8);

[0155] in, Describing the Minkowski difference convex set One of the vectors.

[0156] Based on this, and addressing two major issues in the planning of rigid-flexible coupled rope-driven parallel robot systems—namely, the excessive computational complexity caused by the high-dimensional state space and the difference in performance requirements between the operation and movement phases—this invention proposes a two-stage motion planning framework. For example... Figure 3 As shown, in the initial stage of the task, the robot obtains information about the object to be manipulated and obstacles in the environment through components such as cameras as perception modules, and obtains the target pose that the end effector of the robotic arm needs to achieve. In the first stage (target configuration optimization), the particle swarm optimization algorithm is used to jointly optimize the target pose of the mobile platform. With the target joint vector of the robotic arm The algorithm explicitly considers collision constraints, force feasibility constraints, and various performance indicators to obtain a collision-free target configuration for the robot with high capacity margin and strong maneuverability. In the subsequent second stage (whole-body motion generation), this target configuration is used as the planning objective. The stability-guided hierarchical path planning algorithm proposed in this invention is used to perform path planning sequentially at the mobile platform layer and the robotic arm layer, generating a configuration sequence that satisfies collision-free and high stability requirements. Subsequently, the Minimum-snap method was used to further obtain high-quality trajectories with time parameterization. Ultimately, the full-body trajectory planned by this framework will serve as control input, driving the robot's mobile platform and robotic arm to collaboratively complete the task. These two stages will be further described below.

[0157] Preferably, in step 3 of the above method, the first stage of the two-stage motion planning framework is based on the target pose of the end effector of the robotic arm. Solve for the optimal target configuration of the robot. To reduce the dimensionality of the problem, this invention first performs variable dimensionality reduction on the optimization problem: due to the target pose of the mobile platform With the target joint vector of the robotic arm There are defined kinematic constraints between them, given the target pose of the end effector of the robotic arm. The target pose of the mobile platform can be obtained analytically using the following formula. :

[0158] (9);

[0159] This configuration optimization problem is characterized by strong non-convexity and multiple constraint couplings. It includes geometric constraints such as collisions and workspace constraints, as well as comprehensive trade-offs between multiple performance indicators. Traditional gradient-based methods often easily get trapped in local optima and struggle to handle non-analytic constraints in such high-dimensional and complex environments. Therefore, this invention employs the particle swarm optimization (PSO) algorithm. PSO does not rely on gradient information, possesses good global exploration capabilities, and is suitable for non-convex, multi-objective, and complex constraint-laden optimization problems. Considering that PSO cannot directly handle hard constraints, this invention uses a penalty term to embed the constraints into the objective function, transforming the constrained optimization problem into an unconstrained weighted multi-objective form.

[0160] (10);

[0161] in, and These measures the operability of the robotic arm and the capacity margin of the system, respectively, and their relative importance is controlled by weighting parameters. Weighting parameters for measuring the operability of a robotic arm; The two weighting parameters are the robot's capacity margin. , The two performance metrics are normalized to a unified scale for value selection. Weighting parameters representing the number of collisions; The weight parameter represents the penalty for violating the minimum gap penalty; The weight parameters represent the penalties for exceeding the workspace; the above three penalty weight parameters , , All values ​​are maximized to make the corresponding soft constraints approximately equivalent to hard constraints in the optimization process, ensuring that the constraints are strictly satisfied. Indicates the penalty for the number of collisions; Minimum gap penalty, used to apply a penalty when the safe distance between critical geometries is below a threshold; The penalties used to describe the position or orientation of the mobile platform exceeding the feasible workspace are as follows:

[0162] (11);

[0163] In the above formula, and For the upper and lower bounds of the mobile platform pose; For the element-wise positive operator, penalties are only incurred when constraints are violated; Indicates the index of the key geometry detection pair; Indicates the first The minimum safe distance threshold for each detection pair; Indicates the first position under the current configuration The actual distance between each detection pair; This represents the upper bound of each dimension of the mobile platform pose; Represents the lower bound of each dimension of the mobile platform pose; ||·|| 2 The 2-norm squared of a vector is used to aggregate multi-dimensional out-of-bounds penalties into a scalar for optimizing the objective.

[0164] The second stage of the two-stage motion planning framework is whole-body motion planning, which includes three parts: step 4, establishing a low-dimensional surrogate model; step 5, stability-guided hierarchical path planning; and step 6, a minimum impact trajectory optimization algorithm.

[0165] Preferably, in step 4, to reduce the planning complexity caused by the high-dimensional coupled state space of the rigid-flexible coupled rope-traction parallel robot system, this invention constructs a low-dimensional proxy model of the capacity margin statistical index through MLP fitting mapping, thereby reducing the capacity margin index, which originally depended on twelve-dimensional state variables, from a high-dimensional coupled state space to a low-dimensional coupled state space. Approximately transforms into a low-dimensional proxy model that depends only on the mobile platform pose. This significantly reduces the computational overhead in the subsequent path planning stage. During the offline stage, the robot's workspace is sampled. Mobile platform pose And sample the pose of each mobile platform. The joint angle of the robotic arm Calculate the corresponding capacity margin value. To obtain statistics reflecting the pose stability of the mobile platform, this invention uses the Upper Tail Mean (UTM) for robust aggregation of capacity margin, defined as:

[0166] (12);

[0167] in, This represents the upper tail mean function; (·) denotes the conditional expectation operator, which represents the mathematical expectation under given conditions; For quantile operators; The ratio of the upper and lower tails; Indicates the first The capacity margin sample set of all sampling points under a given mobile platform pose; this statistic characterizes the average capacity margin of the better-performing portion of the robot configuration at a given CDPR pose. This forms the basis for constructing the training dataset. Furthermore, a low-dimensional surrogate model for capacity margin is obtained by fitting the mapping relationship between the mobile platform pose and the UTM index using a multilayer perceptron (MLP). ,for:

[0168] (13);

[0169] in, Indicates pose from mobile platform The mapping from the 6-dimensional real space to the 1-dimensional real space of the mechanical stability index; This represents a low-dimensional proxy model.

[0170] This low-dimensional proxy model places the mechanical information of the robotic arm at the mobile platform layer, and quickly predicts the stability index corresponding to the pose of the mobile platform during the path planning process at the mobile platform layer. This guides the mobile platform into a region with better mechanical performance, thereby effectively reducing the risk of the rigid-flexible coupled rope-traction parallel robot system planning getting stuck in local optima and significantly improving online computing efficiency.

[0171] Preferably, in step 5 of the above method, the low-dimensional proxy model with capacity margin is obtained in step 4. Subsequently, this invention proposes a stability-guided hierarchical planning algorithm (i.e., the Hierarchical Stability-Guided Bi-RRT* algorithm), which constructs search trees sequentially at the mobile platform layer and the robotic arm layer. This algorithm comprises three core mechanisms: an extended decision mechanism that considers both geometric and mechanical feasibility, a cost evaluation mechanism based on capacity margin and surrogate models, and a robotic arm layer search mechanism that integrates heuristic strategies. These mechanisms together constitute a hierarchical path planning algorithm that simultaneously possesses obstacle avoidance capabilities and mechanical stability guidance.

[0172] First, to ensure the geometric and static feasibility of the extended path segment, the stability-guided hierarchical planning algorithm of this invention employs dual extension judgment at both the mobile platform layer and the robotic arm layer, sampling and checking candidate path segments during the extension process, and selecting from the candidate path segments. sampling points And ensure that each sampling point simultaneously satisfies the collision distance constraint. With capacity margin constraints ,Right now:

[0173] (14);

[0174] The capacity margin index of the mobile platform layer is rapidly predicted using a low-dimensional surrogate model, while the capacity margin of the robotic arm layer is directly calculated using the capacity margin function of the real static model; collision distance constraints... To calculate the collision distance between the mobile platform, ropes, robotic arm links, and external obstacles simultaneously using the collision distance index in step 2;

[0175] If any sampling point does not meet the above constraints, the expansion will be considered infeasible and rejected.

[0176] This dual feasibility check based on path segment sampling can effectively filter out invalid extensions and avoid the search entering the collision zone or the tension infeasibility zone, thereby improving the overall search efficiency.

[0177] Secondly, to achieve stability-guided hierarchical planning, both the mobile platform layer and the robotic arm layer adopt a unified form of capacity margin weighted cost function. :

[0178] (15);

[0179] in, Represents the geometric distance of a path segment. This is the average capacity margin metric for path segments. For the mobile platform layer, this average capacity margin metric is determined by a low-dimensional proxy model. The prediction shows that, for the robotic arm layer, this average capacity margin index is determined by the system capacity margin function. This cost function form causes the expansion to naturally favor regions with high capacity margins.

[0180] Furthermore, at the robotic arm level, this invention proposes the Stability-Guided Multilayer Bi-RRT* algorithm, a component of the stability-guided hierarchical planning algorithm. This Stability-Guided Multilayer Bi-RRT* algorithm is used when the mobile platform path has already been obtained. Subsequently, the root nodes of the two search trees in the robotic arm layer are bound to the start and end points of the mobile platform path, respectively. The search trees are organized into a multi-layered structure along the mobile platform path, where the h-th layer corresponds to the h-th discrete pose in the mobile platform path. The two search trees are expanded alternately between adjacent layers in either a forward or reverse direction, and the reconnection process is restricted to between adjacent layers, thus giving the search trees a multi-layered structure along the mobile platform path. Compared to the traditional Bi-RRT*, this algorithm has two main differences: first, it introduces an inter-layer expansion mechanism, allowing node growth only to occur between adjacent layers in either a forward or reverse direction; second, it adopts an inter-layer reconnection strategy, restricting the reconnection process to occur only between adjacent layers. To improve search efficiency in non-uniform feasible regions, this invention introduces three heuristic mechanisms in the layer selection step and failure count update step of the algorithm, as follows:

[0181] Step 5.1) Failure-aware dynamic difficulty estimation: To reflect the expansion difficulty of each layer, the algorithm maintains a failure count for each layer. When a layer is not selected, its failure count will decrease moderately to avoid bias caused by long-term deposition; if the current expansion fails, the count will increase; if the expansion succeeds, it will remain unchanged. The update rules are as follows:

[0182] (16);

[0183] in, Indicates the first The layer maintenance failure count is incremented by 1; This indicates taking the maximum value.

[0184] Step 5.2) Accelerated initialization with priority given to empty layers: If there is a set of empty layers that have not yet generated nodes... When this happens, expansion is prioritized from empty layers, and for selectable empty layers... Its selection probability and failure count Reciprocal correlation:

[0185] (17);

[0186] in, For the first Layer expansion weights; For the first Layer selection probability; For the first The number of nodes contained in a layer; This is the set of layers for which nodes have already been generated; This refers to the set of layers that have already generated nodes. elements, It refers to the first layer.

[0187] Step 5.3) Sparseness-driven balanced expansion: Once all layers have nodes, the stability-guided hierarchical planning algorithm expands based on the number of nodes in each layer. The expansion probability is allocated according to the following sparsity method:

[0188] (18);

[0189] in, For the first Layer expansion weights; For the first Layer selection probability; For the first The number of nodes in the layer; N is the number of nodes in the mobile platform path; This refers to layers 2 to 3. The layer.

[0190] The empty-layer-first approach combined with a failure-counting strategy accelerates the initialization of the tree structure, enabling the search tree to converge to a feasible solution more quickly. Meanwhile, the sparsity-driven balanced expansion strategy effectively avoids local congestion in the later stages, improving search coverage and the performance metrics of the final path. The synergistic effect of these two strategies allows the robotic arm layer to generate higher-quality configuration sequences under strict constraints.

[0191] Preferably, in step 6 of the above method, the whole-body motion path is obtained in step 5. Subsequently, the present invention first performs 7th-order polynomial interpolation to generate a continuous trajectory. Furthermore, the Minimum-snap method is employed to smooth the trajectory and parameterize the time parameters, thereby improving the continuity, executability, and dynamic performance of the robot's motion. Solving for each degree of freedom separately, the optimization problem can be formalized as:

[0192] (19);

[0193] in, Let be the coefficient vector of the polynomial trajectory. Equality constraints ensure the continuity of the trajectory in dimensions such as position, velocity, and acceleration, while inequality constraints are used to satisfy dynamic constraint conditions. Describes the coefficient vector of the polynomial locus Perform a minimal optimization.

[0194] In summary, the two-stage whole-body motion planning method of this invention establishes kinematic and static models of a rigid-flexible coupled rope-traction parallel robot, and constructs performance indicators based on system kinematics and mechanical constraints. This allows for phased solutions to target configuration optimization and whole-body path generation in high-dimensional, multi-constraint planning problems. In the target configuration optimization stage, collision constraints, rope mechanical feasibility constraints, and performance indicators are used, and a particle swarm optimization algorithm is employed to solve for the system target configuration with high operability and mechanical stability. In the whole-body path generation stage, a stability-guided hierarchical path planning algorithm is used. First, a path satisfying obstacle avoidance and mechanical stability requirements is generated in the mobile platform space. Then, a matching joint path is generated in the robotic arm joint space. Finally, a continuous and executable whole-body trajectory is obtained through a minimum impact trajectory optimization algorithm. This two-stage planning framework of the invention can balance obstacle avoidance safety and mechanical stability in complex environments, achieving safe and efficient whole-body motion planning for rigid-flexible coupled rope-traction parallel robots.

[0195] Compared with the prior art, the present invention has at least the following beneficial effects:

[0196] (1) By dividing the whole-body motion planning into two stages, target configuration optimization and whole-body path generation, the performance requirements of the operation stage and the movement stage are optimized in a targeted manner, thereby avoiding mutual interference between the two in the same solution process, achieving synergistic consideration of movement and operation performance, and improving the overall reliability and execution quality of the planning results.

[0197] (2) By explicitly introducing operability index, capacity margin index and collision distance index in the target configuration optimization stage, the comprehensive performance optimization of the target configuration is achieved, making the final target configuration more superior in terms of operability and mechanical stability, and enhancing the stability of the system operation stage.

[0198] (3) By adopting the hierarchical stability-guided path planning algorithm, the high-dimensional planning problem is decomposed into a low-dimensional subspace for solution. The rope mechanics feasibility and stability index are integrated in the planning process, realizing the unity of dimensionality reduction solution and stability guidance, avoiding the path from falling into the boundary region of the mechanically feasible domain, thereby improving the mechanical reliability of the overall planning.

[0199] (4) By using the minimum impact trajectory optimization algorithm to generate a continuous executable trajectory, the planned whole-body configuration sequence can be executed smoothly in the actual robot system, improving the smoothness and controllability of the final trajectory. It is suitable for tasks with high requirements for motion continuity and safety, such as handling and assembly.

[0200] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM), etc.

[0201] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims. The information disclosed in the background section is intended only to enhance the understanding of the overall background technology of the present invention and should not be construed as an admission or implication in any way that such information constitutes prior art known to those skilled in the art.

Claims

1. A motion planning method for a rigid-flexible coupled rope-driven parallel robot, characterized in that, include: Step 1: Establish the kinematic and static models of the rigid-flexible coupled rope-driven parallel robot; Step 2: Using the kinematic and static models from Step 1, construct performance indicators to evaluate the robot; Step 3: Given the target pose of the end effector of the robot arm, use the performance indicators from Step 2 to optimize the target configuration using the particle swarm optimization algorithm to obtain the optimal target configuration. Step 4: Using the kinematic and static models from Step 1 and the performance indicators from Step 2, construct a low-dimensional proxy model based on the statistical characteristics of capacity margin that can establish a mapping relationship between the pose and mechanical stability of the mobile platform. Step 5: Take the optimal target configuration from Step 3 as the target state for whole-body motion planning. Using the low-dimensional surrogate model from Step 4 and a stability-guided hierarchical planning algorithm, generate a mobile platform path that satisfies obstacle avoidance and mechanical stability in the mobile platform space, and generate a robotic arm joint path that matches the mobile platform path in the robotic arm joint space, thereby obtaining a collision-free and mechanically stable whole-body motion path. Step 6: The whole-body motion path from Step 5 is parameterized and smoothed using the minimum impact trajectory optimization algorithm to generate the whole-body motion trajectory of the mobile platform and robotic arm that drive the rigid-flexible coupled rope-traction parallel robot to move in coordination.

2. The motion planning method for a rigid-flexible coupled rope-driven parallel robot according to claim 1, characterized in that, The rigid-flexible coupled rope-traction parallel robot includes: root rope driven Freedom of movement platform, installed below the movement platform by Composed of a number of joints A robotic arm with degrees of freedom; wherein one end of each rope is connected to an extension point on a drum of a fixed frame. The other end is connected to the connection point on the mobile platform. Number of ropes Greater than the freedom of mobile platforms Each rope is connected to a drum that is connected to the power shaft of a motor. The tension and release of the corresponding rope can be changed by the winch connected to the power shaft of each motor.

3. The motion planning method for a rigid-flexible coupled rope-driven parallel robot according to claim 1 or 2, characterized in that, In step 1, the kinematic and static models of the rigid-flexible coupled rope-driven parallel robot are established as follows: The kinematic model of the rigid-flexible coupled rope-traction parallel robot is constructed using four coordinate systems: A global coordinate system fixed on the frame of a parallel robot pulled by a rigid-flexible coupling cable. The mobile platform coordinate system with its origin at the geometric center of the mobile platform. The coordinate system of the robotic arm base attached to the robotic arm base coordinate system with the end effector attached to the end of the robotic arm ; pose of mobile platform Defined as: ; in, This indicates the position of the mobile platform origin in the global coordinate system; Let XYZ be the Euler angles of the orientation, and its corresponding rotation matrix be... ; superscript Represents the transpose of a matrix; It represents the set of real numbers; 6 represents 6 degrees of freedom; Joint vectors of the robotic arm Defined as , Indicates the number of joints in the robotic arm; pose of the end effector of the robotic arm Defined as , Indicates the position of the end effector; The XYZ Euler angles represent the attitude of the end effector; Generalized configuration of a rigid-flexible coupled rope-driven parallel robot writing ; Indicates the pose of the mobile platform. Indicates that there is Degrees of freedom Equal to the number of joints in the robotic arm; In the geometric model of a rope, a point and points In the global coordinate system and the moving platform coordinate system, respectively, they are represented as follows: and Thus, the kinematic model was established, namely the first... Vector of the root rope Written as: (1)； Given the pose of the mobile platform The rope length can be directly calculated. This corresponds to the inverse kinematics problem of a rigid-flexible coupled rope-traction parallel robot; while the forward kinematics problem of a rigid-flexible coupled rope-traction parallel robot requires solving the pose of the moving platform through numerical iteration under the condition of known rope length. The robot arm's base coordinate system is fixedly connected to the mobile platform coordinate system. The robot arm's kinematics is modeled using the DH parameter method: forward kinematics is derived from the robot arm's joint vectors. Homogeneous transformation recursively calculates the pose of the robotic arm's end effector. Inverse kinematics, on the other hand, is based on analytical or numerical methods to solve the joint vectors corresponding to the pose of the end effector of the robotic arm. Based on the constructed kinematic model, a static model of the rigid-flexible coupled rope-traction parallel robot is established. Since the static equilibrium of the rigid-flexible coupled rope-traction parallel robot is determined by both the rope tension and the generalized force applied to the moving platform, let the rope tension vector be... At the same time The unit direction vector of the rope is used This indicates the static model of a parallel robot with rigid-flexible coupling and rope traction. for: (2)； in, (·) represents the structural matrix of a rigid-flexible coupled rope-driven parallel robot; Generalized forces applied to the mobile platform, including the platform's gravity. Generalized force generated by the end effector load and the generalized force generated by the robotic arm linkage ,Should for: (3)； Each of these general forces Written as: (4)； in, For the first The mass of a rigid body; For the first The rigid body relative to the coordinate system of the moving platform The centroid position vector; Represents the unit direction vector of the z-axis in the global coordinate system; Given the generalized configuration of a rigid-flexible coupled rope-driven parallel robot Below, the rope tension is physically constrained. Physical constraints define the feasible set of rope tensions. And through the structure matrix Mapped into the generalized force space, forming a set of feasible generalized forces. for: (5)； in, Represents the set of feasible generalized forces Elements in; When the generalized force required by the task Belongs to set When a rigid-flexible coupled rope-traction parallel robot can maintain equilibrium in a static sense, the set of configurations that satisfy the static feasibility conditions is defined as the force feasible space of the rigid-flexible coupled rope-traction parallel robot.

4. The motion planning method for a rigid-flexible coupled rope-driven parallel robot according to claim 3, characterized in that, The performance indicators constructed in step 2 include: an operability indicator reflecting the manipulator's operational capability; a capacity margin indicator reflecting the mechanical stability of the rigid-flexible coupled rope-traction parallel robot; and a collision distance indicator reflecting the geometric safety of the rigid-flexible coupled rope-traction parallel robot; among which, Operability index, reflecting the manipulator's operational capability Yoshikawa Index: (6)； in, The Jacobian matrix of the robotic arm; superscript Represents the transpose of a matrix; (·) represents the determinant of a matrix; Capacity margin index reflecting the mechanical stability of a rigid-flexible coupled rope-traction parallel robot Defined as: (7)； in, and Denote the sets of feasible generalized forces respectively. The The boundary distance and the first One normal vector; (·) denotes the set of feasible generalized forces that can be traversed. All boundary constraint surfaces, and take the minimum value of the capacity margin corresponding to each constraint surface; The mobile platform and rope of the rigid-flexible coupled rope-driven parallel robot are approximated as directed bounding boxes, and the robotic arm links are modeled as discrete collision spheres. These together form a box-sphere combination. The Gilbert-Johnson-Keerthi algorithm is used to calculate the collision detection and minimum distance between the box and the sphere. The Gilbert-Johnson-Keerthi algorithm utilizes support functions on two convex bodies... , Minkowski difference convex set Iterative search, Indicates origin from convex body set A point, Indicates origin from convex body set A point: if the origin is located at If the two convex bodies intersect, then the minimum distance from the origin to the convex set is the minimum distance between the two convex bodies. This is the collision distance index, which reflects the geometric safety of the rigid-flexible coupled rope-traction parallel robot. The collision distance index is defined as the minimum distance between the element z in the convex set and the origin. : (8)； in, Describing the Minkowski difference convex set One of the vectors.

5. The motion planning method for a rigid-flexible coupled rope-driven parallel robot according to claim 4, characterized in that, In step 3, under the known target pose of the robot's end effector, the optimal target configuration is obtained by using the performance metrics from step 2 and solving the target configuration optimization problem via particle swarm optimization, including: Based on the target pose of the end effector of the robotic arm The target pose of the mobile platform is obtained analytically using the following equation (9). Kinematic mapping function The input is the joint vector of the robotic arm. The output is the position of the moving platform in the global coordinate system. Rotation matrix with attitude Target pose of the mobile platform The mapping relationship is defined as follows: (9)； in, Represents the joint vectors of the robotic arm. Represents the target joint vector of the robotic arm; Indicates the position of the moving platform in the global coordinate system; This represents the rotation matrix corresponding to the attitude of the mobile platform in the global coordinate system. This indicates the position of the end effector of the robotic arm in the global coordinate system; The rotation matrix represents the orientation of the end effector of the robotic arm in the global coordinate system. The rotation matrix represents the orientation of the end effector of the robotic arm in the coordinate system of the moving platform. This indicates the position of the end effector of the robotic arm in the coordinate system of the moving platform; The objective function for the robot's target configuration is obtained by solving the target pose of the end effector of the given robotic arm using the particle swarm optimization algorithm. Constraints are then embedded into the objective function using a penalty term to obtain a constrained optimization problem. Finally, the constrained optimization problem is transformed into an unconstrained weighted multi-objective problem. for: (10)； in, and These respectively measure the operability of the robotic arm and the capacity margin of the robot; Weighting parameters for measuring the operability of a robotic arm; The two weighting parameters are the robot's capacity margin. , The two performance metrics are normalized to a unified scale for value selection. Weighting parameters representing the number of collisions; The weight parameter represents the penalty for violating the minimum gap penalty; The weight parameters represent the penalties for exceeding the workspace; the above three penalty weight parameters , , All values ​​are maximized to make the corresponding soft constraints approximately equivalent to hard constraints in the optimization process, ensuring that the constraints are strictly satisfied. Indicates the penalty for the number of collisions; Minimum gap penalty, used to apply a penalty when the safe distance between critical geometries is below a threshold; This is a penalty used to describe a mobile platform's position or orientation that exceeds the feasible workspace; Let represent the target joint vector of the robotic arm; where, and The specific forms of the two penalty items are as follows: (11)； In the above formula, and For the upper and lower bounds of the mobile platform pose; For the element-wise positive operator, penalties are only incurred when constraints are violated; Indicates the index of the key geometry detection pair; Indicates the first The minimum safe distance threshold for each detection pair; Indicates the first position under the current configuration The actual distance between each detection pair; This represents the upper bound of each dimension of the mobile platform pose; Represents the lower bound of each dimension of the mobile platform pose; ||·|| 2 The 2-norm squared of a vector is used to aggregate multi-dimensional out-of-bounds penalties into a scalar for optimizing the objective.

6. The motion planning method for a rigid-flexible coupled rope-driven parallel robot according to claim 5, characterized in that, In step 4, using the kinematic and static models from step 1 and the performance indicators from step 2, a low-dimensional proxy model based on capacity margin statistical characteristics is constructed to establish a mapping relationship between the pose and mechanical stability of the mobile platform, including: During the offline phase, the robot's workspace is sampled. Mobile platform pose And sample the pose of each mobile platform. The joint angle of the robotic arm The capacity margin value is calculated by sampling the pose of the mobile platform and the corresponding joint angles of the robotic arm. The average capacity margin is obtained by robustly aggregating the capacity margin values ​​using the upper tail mean. Defined as: (12)； in, This represents the upper tail mean function; (·) denotes the conditional expectation operator, which represents the mathematical expectation under given conditions; For quantile operators; The ratio of the upper and lower tails; Indicates the first A capacity margin sample set of all sampling points under the pose of a mobile platform; A training dataset was constructed using the obtained poses and average capacity margins of each mobile platform. Multilayer perceptron is used based on the training dataset By fitting the mapping relationship between the mobile platform pose and the average capacity margin, a low-dimensional surrogate model based on the statistical characteristics of the capacity margin is obtained, which can establish the mapping relationship between the mobile platform pose and mechanical stability. for: (13)； in, Indicates pose from mobile platform The mapping from the 6-dimensional real space to the 1-dimensional real space of the mechanical stability index; This represents a low-dimensional proxy model.

7. The motion planning method for a rigid-flexible coupled rope-driven parallel robot according to claim 6, characterized in that, In step 5, the optimal target configuration from step 3 is used as the target state for whole-body motion planning. Using the low-dimensional surrogate model from step 4 and a stability-guided hierarchical planning algorithm, a mobile platform path satisfying obstacle avoidance and mechanical stability is generated in the mobile platform space. A robotic arm joint path matching the mobile platform path is generated in the robotic arm joint space, resulting in a collision-free and mechanically stable whole-body motion path, including: A stability-guided hierarchical planning algorithm is used to construct search trees sequentially at the robot's mobile platform layer and robotic arm layer to obtain the corresponding bit sequence. First, a dual expansion decision is applied at both the mobile platform layer and the robotic arm layer to sample and check candidate path segments during the expansion process, and then a path is selected from the candidate path segments. sampling points And ensure that each sampling point simultaneously satisfies the collision distance constraint. With capacity margin constraints ,Right now: (14)； Among them, collision distance constraint The collision distance index in step 2 is used to simultaneously calculate the collision distance between the mobile platform, rope, robotic arm link, and external obstacle; the capacity margin of the mobile platform layer is predicted by a low-dimensional proxy model, and the capacity margin of the robotic arm layer is directly calculated by the capacity margin function of the real static model. If any sampling point cannot simultaneously satisfy the above collision distance constraint and capacity margin constraint, then this expansion will be considered infeasible and rejected. Both the mobile platform layer and the robotic arm layer adopt a unified form of capacity margin weighted cost function. : (15)； in, Represents the geometric distance of the candidate path segment; This refers to the average capacity margin of candidate path segments. The Stability-Guided Multilayer Bi-RRT* algorithm, a hierarchical planning algorithm with stability guidance, is employed at the robotic arm level, based on the already obtained mobile platform path. Afterwards, the root nodes of the two search trees of the robotic arm layer are bound to the start and end points of the mobile platform path, respectively. The search trees are organized into a multi-layer structure arranged along the mobile platform path, where the h-th layer corresponds to the h-th discrete pose in the mobile platform path. The two search trees are expanded alternately between adjacent layers in the forward or reverse direction, and the reconnection process is restricted to the adjacent layers. The following heuristic mechanism is introduced into the layer selection step and failure count update step of the stability-guided hierarchical programming algorithm: Step 5.1) Failure-aware dynamic difficulty estimation: A stability-guided hierarchical programming algorithm maintains the failure count for each layer. When a layer is not selected, its failure count will decrease according to a predetermined schedule; if the current expansion fails, the count will increase; if the expansion succeeds, it will remain unchanged. The update rule for the failure count is as follows: (16)； in, Indicates the first The layer maintenance failure count is incremented by 1; This indicates taking the maximum value; Step 5.2) Difficulty-Driven Initial Expansion: During the search process, when there are still layers without nodes, the stability-guided hierarchical programming algorithm enters the initial expansion phase. In this phase, the expanded layers are only selected from the set of layers with already generated nodes. Choose from the layers that can be selected. Its selection probability and failure count Reciprocal correlation: (17)； in, For the first Layer expansion weights; For the first Layer selection probability; For the first The number of nodes contained in a layer; This is the set of layers for which nodes have already been generated; This refers to the set of layers that have already generated nodes. elements, It refers to the first layer; Step 5.3) Sparseness-driven balanced expansion: Once all layers have nodes, the stability-guided hierarchical planning algorithm expands based on the number of nodes in each layer. The expansion probability is allocated according to the following sparsity method: (18)； in, For the first Layer expansion weights; For the first Layer selection probability; For the first The number of nodes in the layer; N is the number of nodes in the mobile platform path; This refers to layers 2 to 3. The layer.

8. The motion planning method for a rigid-flexible coupled rope-driven parallel robot according to claim 7, characterized in that, The minimum impact trajectory optimization algorithm in step 6 includes: First, the discrete sequence of whole-body motion paths obtained in step 5 is used to generate a continuous trajectory through 7th-order polynomial interpolation. Then, the minimum impact optimization method is used for continuous trajectories. After performing time parameterization and smoothing, the problem is solved separately for each degree of freedom, and the optimization problem takes the form of: (19)； in, is the coefficient vector of the polynomial locus; The weight matrix is ​​a symmetric positive semidefinite weight matrix derived from minimizing the impact target; equality constraints. These are parameters used to ensure the continuity of the trajectory in the dimensions of position, velocity, and acceleration, where and Let these represent the coefficient matrix and vector respectively for equality constraints; inequality constraints. Used to satisfy dynamic constraints, where and Let represent the coefficient matrix and vector respectively, which are used to write the inequality constraints. Describes the coefficient vector of the polynomial locus Perform a minimal optimization.

9. A processing device, characterized in that, include: At least one memory for storing one or more programs; At least one processor is capable of executing one or more programs stored in the memory, such that when the one or more programs are executed by the processor, the processor can perform the method according to any one of claims 1-8.

10. A readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it can implement the method described in any one of claims 1-8.

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