Flexible operation control system based on robotic arm control algorithm

Abstract

The present invention relates to a flexible operation control system based on a robotic arm control algorithm, which aims to solve the problems of insufficient perception ability, poor operational flexibility and low efficiency of multi-task scheduling of existing robotic arms in complex environments. The system includes a multimodal sensor module, a control algorithm module, a flexible execution module, a dynamic task allocation and scheduling module, and a cloud collaboration and learning module. The multimodal sensor module obtains comprehensive information about the robotic arm's operating environment in real time through force and torque sensors, visual sensors, tactile sensors, etc. The control algorithm module adopts path planning, adaptive impedance control and model predictive control to achieve dynamic obstacle avoidance, flexible grasping and high-precision operation of the robotic arm in complex environments. The flexible execution module combines a multi-degree-of-freedom robotic arm with a flexible gripper. The dynamic task allocation and scheduling module optimizes the task sequence according to task priority and delay time. The cloud collaboration and learning module continuously optimizes the control algorithm and scheduling model through reinforcement learning.

Description

Technical Field

[0001] The present invention relates to the technical field of robotic arm control systems, and in particular to a flexible operation control system based on a robotic arm control algorithm. Background Art

[0002] With the rapid development of industrial automation technology, robotic arms, as core equipment for intelligent manufacturing, have been widely used in fields such as assembly, handling, flexible grasping and high-precision operation. However, existing robotic arm control systems still have obvious shortcomings in complex task scenarios. First, most robotic arms rely on a single type of sensor (such as a visual sensor or a force sensor) to obtain environmental information, but a single sensor is difficult to fully perceive the operating scene in a dynamic and complex environment. For example, the accuracy of visual sensors decreases in high temperature and strong light environments, and the feedback of force sensors is not accurate enough under dynamic loads or multiple contact points. In addition, the data acquisition and system feedback speeds of existing sensors are slow, and path deviations or even collisions are prone to occur during high-speed operations or real-time obstacle avoidance. This limitation in perception capabilities significantly reduces the adaptability of robotic arms in flexible grasping, dynamic obstacle avoidance and complex working conditions.

[0003] Secondly, most existing control algorithms use traditional fixed parameter methods (such as proportional integral differential control or impedance control) and lack dynamic adjustment capabilities. For example, when flexibly grasping lightweight or fragile objects, fixed impedance parameters may cause excessive grasping force and damage the objects; while in the operation of high-rigidity objects, the grasping force may not be enough to complete the task. In terms of path planning, existing technologies have difficulty in achieving real-time obstacle avoidance and dynamic path adjustment in complex scenarios. Once the obstacle or target position changes, traditional algorithms often cause task failure due to path update lag. In addition, the insufficient model prediction capability makes it difficult for the system to quickly adapt to nonlinear dynamic changes, further limiting the operational flexibility of the robotic arm.

[0004] At the same time, existing robotic arm task scheduling mechanisms also have limitations in multi-task collaborative production lines. Current task scheduling is mostly based on static rules or fixed sequences, lacking dynamic optimization of task priorities and delay times. For example, high-priority tasks cannot be executed promptly due to scheduling rules, and low-priority task delays are not properly controlled. These problems lead to a decrease in overall production efficiency. Furthermore, existing systems generally lack data-driven optimization capabilities and are unable to utilize historical task data to improve scheduling models or control parameters. This results in inefficiency and a lack of adaptability when executing tasks over the long term.

[0005] In summary, existing robotic arm control systems have significant shortcomings in multimodal perception, dynamic adaptive control, intelligent task scheduling, and cloud-based data optimization. These issues limit the breadth and depth of robotic arm applications in complex environments. Therefore, designing a flexible operational control system with multimodal perception, dynamic adaptive control, efficient task scheduling, and data-driven optimization capabilities is key to addressing these challenges. This will meet the demands of complex mission scenarios and significantly improve the operational efficiency and adaptability of robotic arms.

[0006] To this end, we urgently need to design a flexible operation control system based on the robotic arm control algorithm to solve the above problems. Summary of the Invention

[0007] The present invention provides a flexible operation control system based on a robotic arm control algorithm to solve the defects in the prior art.

[0008] Flexible operation control system based on robotic arm control algorithm, including:

[0009] The multimodal sensor module is used to collect real-time data on the robot's operation and environment. The sensors and their output data are as follows:

[0010] Force and torque sensor: contact force F x ,F y ,F z and contact torque τ x ,τ y ,τ z , respectively represent the forces along the X, Y, and Z axes and the moments around the X, Y, and Z axes;

[0011] Vision sensor: 3D position of target object (x v ,y v ,z v ) and attitude angle θ v ;

[0012] Position and attitude sensor: the position of the end of the robotic arm (x now ,y now ,z now ),speed acceleration

[0013] Torque joint sensor: torque of each joint

[0014] Tactile sensor: contact pressure P c and contact area A c ;

[0015] Temperature sensor: Temperature T at the end of the robotic arm e and the target object temperature T o;

[0016] Ultrasonic or laser ranging sensor: obstacle distance d i ;

[0017] The control algorithm module takes the data from the sensor module as input and generates output based on the following algorithms: Path planning algorithm: inputs the target position and current state, and outputs the expected trajectory (x d ,y d ,z d ) and attitude angle θ d ;

[0018] Adaptive impedance control algorithm: input external force and joint torque, output end force F(t) and torque τ(t);

[0019] Model predictive control algorithm: Input the desired trajectory (x d ,y d ,z d ) and the current state, output the optimized control input u(k), including joint force and joint torque

[0020] a flexible execution module, including a multi-degree-of-freedom robotic arm and a flexible gripper, for executing the operations generated by the control algorithm module;

[0021] Dynamic task allocation and scheduling module, dynamically adjusting operation strategies based on sensor feedback and task priorities;

[0022] Cloud collaboration and learning module, used to store sensor data and optimize control algorithm models.

[0023] Preferably, the path planning algorithm is based on the target position (x v ,y v ,z v ) and the current end position (x now ,y now ,z now ) is input and generates the expected trajectory:

[0024] x d =x now +η x (x v -x now ),

[0025] y d =y now +η y (y v -y now ),

[0026] z d =znow +η z (z v -z now ),

[0027] Where: x d ,y d ,z d : expected trajectory; η x ,η y ,η z : Step size coefficient.

[0028] 3. The flexible operation control system based on the manipulator control algorithm according to claim 2, wherein the path planning algorithm uses ultrasonic or laser ranging sensor data d i As input, the following obstacle avoidance constraints are satisfied:

[0029] d i ≥d min ,

[0030] Where: d i : the distance to the i-th obstacle; d min :Safe distance.

[0031] Preferably, the adaptive impedance control algorithm uses force sensor data (F x ,F y ,F z ), torque data (τ x ,τ y ,τ z ) and joint torque sensor data For input, dynamically adjust the impedance parameters:

[0032] K=K0+α·F contat ,

[0033] B=B0+β·τ contact ,

[0034]

[0035] Among them: K, B, M: stiffness, damping and inertia parameters;

[0036] External force modulus; External moment modulus; Maximum joint torque.

[0037] Preferably, the model predictive control algorithm uses the current state (x now ,y now ,z now ) and the desired trajectory generated by path planning (x d ,yd ,z d ) is input and the objective function is optimized:

[0038]

[0039] in:

[0040] x(k)=[x now ,y now ,z now ] T : Current state of the end of the robotic arm;

[0041] x ref (k) = [x d ,y d ,z d ] T : expected trajectory point;

[0042] Optimize control input, including joint forces and torques; λ: regularization coefficient.

[0043] Preferably, the optimized control input u(k) satisfies the following constraints:

[0044]

[0045] in: The minimum and maximum forces allowed for the i-th joint; The minimum and maximum torque allowed for the i-th joint.

[0046] Preferably, the tactile sensor is provided with a contact pressure P c and contact area A c is the input used to control the gripping force of the flexible gripper, satisfying the following conditions:

[0047] F grip =P c ·A c ≤F safe ,

[0048] Among them: F grip : Grasping force; F safe : Safe grasping force threshold.

[0049] Preferably, the temperature sensor is the temperature T of the end of the robot arm. e and the target object temperature T o is the input for operation constraints, satisfying the following conditions:

[0050] T safe =|T e -T o |≤ΔT,

[0051] Where: ΔT: allowable temperature difference range.

[0052] Preferably, the dynamic task allocation module is based on the task time requirement T i 、Task complexity C i and task energy consumption E i As input, calculate the task priority:

[0053] P i =w1T i +w2C i +w3E i ,

[0054] Among them: w1, w2, w3: priority weights.

[0055] Preferably, the task scheduling is based on the task priority P i and task delay time D i As input, optimize the following objective function:

[0056]

[0057] Where: P i : The priority of the i-th task;

[0058] D i =T finish,i -T plan,i : The delay time of the i-th task;

[0059] T flnish,i : The actual completion time of the i-th task is recorded by the flexible execution module;

[0060] T plan,i : The planned completion time of the i-th task is pre-set by the task scheduling module;

[0061] N: Total number of tasks.

[0062] Beneficial effects: This technical solution significantly improves the perception ability of the robotic arm in complex scenarios by introducing a multimodal sensor module. Multimodal sensors (including force and torque sensors, visual sensors, tactile sensors, etc.) achieve comprehensive perception of the robotic arm's surrounding environment and operating status. For example, the visual sensor captures target position and dynamic obstacle information in real time, the tactile sensor monitors clamping pressure, and the temperature sensor ensures safe operation. This multi-sensor collaborative work overcomes the limitations of a single sensor, enabling the robotic arm to operate accurately in dynamic and diverse environments, while reducing operational errors and improving the quality of task completion.

[0063] Through the path planning, adaptive impedance control, and model predictive control functions of the control algorithm module, this technical solution significantly improves the flexible operation capability and environmental adaptability of the robot arm. The dynamic path planning algorithm achieves real-time obstacle avoidance and trajectory optimization in complex environments. The adaptive impedance control can adjust the impedance parameters of the robot arm in real time according to changes in external forces and torques, thereby ensuring safety when grasping lightweight or fragile objects and providing sufficient operating force when handling high-rigidity objects. In addition, model predictive control uses the optimization objective function to generate optimal control instructions, enabling the robot arm to efficiently respond to nonlinear dynamic changes and perform excellently in scenarios with high precision and high dynamic requirements.

[0064] In multi-task collaboration and long-term task execution scenarios, this technical solution improves the overall task scheduling efficiency and system self-optimization capabilities through dynamic task allocation and scheduling modules and cloud collaboration and learning modules. The dynamic task allocation mechanism optimizes the task sequence in real time according to task priority and delay time, so that high-priority tasks are executed in a timely manner. The cloud collaboration module optimizes path planning, adaptive control parameters and task scheduling models through reinforcement learning, realizing continuous iterative upgrades of the control system. This mechanism not only improves the long-term execution efficiency of the system, but also enhances its adaptability to new task scenarios. In summary, this technical solution has the significant advantages of comprehensive perception, flexible operation, intelligent scheduling and strong self-optimization capabilities, providing a more efficient and reliable solution for the application of robotic arms in complex environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] In order to more clearly illustrate the technical solutions in the present invention or the prior art, a brief introduction is given below to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0066] Figure 1 This is a system block diagram of a ventilation control system based on the Internet of Things. DETAILED DESCRIPTION

[0067] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0068] The following is combined with Figure 1 The specific embodiments of the present invention are described in detail with reference to the accompanying drawings and multiple embodiments.

[0069] 1: System architecture, this flexible operation control system includes the following modules:

[0070] Multimodal sensor module: collects status information of the robotic arm and the environment in real time.

[0071] Control algorithm module: including path planning, adaptive impedance control, model predictive control, etc.

[0072] Flexible execution module: includes a multi-degree-of-freedom robotic arm and a flexible gripper, responsible for executing control instructions.

[0073] Dynamic task allocation and scheduling module: optimize task sequence and reduce task delays.

[0074] Cloud collaboration and learning module: data storage and model optimization.

[0075] 2. Working principle of each module;

[0076] Multimodal sensor module: force and torque sensor, output: contact force F x ,F y ,F z and contact torque τ x ,τ y ,τ z Application: used to calculate the external force modulus F contact and the external moment modulus τ contact :

[0077]

[0078] Vision sensor: Output: Target object position (x v ,y v ,z v ) and attitude angle θ v . Purpose: Provide target position input for path planning.

[0079] Position and attitude sensor: Output: Position of the end of the robotic arm (x now ,y now ,z now ),speed acceleration Purpose: Used for state feedback of path planning and control algorithms.

[0080] Tactile sensor: Output: Contact pressure P c and contact area A c Application: Calculate the clamping force F grip :F grip =P c ·A c .

[0081] Temperature sensor: Output: Temperature T at the end of the robotic arm e and the target object temperature T o Purpose: Used to determine safety constraints:

[0082] T safe =|T e -T o |≤ΔT.

[0083] Ultrasonic or laser ranging sensor: Output: obstacle distance d i Application: Obstacle avoidance constraints for path planning:

[0084] d i ≥d min .

[0085] Control algorithm module: path planning algorithm, input: target position (x v ,y v ,z v ) and the current end position (x n ow,y now ,z now ). Output: expected trajectory (x d ,y d ,z d ) and attitude angle θ d .

[0086] Formula: x d =x now +η x (x v -x now ),y d =y now +η y (y v -y now ),z d =z now

[0087] where η x ,η y ,η z is the step size coefficient.

[0088] Adaptive impedance control algorithm input: external force modulus F c ontact, external moment modulus τ c ontact, joint torque

[0089] Output: terminal force F(t) and torque τ(t).

[0090] formula:

[0091] Among them, the impedance parameters are dynamically adjusted:

[0092] K=K0+α·F contact ,B=B0+β·τ contact .

[0093] Model predictive control algorithm: Input: current state (x n ow,y now ,z now ), expected trajectory (x d ,y d ,z d ).

[0094] Output: Optimized control input u(k). Formula:

[0095]

[0096] constraint:

[0097] Dynamic task allocation and scheduling module: task priority calculation, input: task time requirement T i Complexity C i , energy consumption E i .

[0098] Output: Task priority P i :

[0099] P i =w1T i +w2C i +w3E i .

[0100] Task delay time calculation: Input: planned completion time T plan,i , actual completion time T finish,i .

[0101] Scheduling optimization goal, output: delay time D i :

[0102] D i =T finish,i -T plan,i .

[0103] formula:

[0104] Cloud collaboration and learning module: Data upload: sensor data, task completion time, etc. are uploaded in real time.

[0105] Model optimization: Optimize path planning, adaptive impedance control, and task scheduling models based on reinforcement learning.

[0106] Parameter update: The optimized model parameters are sent to the local controller.

[0107] The following is further described with reference to several specific embodiments:

[0108] Example 1: Background: A robotic arm needs to move parts from a storage area to an assembly station for precision assembly. This task requires the robotic arm to avoid excessive force that could damage the parts while ensuring high-precision assembly.

[0109] Specific implementation steps: The visual sensor obtains the position of the parts in the storage area (x v ,y v ,z v ) and assembly position

[0110] (x target ,y target ,z target) .

[0111] The position sensor provides the initial position of the end of the robot arm (x now ,y now ,z now ).

[0112] The system generates the desired trajectory based on the input target position and the current end position of the robot arm:

[0113] η x (x v -x now ),y d =y now +η y (y v -y now ),z d =z r

[0114] Avoid possible obstacles so that the path meets the constraint d i ≥d min .

[0115] Handling process control: The adaptive impedance control algorithm dynamically adjusts the impedance parameters based on the desired trajectory of the path planning and the real-time feedback of the force sensor:

[0116]

[0117] Among them, K, B, and M are adjusted dynamically:

[0118] K=K0+α·F contact ,B=B0+β·τ contact .

[0119] This allows the robotic arm to operate stably during the handling process and avoid path deviation due to external interference.

[0120] Assembly control: Force and torque sensors monitor assembly contact forces and torques:

[0121]

[0122] According to the detection data, the assembly force at the end of the robotic arm is dynamically adjusted so that the assembly torque meets the accuracy requirements.

[0123] Task completion and recording: The system records the actual completion time of the task T f inish and delay time D i =T finish,i -T plan,i .

[0124] The data is uploaded to the cloud and used to optimize the assembly model.

[0125] Example 2: A robotic arm needs to grab fragile objects (such as eggs or fruits) in a complex environment, avoid dynamic obstacles, and move the objects to a designated target area.

[0126] The visual sensor captures the position of the target object (x v ,y v ,z v ) and obstacle distribution. Ultrasonic ranging sensors measure obstacle distance d in real time i The tactile sensor initializes the gripper contact pressure P c and contact area A c .

[0127] Dynamically plan a collision-free trajectory based on the target position and obstacle positions:

[0128] x d =f(x now ,d i ), satisfying d i ≥d min .

[0129] If the obstacle distance is less than d min ,Replan the trajectory to bypass obstacles.

[0130] Grasping control: Tactile sensors provide real-time feedback on gripper contact pressure and contact area, dynamically adjusting gripping force:

[0131] F grip =P c ·A c ,

[0132] Make F grip ≤F safe, to avoid damage to items.

[0133] Transport task execution: The flexible execution module transports items to the target area according to the planned trajectory.

[0134] Adaptive impedance control handles external interference during handling, allowing stable grasping and safe handling of items.

[0135] Task completion and recording: The system records the task completion time T finish,i and transportation path data, and upload them to the cloud for optimization model.

[0136] Example 3: A robotic arm needs to move heated industrial products from a high-temperature area to a cooling area while avoiding contact with other high-temperature objects.

[0137] The temperature sensor monitors the temperature T at the end of the robotic arm e and the target object temperature T o The system determines whether the safety constraints are met:

[0138] T safe =|T e -T o |≤ΔT.

[0139] If not satisfied, the operation is paused and the user is prompted to adjust the environment.

[0140] The system dynamically plans obstacle avoidance paths based on the distribution of high-temperature areas, ensuring safe trajectories:

[0141] x d =f(x now ,d i ), satisfying d i ≥d min .

[0142] If the robot arm detects a high-temperature obstacle during transport, it replans its path to bypass it. Force and torque sensors monitor the stability of objects during transport to prevent them from slipping due to external interference.

[0143] Adaptive impedance control dynamically adjusts the robot's motion stiffness and damping to adapt to different handling conditions.

[0144] Task Completion and Recording: After the object is safely moved to the cooling area, the task completion time and ambient temperature data are recorded and uploaded to the cloud.

[0145] Example 4: A robotic arm performs multiple tasks on a production line (such as parts assembly, material handling, and finished product testing). It is necessary to dynamically adjust the scheduling order based on task priorities to improve overall production efficiency.

[0146] System input task time requirement Y i Complexity Ci , energy consumption E i . Calculate the priority of each task:

[0147] P i =w1T i +w2C i +w3E i .

[0148] According to the priority P i and delay time D i ,Optimize task scheduling order:

[0149]

[0150] Adjust the scheduled time T of low-priority tasks in real time plan,i , reducing overall latency.

[0151] Complete each task in sequence: use force sensors to monitor assembly force during parts assembly, dynamically avoid obstacles during material handling, and use visual sensors to obtain inspection results for finished product inspection.

[0152] After each task is completed, record the actual completion time T finish,io

[0153] Cloud optimization: upload task data, optimize the scheduling model, and improve the execution efficiency of subsequent tasks.

[0154] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A flexible operation control system based on a robotic arm control algorithm, characterized in that: include: The multimodal sensor module is used to collect real-time data on the robot's operation and environment. The sensors and their output data are as follows: Force and torque sensor: contact force F x ,F y ,F x and contact torque τ x ,τ y ,τ z , respectively represent the forces along the X, Y, and Z axes and the moments around the X, Y, and Z axes; Vision sensor: 3D position of target object (x v ,y v ,z v ) and attitude angle θ v ; Position and attitude sensor: the position of the end of the robotic arm (x now ,y now ,z now ),speed acceleration Torque joint sensor: torque of each joint Tactile sensor: contact pressure P c and contact area A c ; Temperature sensor: Temperature T at the end of the robotic arm e and the target object temperature T o ; Ultrasonic or laser ranging sensor: obstacle distance d i ; Control algorithm module: takes the data from the sensor module as input and generates output based on the following algorithms: Path planning algorithm: inputs the target position and current state, and outputs the expected trajectory (x d ,y d ,z d ) and attitude angle θ d ; Adaptive impedance control algorithm: input external force and joint torque, output end force F(t) and torque τ(t); Model predictive control algorithm: Input the desired trajectory (x d ,y d ,z d ) and the current state, output the optimized control input u(k), including joint force and joint torque Flexible execution module: including a multi-degree-of-freedom robotic arm and a flexible gripper, used to execute the operations generated by the control algorithm module; Dynamic task allocation and scheduling module: dynamically adjusts operation strategies based on sensor feedback and task priorities; Cloud collaboration and learning module: used to store sensor data and optimize control algorithm models.

2. The flexible operation control system based on the manipulator control algorithm according to claim 1, characterized in that: The path planning algorithm takes the target position (x v ,y v ,z v ) and the current end position (x now ,y now ,z now ) is input and generates the expected trajectory: x d =x now +η x (x v -x now ), and d =and now +η y (and v -and now ), With d =z now +η z (With v -With now ), Where: x d ,y d ,z d : expected trajectory; η x ,η y ,η z : Step size coefficient.

3. The flexible operation control system based on the manipulator control algorithm according to claim 2, characterized in that: The path planning algorithm uses ultrasonic or laser ranging sensor data d i As input, the following obstacle avoidance constraints are satisfied: d i ≥d min , Where: d i : the distance to the i-th obstacle; d min :Safe distance.

4. The flexible operation control system based on the manipulator control algorithm according to claim 1, characterized in that: The adaptive impedance control algorithm uses the force sensor data (F x ,F y ,F z ), torque data (τ x ,τ y ,τ z ) and joint torque sensor data For input, dynamically adjust the impedance parameters: K=K0+α·F contact , B=B0+β·τ contact , Among them: K, B, M: stiffness, damping and inertia parameters; External force modulus; External moment modulus; Maximum joint torque.

5. The flexible operation control system based on the manipulator control algorithm according to claim 1, characterized in that: The model predictive control algorithm takes the current state (x now ,y now ,z now ) and the desired trajectory generated by path planning (x d ,y d ,z d ) is input and the objective function is optimized: in: x(k)=[x now ,y now ,z now ] T : Current state of the end of the robotic arm; x ref (k) = [x d ,y d ,z d ] T : expected trajectory point; Optimize control input, including joint forces and torques; λ: regularization coefficient.

6. The flexible operation control system based on the manipulator control algorithm according to claim 5, characterized in that: The optimized control input u(k) satisfies the following constraints: in: The minimum and maximum forces allowed for the i-th joint; The minimum and maximum torque allowed for the i-th joint.

7. The flexible operation control system based on the manipulator control algorithm according to claim 1, characterized in that: The tactile sensor is provided with a contact pressure P c and contact area A c is the input used to control the gripping force of the flexible gripper, satisfying the following conditions: F grip =P c ·A c ≤F safe , Among them: F grip : Grasping force; F safe : Safe grasping force threshold.

8. The flexible operation control system based on the manipulator control algorithm according to claim 1, characterized in that: The temperature sensor is based on the temperature T of the end of the robot arm. e and the target object temperature T o is the input for operation constraints, satisfying the following conditions: T safe =|T e -T o |≤ΔT, Where: ΔT: allowable temperature difference range.

9. The flexible operation control system based on the manipulator control algorithm according to claim 1, characterized in that: The dynamic task allocation module is based on the task time requirement T i 、Task complexity C i and task energy consumption E i As input, calculate the task priority: P i =w1T i +w2C i +w3E i , Among them: w1, w2, w3: priority weights.

10. The flexible operation control system based on the manipulator control algorithm according to claim 9, characterized in that: The task scheduling is based on the task priority P i and task delay time D i As input, optimize the following objective function: Where: P i : The priority of the i-th task; D i =T finish,i -T plan,i : The delay time of the i-th task; T finish,i : The actual completion time of the i-th task is recorded by the flexible execution module; T plan,i : The planned completion time of the i-th task is pre-set by the task scheduling module; N: Total number of tasks.

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