Mechanical arm optimal motion control method and system based on jerk constraint

Abstract

The invention discloses a mechanical arm optimal motion control method and system based on jerk constraint, belongs to the technical field of robot kinematics, and solves the problems that an existing method depends on piecewise polynomial interpolation or a simplified dynamical model, time is consumed, and global optimality is difficult to consider. The method comprises the steps that modeling is conducted on the overall dynamic process of the mechanical arm, a continuous time domain path is converted into a parameter domain discrete path point, a linear programming parameter domain solution of a general linear programming model is determined, a jerk constraint programming model constrained by a nonlinear objective function is constructed, and a final convex optimization programming parameter domain solution is solved. Converting the parameter domain track into a time domain track; according to the method, on the premise of strictly meeting the dynamics and kinematics constraints of the robot, the jerk is introduced into the convex optimization framework as an independent optimization variable, so that the time for generating the trajectory is shortened, the trajectory has high-order smoothness, and the impact and residual vibration in the motion process are effectively inhibited.

Description

Technical Field

[0001] This invention belongs to the field of robot kinematics technology, specifically relating to a method and system for optimal motion control of a robotic arm based on jerk constraints. Background Technology

[0002] Time-optimal trajectory planning, a key technology in robotic arm control, has profoundly impacted modern intelligent manufacturing. With improved dynamic modeling capabilities and the widespread adoption of real-time computing hardware, its trajectory generation capabilities in highly dynamic and multi-obstacle environments have continuously strengthened, becoming a core engine driving efficient and precise robotic arm operations. In various application scenarios such as welding, assembly, logistics, and healthcare, time-optimal planning is revolutionizing the traditional teach-and-reproduce model, shortening cycle times, optimizing energy consumption, and even surpassing the experience limits of human engineers under certain extreme conditions, bringing a paradigm shift to the development of flexible manufacturing and high-end equipment.

[0003] In the motion of a six-DOF articulated robotic arm, due to issues such as singularities, gimbal lock-up, and arm span limitations, generating a fast and stable trajectory in the complex joint space is crucial. Unsmooth motion not only reduces positioning accuracy but can also damage actuators due to excessive acceleration and jerk. Traditional methods often rely on piecewise polynomial interpolation or simplified dynamic models, which are not only time-consuming but also struggle to achieve global optimality and handle the real-time requirements of high-dimensional coupling constraints. The surge in constraint dimensions and nonlinear coupling makes simultaneously achieving time optimality, dynamic feasibility, and smoothness a challenge. The robotic arm motion control method based on jerk constraints discretizes the infinite-dimensional optimal control problem into solvable linear programming subproblems, increasing the solution speed by more than an order of magnitude. It also explicitly incorporates jerk constraints into the linear framework, enabling millisecond-level online reprogramming. This is of great significance for preventing mechanical wear, extending equipment life, and ensuring the safety of high-speed, high-precision operations. To address the problems that existing methods rely on piecewise polynomial interpolation or simplified dynamic models, which are not only time-consuming and difficult to achieve global optimality, but also struggle to meet the real-time requirements of high-dimensional coupled constraints, we propose an optimal motion control method and system for robotic arms based on jerk constraints. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies by providing a method and system for optimal motion control of robotic arms based on jerk constraints. This solves the problems of existing methods relying on piecewise polynomial interpolation or simplified dynamic models, which are not only time-consuming but also difficult to achieve global optimality and even more difficult to meet the real-time requirements of high-dimensional coupled constraints.

[0005] This invention is implemented as follows: an optimal motion control method for a robotic arm based on jerk constraints, wherein the optimal motion control method for a robotic arm based on jerk constraints includes:

[0006] Based on the structural characteristic parameters of the six-degree-of-freedom articulated robotic arm, the overall dynamic process of the robotic arm is modeled to obtain the dynamic model of the robotic arm.

[0007] Obtain the motion path of the robotic arm, decompose the motion path of the robotic arm, and transform the continuous time domain path into discrete path points in the parameter domain controlled by a finite-dimensional parameter set.

[0008] Load the discrete path points in the parameter domain controlled by the finite-dimensional parameter set and the dynamic model of the robotic arm. Using the discrete path points in the parameter domain controlled by the finite-dimensional parameter set as constraints, unify the dynamic model of the robotic arm and the kinematic model of the robotic arm based on the motion state domain data of the robotic arm joints, and output the unified motion state domain data of the robotic arm.

[0009] Based on discrete path point constraints, a general linear programming model is constructed with the objective of minimizing motion time, and the linear programming parameter domain solution of the general linear programming model is determined.

[0010] Based on the motion state domain data of the robotic arm and the solution of the linear programming parameter domain, an acceleration constraint programming model with nonlinear objective function constraints is constructed, and the final convex optimization programming parameter domain solution is obtained.

[0011] Based on the parameter domain solution of convex optimization programming, the parameter domain trajectory is generated, and the parameter domain trajectory is converted into the time domain trajectory to generate the optimal time trajectory for the robotic arm.

[0012] Preferably, the method for modeling the overall dynamics of the robotic arm includes:

[0013] The structural feature parameters of the six-degree-of-freedom articulated manipulator are traversed, and the inertial vector matrix, Coriolis and centrifugal force vector matrix, gravity vector matrix and Coulomb friction force matrix are constructed based on the structural feature parameters of the six-degree-of-freedom articulated manipulator.

[0014] Load the inertia vector matrix, Coriolis and centrifugal force vector matrix, gravity vector matrix and Coulomb friction force matrix, and construct the overall joint torque motion equation of the robotic arm based on the inertia vector matrix, Coriolis and centrifugal force vector matrix, gravity vector matrix and Coulomb friction force matrix;

[0015] The equation of motion for the overall joint torque of the robotic arm is expressed as follows:

[0016]

[0017] in, Joint torque is used to directly represent the motion state of the robotic arm. , and These are the angles, velocities, and accelerations of the robotic arm joints. For the robotic arm joint angle to be at The inertial vector matrix at time, For the robotic arm to be in Joint angles and The Coriolis and centrifugal force vector matrices at the velocity of motion, When the robotic arm is in The gravity vector matrix at joint angles. For the robotic arm to be in Coulomb friction matrix at joint angles For symbolic functions, when input Returns 1 if greater than 0, 0 if equal to 0, and -1 if less than 0.

[0018] Preferably, the method for converting a continuous time-domain path into a discrete path point controlled by a finite-dimensional parameter set includes:

[0019] Based on the dynamic model of the robotic arm, the joint torque, velocity, acceleration, and jerk are identified. Combined with the task requirements, the initial motion path is generated by using the joint torque, velocity, acceleration, and jerk as constraints through fifth-order polynomial interpolation.

[0020] Load the initial motion path, consider the constraints of joint torque, velocity, acceleration, and jerk, optimize the initial motion path, and output the optimal time domain path;

[0021] Substitute the optimal time-domain path into the robot arm dynamics model to verify whether the optimal time-domain path satisfies the overall joint torque motion equation of the robot arm. If the optimal time-domain path satisfies the overall joint torque motion equation of the robot arm, the optimal time-domain path is taken as the final continuous time-domain path.

[0022] Obtaining continuous time domain paths , continuous time domain path If the path is evenly divided into n segments, at least one set of discrete path points is obtained, forming parameter domain discrete path points controlled by a finite-dimensional parameter set.

[0023] Preferably, the method for optimizing the initial motion path includes:

[0024] Obtain the constraint conditions associated with the initial motion path, such as joint torque, velocity, acceleration, and jerk. Generate a set of constraints for the robotic arm based on the joint torque, velocity, acceleration, and jerk, and identify the initial point and end point of the initial motion path.

[0025] A three-dimensional trajectory model is constructed by combining the initial point, the end point, and the initial motion path. The three-dimensional trajectory model is divided into model meshes. The relationship between the initial motion path and the model meshes is established based on the coordinate information of the initial motion path in the three-dimensional trajectory model. A path mesh set representing the relationship between the initial motion path and the model meshes is generated.

[0026] Traverse the path grid set, using the path grid set as prior information, perform path obstacle avoidance search on the path from the initial point to the end point, and generate at least one set of optimized obstacle avoidance paths;

[0027] When performing obstacle avoidance search on the path from the initial point to the destination, the search formula is expressed as:

[0028]

[0029] in, Indicates in The probability that the robotic arm's constraint member set finds the model's mesh at any given time. They are respectively in Time-based model gridding The amount of constraint information, the expected value of grid transition, and the grid obstacle avoidance factor. This represents the total number of paths from the initial point to the destination. These are respectively the path heuristic coefficient, the expected heuristic coefficient, and the obstacle coefficient;

[0030] The optimization obstacle avoidance path is iterated, and the motion path time from the initial point to the end point is calculated. The optimization obstacle avoidance path corresponding to the shortest path time is selected as the optimal time domain path.

[0031] Preferably, the method for constructing a three-dimensional trajectory model by combining the initial point, the end point, and the initial motion path includes:

[0032] The geometric information of the initial motion path, the pose representation of the initial motion path, and the associated constraints are obtained. The joint angles are converted into Cartesian coordinates of the end effector through the kinematic model of the robotic arm. The initial three-dimensional trajectory in the world coordinate system is constructed based on the Cartesian coordinates of the end effector.

[0033] The spatial boundary of the initial 3D trajectory is determined by the geometric information and pose representation of the initial motion path, and the initial 3D trajectory after defining the spatial boundary is optimized by combining the associated constraint conditions to obtain the 3D trajectory model.

[0034] The spatial extent of the 3D trajectory model is divided into adaptive cubic model meshes. Mesh identifiers are assigned to the model meshes, and the association between the initial motion path and the model meshes is established based on the coordinate information of the initial motion path in the 3D trajectory model.

[0035] Preferably, the method for unifying the robotic arm dynamics model and the robotic arm kinematics model based on the motion state domain data of the robotic arm joints includes:

[0036] Identify the parameter domains of the robot arm joints' angles, velocities, and accelerations in the motion state domain data. The parameter domains of the robot arm joints' angles, velocities, and accelerations are represented as follows:

[0037]

[0038] in , and A parameterized representation of the angles, velocities, and accelerations of the robotic arm joints. Path parameters The first, second, and third derivatives, These are the first, second, and third derivatives of the path parameters with respect to time, representing velocity, acceleration, and jerk, respectively.

[0039] The parameter domain representation of the overall joint torque motion equation of the robotic arm is constructed based on the parameter domains of the angle, velocity, and acceleration of the robotic arm joints;

[0040] The parameter domain of the overall joint torque motion equation of the robotic arm is expressed as follows:

[0041]

[0042] in, for The set of representations of (parameterization of the angles, velocities, and accelerations of robotic arm joints), specifically explained as follows:

[0043]

[0044] In the formula , , and These are the parameterized representations of the robotic arm's inertia vector matrix, Coriolis and centrifugal force vector matrices, Coulomb friction force matrix, and gravity vector matrix, respectively.

[0045] By substituting the discrete path point constraints into the overall joint torque motion equation of the robotic arm, the dynamic model and kinematic model of the robotic arm are unified. Specifically, substituting the discrete path point constraints into the overall joint torque motion equation of the robotic arm yields the following:

[0046]

[0047] in .

[0048] Preferably, the method for determining the linear programming parameter domain solution of a general linear programming model includes:

[0049] Obtain unified robotic arm motion state domain data, identify the path planning time in the continuous time domain corresponding to the unified robotic arm motion state domain data, and decompose the path planning time variable in the continuous time domain by differentiation.

[0050] Specifically, by differentially decomposing the time variables of path planning in the continuous time domain, we can obtain:

[0051]

[0052] Under the discrete-domain timeline, the differential decomposition results of the path planning time variables are further constrained, and these results are further expressed as the following differential decomposition constraints:

[0053]

[0054] In the formula Divide the path into evenly distributed segments;

[0055] To obtain the differential decomposition constraints, with the premise that the minimum motion time is equivalent to the maximum velocity at the sampling points, the differential decomposition constraints are transformed into:

[0056]

[0057] Obtain the results of discrete path point constraints and differential decomposition constraints, and construct a general linear programming model with the objective of minimizing motion time. The equivalent solution equations of the general linear programming model are:

[0058]

[0059] in For the number of discretized path segments, and They are respectively and The maximum value is obtained by the following formula:

[0060]

[0061] By using a general linear solver, the linear programming parameter domain solution of the equal-quantity solution equation of a general linear programming model is determined.

[0062] Preferably, the method for solving the final convex optimization programming parameter domain solution includes:

[0063] Load discrete path point constraints, and approximate linear and nonlinear objective functions based on the relationship between discrete path points and time:

[0064]

[0065] in The number of discretized path segments is a variable;

[0066] Based on discrete path point constraints, jerk constraints are defined, where the inequalities under jerk constraints are expressed as:

[0067]

[0068] in , and The constraints between the total path and the segment distance are expressed as follows:

[0069]

[0070] Combining discrete path points, the jerk constraints for the initial and final points of the robotic arm's motion are defined as follows:

[0071]

[0072] Obtain the linear programming parameter domain solution of the general linear programming model, and simultaneously solve the inequalities under the jerk constraint, the jerk constraint of the robot arm's initial and final points, to obtain the optimal convex optimization programming constraint equation under the jerk constraint.

[0073]

[0074] in This is the solution in the parameter domain of a general linear programming model. It is the weighting coefficient, which ranges from [0, 1].

[0075] On the other hand, the present invention also provides an optimal motion control system for a robotic arm based on jerk constraints, the optimal motion control system for a robotic arm based on jerk constraints comprising:

[0076] The system input module is used to collect robot dynamics and kinematics models, path parameterization models, and constraint sets, and to load the collected robot dynamics and kinematics models, path parameterization models, and constraint sets.

[0077] The dynamics modeling module is used to model the overall dynamics of the robotic arm based on the structural characteristic parameters of the six-degree-of-freedom joint robotic arm, and obtain the dynamics model of the robotic arm.

[0078] The path discretization module is used to obtain the motion path of the robotic arm, decompose the motion path of the robotic arm, and transform the continuous time domain path into parameter domain discrete path points controlled by a finite-dimensional parameter set.

[0079] The model integration module is used to load the discrete path points in the parameter domain controlled by the finite-dimensional parameter set and the dynamic model of the robotic arm. With the discrete path points in the parameter domain controlled by the finite-dimensional parameter set as constraints, the dynamic model of the robotic arm and the kinematic model of the robotic arm are unified based on the motion state domain data of the robotic arm joints, and the unified motion state domain data of the robotic arm is output.

[0080] The linear programming module, based on discrete path point constraints, constructs a general linear programming model with the objective of minimizing motion time and determines the linear programming parameter domain solution of the general linear programming model.

[0081] The convex optimization planning module is used to construct an acceleration constraint planning model with nonlinear objective function constraints based on the motion state domain data of the robotic arm and the solution of the linear programming parameter domain, and solve the final convex optimization planning parameter domain solution.

[0082] The trajectory conversion module generates a parameter domain trajectory based on the parameter domain solution of convex optimization programming, converts the parameter domain trajectory into a time domain trajectory, and generates the optimal time trajectory for the robotic arm.

[0083] Preferably, the path discretization module includes:

[0084] The initial path generation unit identifies joint torque, velocity, acceleration, and jerk based on the robotic arm dynamics model. Combining task requirements, it generates the initial motion path using fifth-order polynomial interpolation, with joint torque, velocity, acceleration, and jerk as constraints.

[0085] The path optimization unit is used to load the initial motion path, consider the constraints of joint torque, velocity, acceleration, and jerk, optimize the initial motion path, and output the optimal time domain path.

[0086] The continuous time domain unit is used to substitute the optimal time domain path into the robot arm dynamics model to verify whether the optimal time domain path satisfies the overall joint torque motion equation of the robot arm. If the optimal time domain path satisfies the overall joint torque motion equation of the robot arm, the optimal time domain path is used as the final continuous time domain path.

[0087] The parameter-domain discrete path point generation unit is used to obtain the continuous-time domain path. , continuous time domain path If the path is evenly divided into n segments, at least one set of discrete path points is obtained, forming parameter domain discrete path points controlled by a finite-dimensional parameter set.

[0088] Compared with the prior art, the embodiments of this application have the following main advantages:

[0089] In this embodiment of the invention, the proposed optimal motion control method for a robotic arm based on jerk constraints satisfies the real-time requirements of high-dimensional coupling constraints while strictly meeting the constraints of robot dynamics and kinematics. Furthermore, by introducing jerk as an independent optimization variable into the convex optimization framework, the generated trajectory not only shortens the time but also exhibits high-order smoothness, effectively suppressing impacts and residual vibrations during the motion process.

[0090] In this embodiment of the invention, when transforming a continuous time-domain path into discrete path points in the parameter domain controlled by a finite-dimensional parameter set, an initial motion path is generated using a fifth-order polynomial interpolation method and optimized by combining multi-dimensional constraints such as joint torque, velocity, acceleration, and jerk. This ensures that the generated optimal time-domain path meets both task requirements and the overall joint torque motion equation of the robotic arm's dynamics model, thereby guaranteeing the physical feasibility and motion stability of the path. Furthermore, the continuous time-domain path is uniformly discretized into discrete path points in the parameter domain controlled by a finite-dimensional parameter set. This not only achieves a precise parameterized expression of complex motion trajectories but also provides an efficient and computable discrete optimization foundation for subsequent time-optimal trajectory planning based on linear programming and convex optimization. This significantly improves the trajectory generation efficiency and control accuracy of the robotic arm in highly dynamic and multi-obstacle environments, effectively suppresses impacts and residual vibrations during motion, and ensures the safety and reliability of the robotic arm's high-speed and high-precision operations.

[0091] In this embodiment of the invention, when optimizing the initial motion path, the constraints such as joint torque, velocity, acceleration, and jerk of the initial motion path are systematically obtained. A set of constraint members for the robotic arm is constructed, and the initial and final points of the path are clearly defined. Then, based on this key information, a three-dimensional trajectory model is constructed and discretized into model meshes. The association between the initial motion path and the meshes is accurately established to generate a path mesh set. Subsequently, using the path mesh set as prior information, obstacle avoidance path search from the initial point to the final point is carried out efficiently, generating multiple sets of optimized obstacle avoidance paths. Finally, by iteratively optimizing these paths and accurately calculating the motion duration of each path, the optimized obstacle avoidance path corresponding to the shortest path duration is selected as the optimal time domain path. This not only effectively ensures the physical feasibility and safety of the robotic arm's motion path under complex constraints and significantly reduces the risk of collisions between the path and obstacles, but also minimizes the motion time through accurate duration calculation and optimization selection, greatly improving the efficiency and accuracy of the robotic arm's operation. This provides solid and reliable technical support for the efficient, safe, and precise motion control of the robotic arm in dynamic and complex environments.

[0092] In this embodiment of the invention, when determining the linear programming parameter domain solution of a general linear programming model, a linear programming model with the objective of minimizing motion time is constructed, enabling the problem to be solved using mature linear programming theory. Furthermore, the linear programming parameter domain solution is directly obtained through a general linear solver, which not only significantly reduces computational complexity but also ensures the real-time performance and reliability of the solution results. Through rigorous mathematical derivation and reasonable simplification, this method achieves faster generation of time-optimal motion trajectories while strictly satisfying the dynamic constraints of the robotic arm.

[0093] In this embodiment of the invention, when solving the final convex optimization programming parameter domain solution, firstly, the time relationship of discrete path points is approximated with the objective function (linear and nonlinear), accurately characterizing the key characteristics of the motion trajectory while ensuring computational efficiency. Secondly, jerk constraints are defined hierarchically for the entire trajectory (discrete path points) and boundaries (initial / endpoint), suppressing the risk of impact and vibration during joint movement and ensuring a smooth transition during start-stop phases. Finally, by integrating the previous linear programming parameter domain solution with multi-level jerk constraint inequalities, a convex optimization model that balances time optimality and motion smoothness is constructed. Its strict convexity ensures the uniqueness of the global optimal solution, while the direct applicability of the linear solver significantly improves real-time computational efficiency. This method, under the premise of strictly satisfying dynamic constraints, achieves multi-objective collaboration with the shortest trajectory time, minimal impact, and optimal smoothness, effectively extending the service life of the robotic arm and improving operational reliability under complex working conditions. Attached Figure Description

[0094] Figure 1 This is a schematic diagram of the implementation process of the optimal motion control method S for a robotic arm based on jerk constraints provided by the present invention.

[0095] Figure 2 A schematic diagram of the implementation process of the initial motion path optimization method is shown.

[0096] Figure 3 A schematic diagram illustrating the implementation process of a general linear programming model construction method with the goal of minimizing motion time is shown.

[0097] Figure 4 A schematic diagram illustrating the implementation process of constructing a jerk constraint planning model with nonlinear objective function constraints is shown.

[0098] Figure 5 A schematic diagram of the optimal motion control system for a robotic arm based on jerk constraints is shown.

[0099] Figure 6 This illustration shows a schematic diagram of the workflow of the system input module loading the dynamics and kinematics model, path parameterization model, and constraint set of the acquisition robot in an embodiment of the present invention. Detailed Implementation

[0100] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs; the terminology used herein in the specification of the application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application; the terms "comprising" and "having," and any variations thereof, in the specification, claims, and foregoing drawings of this application are intended to cover non-exclusive inclusion. The terms "first," "second," etc., in the specification, claims, or foregoing drawings of this application are used to distinguish different objects, not to describe a particular order.

[0101] Existing methods rely on piecewise polynomial interpolation or simplified dynamic models, which are not only time-consuming but also difficult to achieve global optimality and handle the real-time requirements of high-dimensional coupling constraints. We propose a method and system for optimal motion control of a robotic arm based on jerk constraints. In short, the method first models the overall dynamic process of the robotic arm, decomposes the motion path of the robotic arm, and transforms the continuous time domain path into discrete path points in the parameter domain controlled by a finite-dimensional parameter set. Based on the motion state domain data of the robotic arm joints, the dynamic model and kinematic model of the robotic arm are unified. A general linear programming model with the goal of minimizing motion time is constructed, the linear programming parameter domain solution of the general linear programming model is determined, a jerk constraint programming model with nonlinear objective function constraints is constructed, the final convex optimization programming parameter domain solution is solved, the parameter domain trajectory is transformed into a time domain trajectory, and the time-optimal trajectory of the robotic arm is generated. In this embodiment of the invention, the proposed optimal motion control method for a robotic arm based on jerk constraints satisfies the real-time requirements of high-dimensional coupling constraints while strictly meeting the constraints of robot dynamics and kinematics. Furthermore, by introducing jerk as an independent optimization variable into the convex optimization framework, the generated trajectory not only shortens the time but also exhibits high-order smoothness, effectively suppressing impacts and residual vibrations during the motion process.

[0102] This invention provides an optimal motion control method for a robotic arm based on jerk constraints. Figure 1 A schematic diagram illustrating the implementation process of an optimal motion control method for a robotic arm based on jerk constraints is shown. Specifically, this optimal motion control method for a robotic arm based on jerk constraints includes:

[0103] S10. Based on the structural characteristic parameters of the six-degree-of-freedom joint manipulator, the overall dynamic process of the manipulator is modeled to obtain the dynamic model of the manipulator. The manipulator can be a six-degree-of-freedom joint manipulator.

[0104] S20: Obtain the motion path of the robotic arm, decompose the motion path of the robotic arm, and transform the continuous time domain path into discrete path points in the parameter domain controlled by a finite-dimensional parameter set.

[0105] S30, load the discrete path points in the parameter domain controlled by the finite-dimensional parameter set and the dynamic model of the robotic arm, use the discrete path points in the parameter domain controlled by the finite-dimensional parameter set as constraints, unify the dynamic model of the robotic arm and the kinematic model of the robotic arm based on the motion state domain data of the robotic arm joints, and output the unified motion state domain data of the robotic arm.

[0106] S40, Based on discrete path point constraints, construct a general linear programming model with the objective of minimizing motion time, and determine the linear programming parameter domain solution of the general linear programming model;

[0107] S50: Based on the motion state domain data of the robotic arm and the solution of the linear programming parameter domain, construct an acceleration constraint programming model with nonlinear objective function constraints, and solve the final convex optimization programming parameter domain solution.

[0108] S60 generates a parameter domain trajectory based on the parameter domain solution of convex optimization programming, converts the parameter domain trajectory into a time domain trajectory, and generates the optimal time trajectory for the robotic arm.

[0109] In this embodiment, when the optimal motion control method for the robotic arm based on jerk constraints is implemented, such as... Figure 1 As shown, the system is first initialized, and then the system parameters (structural characteristic parameters of the six-DOF articulated robotic arm) are input. During the input process, the system checks whether the input is complete. If the input is not complete, the system parameters are inputted again; if the input is complete, the path is discretized (that is, the continuous time domain path is converted into a parameter domain discrete path point controlled by a finite-dimensional parameter set).

[0110] After path discretization is completed, the system checks whether discretization is finished. If discretization is not finished, path discretization continues; if discretization is finished, model parameter unification processing is performed (i.e., unifying the robot arm dynamics model with the robot arm kinematics model based on the motion state domain data of the robot arm joints). During processing, the system checks whether processing is finished. If processing is not finished, model parameter unification processing continues; if processing is finished, the system proceeds to the next step.

[0111] Next, the system constructs a linear programming model (i.e., a general linear programming model with the objective of minimizing motion time) and calls the linear programming solver to solve it. If the solution fails, the model and constraints need to be reset, the linear programming model is reconstructed, and the solver is called again. If the solution succeeds, an acceleration-constrained programming model is constructed (i.e., an acceleration-constrained programming model with nonlinear objective function constraints), and the linear programming solver is called again to solve it.

[0112] During the solution process, if the solution fails, the model and constraints need to be reset, the jerk-constrained programming model needs to be rebuilt, and the solver needs to be called again. If the solution is successful, a smoothing verification is performed. If the verification fails, parameter tuning and fine-tuning of sampling are required, the jerk-constrained programming model needs to be rebuilt, and the solver needs to be called again. If the verification is successful, proceed to the next step.

[0113] Finally, during time-domain interpolation, the system transforms the discrete velocity distribution into a continuous trajectory. The trajectory is then issued and executed via the robot controller. During execution, the system records operational data for future optimization.

[0114] In this embodiment of the invention, the proposed optimal motion control method for a robotic arm based on jerk constraints satisfies the real-time requirements of high-dimensional coupling constraints while strictly meeting the constraints of robot dynamics and kinematics. Furthermore, by introducing jerk as an independent optimization variable into the convex optimization framework, the generated trajectory not only shortens the time but also exhibits high-order smoothness, effectively suppressing impacts and residual vibrations during the motion process.

[0115] This invention provides a method for modeling the overall dynamics of a robotic arm, which specifically includes:

[0116] S101, traverse the structural feature parameters of the six-degree-of-freedom articulated manipulator, and construct the inertial vector matrix M, Coriolis and centrifugal force vector matrix C, gravity vector matrix G and Coulomb friction force matrix F based on the structural feature parameters of the six-degree-of-freedom articulated manipulator;

[0117] S102, load the inertia vector matrix, Coriolis and centrifugal force vector matrix, gravity vector matrix and Coulomb friction force matrix, and construct the overall joint torque motion equation of the robotic arm based on the inertia vector matrix, Coriolis and centrifugal force vector matrix, gravity vector matrix and Coulomb friction force matrix;

[0118] The equation of motion for the overall joint torque of the robotic arm is expressed as follows:

[0119]

[0120] in, Joint torque is used to directly represent the motion state of the robotic arm. , and These are the angles, velocities, and accelerations of the robotic arm joints. For the robotic arm joint angle to be at The inertial vector matrix at time, For the robotic arm to be in Joint angles and The Coriolis and centrifugal force vector matrices at the velocity of motion, When the robotic arm is in The gravity vector matrix at joint angles. For the robotic arm to be in Coulomb friction matrix at joint angles For symbolic functions, when input Returns 1 if greater than 0, 0 if equal to 0, and -1 if less than 0.

[0121] This invention provides a method for converting continuous-time-domain paths into discrete path points in the parameter domain controlled by a finite-dimensional parameter set. Specifically, this method includes:

[0122] S201 identifies joint torque, velocity, acceleration, and jerk based on the robotic arm dynamics model. Combining task requirements, it generates the initial motion path using fifth-order polynomial interpolation, with joint torque, velocity, acceleration, and jerk as constraints.

[0123] S202, load the initial motion path, consider the constraints of joint torque, velocity, acceleration, and jerk, optimize the initial motion path, and output the optimal time domain path;

[0124] S203, Substitute the optimal time domain path into the robot arm dynamics model to verify whether the optimal time domain path satisfies the overall joint torque motion equation of the robot arm. If the optimal time domain path satisfies the overall joint torque motion equation of the robot arm, the optimal time domain path is used as the final continuous time domain path.

[0125] S204, Obtain the continuous time domain path , continuous time domain path If the path is evenly divided into n segments, at least one set of discrete path points is obtained, forming parameter domain discrete path points controlled by a finite-dimensional parameter set.

[0126] Wherein, for a given robotic arm's continuous time domain path Dividing the continuous-time domain path evenly into n segments yields the discrete path points in the parameter domain:

[0127]

[0128] In the formula The discrete motion trajectory of the robotic arm. Let be the step length of the motion trajectory, and . The path parameter is a time-constrained variable, described as follows:

[0129]

[0130] in This represents the total time of the robotic arm's movement.

[0131] In this embodiment of the invention, when transforming a continuous time-domain path into discrete path points in the parameter domain controlled by a finite-dimensional parameter set, an initial motion path is generated using a fifth-order polynomial interpolation method and optimized by combining multi-dimensional constraints such as joint torque, velocity, acceleration, and jerk. This ensures that the generated optimal time-domain path meets both task requirements and the overall joint torque motion equation of the robotic arm's dynamics model, thereby guaranteeing the physical feasibility and motion stability of the path. Furthermore, the continuous time-domain path is uniformly discretized into discrete path points in the parameter domain controlled by a finite-dimensional parameter set. This not only achieves a precise parameterized expression of complex motion trajectories but also provides an efficient and computable discrete optimization foundation for subsequent time-optimal trajectory planning based on linear programming and convex optimization. This significantly improves the trajectory generation efficiency and control accuracy of the robotic arm in highly dynamic and multi-obstacle environments, effectively suppresses impacts and residual vibrations during motion, and ensures the safety and reliability of the robotic arm's high-speed and high-precision operations.

[0132] This invention provides a method for optimizing the initial motion path. Figure 2 The diagram illustrates the implementation flow of the initial motion path optimization method, which specifically includes:

[0133] S301, obtain the constraint conditions joint torque, velocity, acceleration, and jerk associated with the initial motion path, generate a set of constraints for the robotic arm based on the joint torque, velocity, acceleration, and jerk, and identify the initial point and end point of the initial motion path;

[0134] S302, combine the initial point and end point of the initial motion path to construct a three-dimensional trajectory model, divide the three-dimensional trajectory model into model meshes, establish the relationship between the initial motion path and the model meshes based on the coordinate information of the initial motion path in the three-dimensional trajectory model, and generate a path mesh set representing the relationship between the initial motion path and the model meshes.

[0135] S303, Traverse the path grid set, using the path grid set as prior information, perform path obstacle avoidance search on the path from the initial point to the end point, and generate at least one set of optimized obstacle avoidance paths;

[0136] When performing obstacle avoidance search on the path from the initial point to the destination, the search formula is expressed as:

[0137]

[0138] in, Indicates in The probability that the robotic arm's constraint member set finds the model's mesh at any given time. They are respectively in Time-based model gridding The amount of constraint information, the expected value of grid transition, and the grid obstacle avoidance factor. This represents the total number of paths from the initial point to the destination. These are respectively the path heuristic coefficient, the expected heuristic coefficient, and the obstacle coefficient;

[0139] S304 Iterate the optimized obstacle avoidance path and calculate the motion path duration from the initial point to the end point. Select the optimized obstacle avoidance path corresponding to the shortest path duration as the optimal time domain path.

[0140] In this embodiment of the invention, when optimizing the initial motion path, the constraints such as joint torque, velocity, acceleration, and jerk of the initial motion path are systematically obtained. A set of constraint members for the robotic arm is constructed, and the initial and final points of the path are clearly defined. Then, based on this key information, a three-dimensional trajectory model is constructed and discretized into model meshes. The association between the initial motion path and the meshes is accurately established to generate a path mesh set. Subsequently, using the path mesh set as prior information, obstacle avoidance path search from the initial point to the final point is carried out efficiently, generating multiple sets of optimized obstacle avoidance paths. Finally, by iteratively optimizing these paths and accurately calculating the motion duration of each path, the optimized obstacle avoidance path corresponding to the shortest path duration is selected as the optimal time domain path. This not only effectively ensures the physical feasibility and safety of the robotic arm's motion path under complex constraints and significantly reduces the risk of collisions between the path and obstacles, but also minimizes the motion time through accurate duration calculation and optimization selection, greatly improving the efficiency and accuracy of the robotic arm's operation. This provides solid and reliable technical support for the efficient, safe, and precise motion control of the robotic arm in dynamic and complex environments.

[0141] This invention provides a method for constructing a three-dimensional trajectory model by combining the initial point, the end point, and the initial motion path. Specifically, this method includes:

[0142] S3021: Obtain the geometric information, pose representation, and associated constraints of the initial motion path. Then, convert the joint angles into Cartesian coordinates of the end effector through the kinematic model of the robotic arm. Based on the Cartesian coordinates of the end effector, construct the initial three-dimensional trajectory in the world coordinate system. The initial three-dimensional trajectory is constructed based on the actual geometric information and pose representation of the initial motion path, which can realistically reflect the spatial position and posture changes of the robotic arm during the motion process. This makes the constructed trajectory closely match the actual motion of the robotic arm, providing an accurate reference for subsequent model optimization and path planning.

[0143] S3022 uses the geometric information and pose representation of the initial motion path to determine the spatial boundary of the initial three-dimensional trajectory. Combined with associated constraints, the initial three-dimensional trajectory after defining the spatial boundary is optimized to obtain a three-dimensional trajectory model. By optimizing the initial three-dimensional trajectory, parts that may not meet the constraints are removed, improving the reliability and safety of the three-dimensional trajectory model. This reduces the possibility of dangerous situations such as collisions and overloads during the movement of the robotic arm, ensuring the normal operation of the robotic arm and the safety of the operator.

[0144] S3023 divides the spatial range of the 3D trajectory model into adaptive cubic model meshes, assigns mesh identifiers to the model meshes, and establishes the association between the initial motion path and the model meshes based on the coordinate information of the initial motion path in the 3D trajectory model.

[0145] In this embodiment, grid identifiers are assigned to the model mesh, and a correlation is established between the initial motion path and the model mesh based on the coordinate information of the initial motion path in the 3D trajectory model. This clearly records the position and distribution of the initial motion path in 3D space, facilitating subsequent path search and optimization in the mesh space. Through this correlation, the mesh cell containing the initial motion path can be quickly located, providing convenience for path obstacle avoidance search and optimization, and improving the efficiency and accuracy of path planning.

[0146] This invention provides a method for unifying the dynamics model and kinematics model of a robotic arm based on motion state domain data of robotic arm joints. Specifically, this method includes:

[0147] S401, Identify the parameter domains of the robot arm joints' angles, velocities, and accelerations in the motion state domain data, wherein the parameter domains of the robot arm joints' angles, velocities, and accelerations are represented as follows:

[0148]

[0149] in , and A parameterized representation of the angles, velocities, and accelerations of the robotic arm joints. Path parameters The first, second, and third derivatives, These are the first, second, and third derivatives of the path parameters with respect to time, representing velocity, acceleration, and jerk, respectively.

[0150] S402, a parameter domain representation of the overall joint torque motion equation of the robotic arm is constructed based on the parameter domains of the angle, velocity and acceleration of the robotic arm joints;

[0151] The parameter domain of the overall joint torque motion equation of the robotic arm is expressed as follows:

[0152]

[0153] in, for The set of representations of (parameterization of the angles, velocities, and accelerations of robotic arm joints), specifically explained as follows:

[0154]

[0155] In the formula , , and These are the parameterized representations of the robotic arm's inertia vector matrix, Coriolis and centrifugal force vector matrices, Coulomb friction force matrix, and gravity vector matrix, respectively.

[0156] S403, by substituting the discrete path point constraints into the overall joint torque motion equation of the robotic arm, the dynamic model and kinematic model of the robotic arm are unified. Specifically, substituting the discrete path point constraints into the overall joint torque motion equation of the robotic arm yields:

[0157]

[0158] in .

[0159] This invention provides a method for constructing a general linear programming model with the objective of minimizing motion time. Figure 3 A schematic diagram illustrating the implementation process of a general linear programming model construction method with the objective of minimizing motion time is shown. The method specifically includes:

[0160] S501, Initialize the objective function: First, take "maximizing the sum of squared velocities at all discrete sampling points" as the time-optimal approximate objective, and transform the total trajectory motion time into the problem of maximizing this objective function, providing an optimization direction for subsequent linearization.

[0161] S502, Set velocity constraints: After the objective function is determined, apply an upper limit constraint on the velocity at each sampling point to ensure the joint angular velocity. Never exceed the physical limits of the robot's joints. To prevent overspeeding.

[0162] S503, Set acceleration constraints: Further introduce upper limit constraints on acceleration for the same batch of sampling points, limiting the joint angular acceleration. Not exceeding the maximum allowed value This ensures that the robotic arm will not saturate or be damaged due to excessive acceleration.

[0163] S504, Set torque constraints: Based on the loaded robotic arm dynamics model, set the joint torques at each sampling point. It is represented as a linear combination of state variables (position, velocity, acceleration), and an application is made. The hard constraints ensure that the motor and reducer always operate within a safe range.

[0164] S505, Set boundary conditions: To ensure smooth start and stop of the trajectory at the beginning and end of the path, the velocity of the sampling points at both ends is forcibly constrained to zero, i.e. .

[0165] S506, Model Integrity Check: The system self-checks whether the above objective function, four types of constraints and boundary conditions are all loaded and without conflict; if any link is missing or the dimension is inconsistent, it is determined that "the model is incomplete" and the process returns to adjustment; if all passes, it proceeds to the next step.

[0166] S507, Linear programming model construction completed: At this point, all variables, objective functions and constraints have been linearized and integrated into a standard linear programming form, and the solver can be directly called to perform numerical solutions for subsequent time-optimal trajectories.

[0167] This invention provides a method for determining the solution of a general linear programming model in the parameter domain. The method specifically includes:

[0168] S601, acquire the unified robotic arm motion state domain data, identify the path planning time in the continuous time domain corresponding to the unified robotic arm motion state domain data, and decompose the path planning time variable in the continuous time domain by differential decomposition.

[0169] Specifically, by differentially decomposing the time variables of path planning in the continuous time domain, we can obtain:

[0170]

[0171] S602, under the discrete-domain time line, further constraints are imposed on the differential decomposition results of the path planning time variables. The differential decomposition results of the path planning time variables are further expressed as the following differential decomposition constraints:

[0172]

[0173] In the formula Divide the path into evenly distributed segments;

[0174] S603, Obtain the differential decomposition constraints. Using the premise that the minimum motion time is equivalent to the maximum speed at the sampling points, transform the differential decomposition constraints into:

[0175]

[0176] S604: Obtain the results of discrete path point constraints and differential decomposition constraints, and construct a general linear programming model with the objective of minimizing motion time. The equivalent solution equations of the general linear programming model are:

[0177]

[0178] in For the number of discretized path segments, and They are respectively and The maximum value is obtained by the following formula:

[0179]

[0180] S605 uses a general linear solver to determine the linear programming parameter domain solution of the equal-quantity solution equations of a general linear programming model.

[0181] In this embodiment of the invention, when determining the linear programming parameter domain solution of a general linear programming model, a linear programming model with the objective of minimizing motion time is constructed, enabling the problem to be solved using mature linear programming theory. Furthermore, the linear programming parameter domain solution is directly obtained through a general linear solver, which not only significantly reduces computational complexity but also ensures the real-time performance and reliability of the solution results. Through rigorous mathematical derivation and reasonable simplification, this method achieves faster generation of time-optimal motion trajectories while strictly satisfying the dynamic constraints of the robotic arm.

[0182] This invention provides a method for constructing an acceleration-constrained planning model with a nonlinear objective function constraint. Figure 4 A schematic diagram illustrating the implementation process of a method for constructing a jerk constraint planning model with a nonlinear objective function constraint is shown. The method for constructing the jerk constraint planning model with a nonlinear objective function constraint specifically includes:

[0183] S701, Initialize the objective function: First, based on the linear programming solution without jerk constraints, upgrade the objective function to "maximize the sum of squared velocities of all discrete sampling points, while explicitly adding an energy penalty term for the rate of change of acceleration (i.e., jerk)," thereby suppressing joint impact while pursuing time optimization.

[0184] S702, Set velocity constraints: Using the velocity solution given by the model without jerk constraints in step S701 as a priori, construct tight constraints on the square of velocity to ensure that the square of velocity at each sampling point does not exceed the priori result, thus ensuring that the new model does not unnecessarily relax the velocity limit.

[0185] S703, Set jerk constraint: Apply an upper limit to the joint jerk for each sampling point after trajectory discretization. This linearizes the equation into an inequality between the difference in adjacent accelerations and the sampling time interval, ensuring that the dynamics of the robotic arm and the physical limits of the actuators are not exceeded.

[0186] S704, Set boundary jerk constraints: Further restrict the jerk separately at the start and end points of the path, let This eliminates abrupt changes during startup and shutdown, achieving a smooth transition.

[0187] S705, Set boundary conditions: Continuing the requirements of the linear programming model, constrain the velocities at both ends of the trajectory to zero, i.e. This satisfies the need for smooth start-stop operation.

[0188] S706, Model Integrity Check: The system self-checks whether the objective function, velocity constraints, jerk constraints, and all boundary conditions are fully loaded, dimension-matched, and conflict-free; if any missing or contradictory elements are found, it returns "No" and prompts for readjustment; if all passes, it marks "Model Integrity" as "Yes".

[0189] S707, Acceleration Constraint Model Construction Completed: At this point, all decision variables, quadratic objective terms, and linear constraints have been integrated into a convex optimization programming model with acceleration constraints (i.e., acceleration constraint programming model), which can directly call an efficient solver to complete the generation of time-optimal and impact-limited trajectories.

[0190] This invention provides a method for solving the parameter domain solution of a final convex optimization program. The method specifically includes:

[0191] S801, loading discrete path point constraints, approximating linear and nonlinear objective functions based on the relationship between discrete path points and time:

[0192]

[0193] in The number of discretized path segments is a variable;

[0194] S802, combining the discrete path point constraint condition, defines the jerk constraint, where the inequality under the jerk constraint is expressed as:

[0195]

[0196] in , and The constraints between the total path and the segment distance are expressed as follows:

[0197]

[0198] S803 defines the jerk constraints for the initial and final points of the robotic arm's motion based on discrete path points. The jerk constraints for the initial and final points of the robotic arm's motion are expressed as follows:

[0199]

[0200] S804, obtain the linear programming parameter domain solution of the general linear programming model, and solve the inequalities under the jerk constraint, the jerk constraint of the robot arm's initial point and end point, to obtain the optimal convex optimization programming constraint equation under the jerk constraint.

[0201]

[0202] in This is the solution in the parameter domain of a general linear programming model. It is the weighting coefficient, which ranges from [0, 1].

[0203] In this embodiment of the invention, the process of converting the parameter domain trajectory into a time domain trajectory is as follows:

[0204] Taylor series are used to transform curves from the parameter domain to the time domain, thereby allowing interpolation information to be sent at a certain time frequency.

[0205]

[0206] Among them Indicates the sampling period of the controller. Let i be the path parameter value at the i-th sampling time. The path parameter value is at the (i+1)th sampling time.

[0207] In this embodiment of the invention, when solving the final convex optimization programming parameter domain solution, firstly, the time relationship of discrete path points is approximated with the objective function (linear and nonlinear), accurately characterizing the key characteristics of the motion trajectory while ensuring computational efficiency. Secondly, jerk constraints are defined hierarchically for the entire trajectory (discrete path points) and boundaries (initial / endpoint), suppressing the risk of impact and vibration during joint movement and ensuring a smooth transition during start-stop phases. Finally, by integrating the previous linear programming parameter domain solution with multi-level jerk constraint inequalities, a convex optimization model that balances time optimality and motion smoothness is constructed. Its strict convexity ensures the uniqueness of the global optimal solution, while the direct applicability of the linear solver significantly improves real-time computational efficiency. This method, under the premise of strictly satisfying dynamic constraints, achieves multi-objective collaboration with the shortest trajectory time, minimal impact, and optimal smoothness, effectively extending the service life of the robotic arm and improving operational reliability under complex working conditions.

[0208] On the other hand, embodiments of the present invention also provide an optimal motion control system for a robotic arm based on jerk constraints. Figure 5 A schematic diagram of an optimal motion control system for a robotic arm based on jerk constraints is shown. This optimal motion control system specifically includes:

[0209] The system input module 100 is used to acquire robot dynamics and kinematics models, path parameterization models, and constraint sets, and to load the acquired robot dynamics and kinematics models, path parameterization models, and constraint sets.

[0210] in, Figure 6 This diagram illustrates the workflow of the system input module 100 loading the dynamics and kinematics model, path parameterization model, and constraint set of the acquisition robot in an embodiment of the present invention. The method for the system input module 100 to load the dynamics and kinematics model, path parameterization model, and constraint set of the acquisition robot is as follows:

[0211] Loading robot dynamics and kinematics models: First, the complete dynamics model of the six-degree-of-freedom articulated robot (including mass matrix, Coriolis force, gravity, etc.) and the forward / inverse kinematics models are imported into the system to provide a foundation for subsequent path-time coupling optimization.

[0212] Load the path parameterization model and confirm the start and end points: Read the pre-designed or taught spatial path (which can be represented as a parameterized curve in joint space or Cartesian space), and clarify the poses of the start and end points of the motion to ensure that subsequent interpolation and discretization are performed within this range.

[0213] Load constraint set: Load the four key constraints—moment constraints ( ), speed constraints ( ), acceleration constraints ( ) and jerk constraints ( — Loaded uniformly in the form of vectors or piecewise functions, and the corresponding dimension and joint correspondence are recorded.

[0214] Check constraint-model-path consistency: Compare the constraint dimensions and number of joints, and the path parameterization order with the constraint differentiability order. If a mismatch is found (e.g., the path order is lower than the third-order differentiability required by the jerk constraint), return "No" and prompt to readjust the model or constraints. If they are completely consistent, proceed to the next step.

[0215] Consistency passed: Once all constraints, robot model, and path parameter dimensions and variable ranges have been verified to be correct, the system marks it as "matched".

[0216] The system input module has been loaded: At this point, all necessary inputs are ready, and the system moves on to the subsequent "path discretization-linear programming solution" stage, laying the foundation for time-optimal trajectory calculation.

[0217] The dynamic modeling module 200 is used to model the overall dynamic process of the robotic arm based on the structural characteristic parameters of the six-degree-of-freedom joint robotic arm, and obtain the dynamic model of the robotic arm.

[0218] The path discretization module 300 is used to acquire the motion path of the robotic arm, decompose the motion path of the robotic arm, and transform the continuous time domain path into parameter domain discrete path points controlled by a finite-dimensional parameter set.

[0219] The path discretization module 300 includes:

[0220] The initial path generation unit 310 identifies joint torque, velocity, acceleration, and jerk based on the robotic arm dynamics model. Combining task requirements, it generates the initial motion path using the joint torque, velocity, acceleration, and jerk as constraints through a fifth-order polynomial interpolation method.

[0221] The path optimization unit 320 is used to load the initial motion path, consider the constraints of joint torque, velocity, acceleration, and jerk, optimize the initial motion path, and output the optimal time domain path.

[0222] The continuous time domain unit 330 is used to substitute the optimal time domain path into the robot arm dynamics model to verify whether the optimal time domain path satisfies the overall joint torque motion equation of the robot arm. If the optimal time domain path satisfies the overall joint torque motion equation of the robot arm, the optimal time domain path is used as the final continuous time domain path.

[0223] The parameter domain discrete path point generation unit 340 is used to obtain the continuous time domain path. , continuous time domain path If the path is evenly divided into n segments, at least one set of discrete path points is obtained, forming parameter domain discrete path points controlled by a finite-dimensional parameter set.

[0224] The model integration module 400 is used to load the discrete path points in the parameter domain controlled by the finite-dimensional parameter set and the dynamic model of the robotic arm. With the discrete path points in the parameter domain controlled by the finite-dimensional parameter set as constraints, the dynamic model of the robotic arm and the kinematic model of the robotic arm are unified based on the motion state domain data of the robotic arm joints, and the unified motion state domain data of the robotic arm is output.

[0225] Linear Programming Module 500, based on discrete path point constraints, constructs a general linear programming model with the objective of minimizing motion time, and determines the linear programming parameter domain solution of the general linear programming model;

[0226] The convex optimization planning module 600 is used to construct an acceleration constraint planning model with nonlinear objective function constraints based on the motion state domain data of the robotic arm and the solution of the linear programming parameter domain, and solve the final convex optimization planning parameter domain solution.

[0227] The trajectory conversion module 700 generates a parameter domain trajectory based on the parameter domain solution of convex optimization programming, converts the parameter domain trajectory into a time domain trajectory, and generates the optimal time trajectory for the robotic arm.

[0228] In summary, this invention provides a method and system for optimal motion control of a robotic arm based on jerk constraints. In the embodiments of this invention, the proposed optimal motion control method for a robotic arm based on jerk constraints satisfies the real-time requirements of high-dimensional coupling constraints while strictly satisfying the constraints of robot dynamics and kinematics. Furthermore, by introducing jerk as an independent optimization variable into the convex optimization framework, the generated trajectory not only shortens the time but also has high-order smoothness, effectively suppressing impacts and residual vibrations during the motion process.

[0229] It should be noted that, for the sake of simplicity, the foregoing embodiments are all described as a series of actions. However, those skilled in the art should understand that the present invention is not limited to the described order of actions, as some steps may be performed in other orders or simultaneously according to the present invention. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to the present invention.

[0230] It should be understood that the disclosed apparatus can be implemented in other ways, given the several embodiments provided in this application. For example, the apparatus embodiments described above are merely illustrative; the division of units described above is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or communication connections shown or discussed may be through some interfaces; the indirect coupling or communication connections between devices or units may be telecommunications or other forms.

[0231] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit the scope of protection of the invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on these embodiments, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art can still combine, add, delete, or otherwise adjust the features of the various embodiments of the present invention according to the circumstances without conflict or creative effort, thereby obtaining different technical solutions that do not fundamentally depart from the concept of the present invention. These technical solutions also fall within the scope of protection of the present invention.

Claims

1. A method for optimal motion control of a robot arm based on jerk constraint, characterized in that, The method comprises: According to the structural feature parameters of the six-degree-of-freedom joint mechanical arm, the overall dynamics process of the mechanical arm is modeled to obtain a mechanical arm dynamics model; An operation path of the mechanical arm is acquired, the operation path of the mechanical arm is decomposed, and the continuous time domain path is converted into a parameter domain discrete path point controlled by a finite-dimensional parameter set; The parameter domain discrete path point controlled by the finite-dimensional parameter set and the mechanical arm dynamics model are loaded, the parameter domain discrete path point controlled by the finite-dimensional parameter set is taken as a constraint, the mechanical arm dynamics model and the mechanical arm kinematics model are unified based on the motion state domain data of the joints of the mechanical arm, and unified motion state domain data of the mechanical arm is output; Based on the discrete path point constraint, a general linear programming model with the minimum motion time as a target is constructed, and a linear programming parameter domain solution of the general linear programming model is determined; According to the motion state domain data of the mechanical arm, the linear programming parameter domain solution is combined to construct a jerk constraint programming model with a nonlinear objective function constraint, and a final convex optimization programming parameter domain solution is solved; Based on the convex optimization programming parameter domain solution, a parameter domain trajectory is generated, the parameter domain trajectory is converted into a time domain trajectory, and a time optimal trajectory of the mechanical arm is generated.

2. The jerk-constrained manipulator optimal motion control method of claim 1, wherein: The method for modeling the overall dynamics process of the mechanical arm comprises: The structural feature parameters of the six-degree-of-freedom joint mechanical arm are traversed, and inertia vector matrices, Coriolis and centrifugal force vector matrices, gravity vector matrices, and Coulomb friction matrices are respectively constructed based on the structural feature parameters of the six-degree-of-freedom joint mechanical arm; The inertia vector matrices, the Coriolis and centrifugal force vector matrices, the gravity vector matrices, and the Coulomb friction matrices are loaded, and a mechanical arm overall joint torque motion equation is constructed based on the inertia vector matrices, the Coriolis and centrifugal force vector matrices, the gravity vector matrices, and the Coulomb friction matrices; The mechanical arm overall joint torque motion equation is expressed as: in, Joint torque is used to directly represent the motion state of the robotic arm. , and These are the angles, velocities, and accelerations of the robotic arm joints. For the robotic arm joint angle to be at The inertial vector matrix at time, For the robotic arm to be in Joint angles and The Coriolis and centrifugal force vector matrices at the velocity of motion. When the robotic arm is in The gravity vector matrix at joint angles. For the robotic arm to be in Coulomb friction matrix at joint angle.

3. The jerk-constrained manipulator optimal motion control method of claim 1, wherein: The method for converting the continuous time domain path into the parameter domain discrete path point controlled by the finite-dimensional parameter set comprises: Joint torques, velocities, accelerations, and jerk are identified based on the mechanical arm dynamics model, and an initial motion path is generated by a quintic polynomial interpolation method with the joint torques, the velocities, the accelerations, and the jerk as constraints according to a task requirement; The initial motion path is loaded, and the initial motion path is optimized by considering the constraint conditions of the joint torques, the velocities, the accelerations, and the jerk, and an optimal time domain path is output; The optimal time domain path is substituted into the mechanical arm dynamics model, and it is verified whether the optimal time domain path satisfies the mechanical arm overall joint torque motion equation, and the optimal time domain path is taken as the final continuous time domain path if the optimal time domain path satisfies the mechanical arm overall joint torque motion equation; Acquiring continuous time domain path The continuous time domain path The path is evenly divided into n segments, and at least one set of discrete path points is obtained, forming a finite-dimensional parameter set controlled parameter domain discrete path point.

4. The jerk-constrained manipulator optimal motion control method of claim 3, wherein: The method for optimizing the initial motion path comprises: Constraint conditions of joint torques, velocities, accelerations, and jerk associated with the initial motion path are acquired, a mechanical arm constraint member set is generated based on the joint torques, the velocities, the accelerations, and the jerk, and an initial point and a terminal point of the initial motion path are identified. The initial point, the end point and the initial motion path of the initial motion path are combined to construct a three-dimensional trajectory model, the three-dimensional trajectory model is divided into model sub-grids, an association relationship between the initial motion path and the model sub-grids is established based on coordinate information of the initial motion path in the three-dimensional trajectory model, and a path grid set representing the association relationship between the initial motion path and the model sub-grids is generated; The path grid set is traversed, and path obstacle avoidance search is performed on the path from the initial point to the end point based on the path grid set as prior information, so as to generate at least one group of optimized obstacle avoidance paths; The optimized obstacle avoidance paths are iterated, and the motion path time length from the initial point to the end point is calculated, and the optimized obstacle avoidance path corresponding to the shortest path time length is selected as the optimal time domain path.

5. The jerk-constrained manipulator optimal motion control method of claim 4, wherein: The method for constructing a three-dimensional trajectory model by combining the initial point, the end point and the initial motion path of the initial motion path, comprising: Obtaining the geometric information of the initial motion path, the pose representation of the initial motion path and the associated constraint condition, and converting the joint angle into the Cartesian coordinates of the end effector through the kinematics model of the robot arm, and constructing the initial three-dimensional trajectory in the world coordinate system based on the Cartesian coordinates of the end effector; Determine the spatial boundary of the initial three-dimensional trajectory based on the geometric information of the initial motion path and the pose representation of the initial motion path, and optimize the initial three-dimensional trajectory after defining the spatial boundary in combination with the associated constraint condition to obtain a three-dimensional trajectory model; The spatial range of the three-dimensional trajectory model is divided into adaptive cubic model sub-grids, the model sub-grids are assigned grid identifiers, and the association relationship between the initial motion path and the model sub-grids is established based on the coordinate information of the initial motion path in the three-dimensional trajectory model.

6. The jerk-constrained manipulator optimal motion control method of claim 2, wherein: The method for unifying the robot arm dynamics model and the robot arm kinematics model based on the motion state domain data of the robot arm joint, comprising: Identify the angle, speed and acceleration parameter domain of the robot arm joint in the motion state domain data; Construct the parameter domain representation of the overall joint torque motion equation of the robot arm based on the angle, speed and acceleration parameter domain of the robot arm joint; Bring the discrete path point constraint condition into the overall joint torque motion equation of the robot arm to unify the robot arm dynamics model and the robot arm kinematics model.

7. The jerk-constrained manipulator optimal motion control method of claim 6, wherein: The method for determining the linear programming parameter domain solution of the general linear programming model, comprising: Obtain the unified robot arm motion state domain data, identify the path planning time in the continuous time domain corresponding to the unified robot arm motion state domain data, and decompose the path planning time variable differential; Further constrain the path planning time variable differential decomposition result in the discrete domain time line; Obtain the differential decomposition constraint, and convert the differential decomposition constraint with the minimum motion time equivalent to the maximum speed of the sampling point as the prior; Obtain the discrete path point constraint and the differential decomposition constraint conversion result, and construct a general linear programming model with the minimum motion time as the target; Determine the linear programming parameter domain solution of the equivalent solving equation of the general linear programming model through a general linear solver.

8. The jerk-constrained manipulator optimal motion control method of claim 6, wherein: The method for solving the final convex optimization programming parameter domain solution, comprising: Load the discrete path point constraint, and approximate the linear objective function and the nonlinear objective function based on the relationship between the discrete path point and the time; The jerk constraint is defined in combination with the discrete path point constraint; The jerk constraint of the initial point and the terminal point of the mechanical arm motion is defined in combination with the discrete path point, and the jerk constraint of the initial point and the terminal point of the mechanical arm motion is respectively represented as: The linear programming parameter domain solution of the general linear programming model is obtained, and the optimal convex optimization programming constraint equation under the jerk constraint is obtained by simultaneously considering the inequality under the jerk constraint, the jerk constraint of the initial point and the terminal point of the robot arm motion.

9. A jerk-constrained optimal motion control system for a robot arm, for implementing the jerk-constrained optimal motion control method for a robot arm according to any one of claims 1-8, characterized in that: The jerk constraint-based optimal motion control system of the mechanical arm comprises: A system input module is configured to collect and load a robot dynamics and kinematics model, a path parameterization model and a constraint set; A dynamics modeling module is configured to model an overall dynamics process of the mechanical arm according to structural characteristic parameters of the six-degree-of-freedom joint mechanical arm, and obtain a dynamics model of the mechanical arm; A path discretization module is configured to obtain a motion path of the mechanical arm, decompose the motion path of the mechanical arm, and convert a continuous time domain path into a parameter domain discrete path point controlled by a finite-dimensional parameter set; A model integration module is configured to load the parameter domain discrete path point controlled by the finite-dimensional parameter set and the dynamics model of the mechanical arm, constrain the parameter domain discrete path point, unify the dynamics model of the mechanical arm and a kinematics model of the mechanical arm based on motion state domain data of the joints of the mechanical arm, and output unified motion state domain data of the mechanical arm; A linear programming module is configured to construct a general linear programming model with a minimized motion time as a target based on the discrete path point constraint, and determine a linear programming parameter domain solution of the general linear programming model; A convex optimization programming module is configured to construct a jerk constraint programming model with a nonlinear objective function constraint based on the motion state domain data of the mechanical arm and the linear programming parameter domain solution, and solve a final convex optimization programming parameter domain solution; A trajectory conversion module is configured to generate a parameter domain trajectory based on the convex optimization programming parameter domain solution, convert the parameter domain trajectory into a time domain trajectory, and generate a time optimal trajectory of the mechanical arm.

10. The jerk-constrained based optimal motion control system for a robotic arm of claim 9, wherein: The path discretization module comprises: An initial path generation unit is configured to identify joint torque, velocity, acceleration and jerk based on the dynamics model of the mechanical arm, generate an initial motion path by a quintic polynomial interpolation method based on the joint torque, velocity, acceleration and jerk, and combine the joint torque, velocity, acceleration and jerk as constraints; A path optimization unit is configured to load the initial motion path, optimize the initial motion path by considering the constraint conditions of joint torque, velocity, acceleration and jerk, and output an optimal time domain path; A continuous time domain unit is configured to verify whether the optimal time domain path satisfies an overall joint torque motion equation of the mechanical arm by substituting the optimal time domain path into the dynamics model of the mechanical arm, and use the optimal time domain path as a final continuous time domain path if the optimal time domain path satisfies the overall joint torque motion equation of the mechanical arm. a parameter domain discrete path point generating unit for obtaining a continuous time domain path dividing the continuous time domain path into n segments, at least one group of discrete path points is obtained, forming a parameter domain discrete path point controlled by a finite dimensional parameter set.

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