Linear trajectory planning method for space manipulator load operation task

Abstract

The application discloses a linear trajectory planning method for a space manipulator load operation task and relates to the technical field of space manipulator trajectory planning. A multi-objective optimization model is designed, and optimization targets include straightness vector optimization, obstacle avoidance optimization and jerk optimization; a trajectory planner is designed, an individual searched is a middle node configuration of a quintic polynomial trajectory, a quantum state coding mode is adopted to code the configuration of the manipulator, a QBSO algorithm is provided, a complete trajectory of the manipulator is sequentially connected by a plurality of middle node configurations, the next node configuration is searched according to a current configuration position and a target trajectory each time, and finally, a joint trajectory connected according to a quintic polynomial equation by n middle node configurations is formed. By designing a mathematical coding mode of the quintic polynomial trajectory, designing a linear trajectory planner framework based on a sampling algorithm and designing a straightness vector constraint model, an optimal trajectory meeting constraint requirements can be generated.

Description

Technical Field

[0001] This invention relates to the field of trajectory planning technology for space robotic arms, specifically a linear trajectory planning method for space robotic arm load operation tasks. Background Technology

[0002] With its powerful on-orbit operation capabilities, the space robotic arm system has become one of the essential pieces of equipment for maintaining the operation of the space station. The space robotic arm has a large working space and flexible movement, and can assist astronauts or complete tasks independently. It can effectively reduce the working time of astronauts in the harsh space environment and greatly improve the efficiency of mission execution.

[0003] The Chinese space robotic arm is a seven-joint space robotic arm. The mathematical model for its joint trajectories is a fifth-order polynomial. However, in actual missions, directly connecting the initial and target configurations using the fifth-order polynomial programming method often fails to meet constraints such as obstacle avoidance and singularity. Therefore, it is necessary to design several intermediate configurations and connect them sequentially using fifth-order polynomial joint trajectories. Payload manipulation is one of the main tasks of the Chinese space robotic arm. The motion process is divided into a large-scale transfer phase and a small-scale approach phase. The large-scale transfer phase refers to the robotic arm carrying the payload performing a wide range of joint maneuvers, moving to a designated position near the payload or target point. The small-scale approach phase refers to the robotic arm gradually approaching the payload from the end position of the large-scale transfer phase until docking. The large-scale transfer phase has no constraints on the end-effector trajectory, while the small-scale approach phase typically specifies the end-effector trajectory as a straight line. Because it is difficult to impose constraints on the end-effector trajectory using fifth-order polynomial joint trajectories, the trajectory of the small-scale approach phase is usually formed by connecting dense intermediate configurations, and the end-effector trajectory is approximately a straight line.

[0004] The space robotic arm employs offline trajectory planning algorithms, which are divided into sampling-based trajectory planning algorithms and trajectory optimization algorithms. These two planners are competing frameworks for generating optimal motion plans, but they also have complementary characteristics: sampling-based planners typically converge slowly but provide optimality guarantees; trajectory optimizers typically converge quickly but cannot provide global optimality guarantees in non-convex problems (such as scenarios with obstacles). Trajectory optimization algorithms cannot generate fifth-degree polynomial joint trajectories, so only sampling-based trajectory planning algorithms can be used. Sampling-based methods typically work in two steps: first, several collision-free paths are generated as an initial sample set without considering any cost metrics, and the cost is evaluated according to the constraint function; then, the samples are updated by applying certain heuristics to improve them.

[0005] I. Sample Generation Method

[0006] The initial trajectory samples for the forearm need to be generated strictly according to the specifications of a quintic polynomial. Quintic polynomial programming is a classic trajectory planning technique, and its prescribed mathematical model for joint trajectories is as follows: , , At the initial moment of motion, The end of the exercise. For a certain joint angle, , , , , , The intrinsic parameters of the fifth-order polynomial joint trajectory are given. Based on six constraints—starting position, ending position, starting velocity, ending velocity, starting acceleration, and ending acceleration—the solution is obtained. arrive These are the six parameters. Fifth-order polynomial trajectories can guarantee the continuity of joint position, velocity, and acceleration, and are a commonly used trajectory planning technique in industrial fields.

[0007] II. Sampling-based trajectory planning algorithm

[0008] 1. Classification of Algorithms

[0009] There are many sampling-based trajectory planning algorithms, the most classic being the Rapid Exploratory Random Tree (RRT) method and the Probabilistic Route Graph (PRM) method. Conceptually, this method first determines the state of the joint space, and then generates a trajectory connecting the starting point and the target point in the joint space through sampling. Karaman et al. proposed RRT based on RRT and PRM. and PRM An improvement on the solutions for RRT and PRM was proposed, but this method also has significant drawbacks. Searching for paths in high-dimensional spaces leads to an exponential increase in computational cost, and the computation time increases dramatically with the refinement of the sample grid. Genetic algorithms, inspired by the theory of biological evolution in nature, are widely used due to their excellent global search capabilities. Yu et al. and Zacharia et al. used genetic algorithms to plan the trajectory of a robotic arm for a multi-objective optimization task. Experimental results verified the global search capability of genetic algorithms. However, the search performance of genetic algorithms is directly related to the sample library, and constructing a sample library with complete probability distribution in complex environments is extremely difficult. Particle swarm optimization (PSO) is also a common sampling-based trajectory planning algorithm. Based on research on bird predation behavior, a PSO algorithm was proposed. This algorithm adapts to different environments through information sharing among individuals. However, PSO is more suitable for continuous problems than discrete or complex combinatorial optimization problems. The algorithm's performance is significantly affected by internal parameters, and it is prone to getting trapped in local optima for multimodal problems. In addition, many researchers have proposed improved algorithms based on the particle swarm optimization algorithm, among which the beetle swarm optimization algorithm stands out and has been widely used due to its excellent convergence speed and stable convergence performance. and D The algorithm is also one of the classic trajectory planning algorithms. Both of these algorithms have excellent trajectory planning capabilities in two-dimensional and three-dimensional spaces, but they perform poorly in trajectory planning problems in high-dimensional spaces, especially in multimodal and non-convex problems. Ant colony optimization is an optimization method inspired by the process of ants searching for food. It gradually approaches the optimal solution through an approximate positive feedback mechanism. However, ant colony optimization has many parameters, which are coupled with each other. Currently, the algorithm is optimized by iterative trial and error, so optimization efficiency is its biggest disadvantage.

[0010] 2. Constraints

[0011] Multi-objective optimization models are a very active research field. Without a reasonable optimization model, even excellent algorithms cannot calculate the desired trajectory. The mission trajectory of the forearm in the space station often needs to satisfy multiple constraints and optimization objectives, including constraint objectives such as obstacle avoidance and singularity avoidance, and optimization objectives such as joint path and joint jerk extrema. In this scheme, the constraint objectives and optimization objectives are collectively referred to as constraint objectives.

[0012] Singularity avoidance is a crucial constraint. When a robotic arm is in a singular configuration, a certain degree of freedom cannot change instantaneously, and the arm's links become locked. Mathematically, this manifests as a Jacobian matrix approaching singularity and being incompletely rank. In this case, the end effector loses one or more degrees of freedom in certain directions. Furthermore, small changes in the end effector's Cartesian space can cause significant velocity abrupt changes in the joint space, posing a significant risk to spatial manipulation tasks. The singularity of the robotic arm configuration can be measured by the condition number. To avoid singular configurations, the condition number constraint should be minimized. The condition number constraint model is as follows:

[0013]

[0014]

[0015] Obstacle avoidance is the core objective of trajectory planning. The primary goal of a robotic arm during movement is to ensure safety, including the safety of the robotic arm's structure and the surrounding environment to avoid collisions.

[0016] To complete a given task in the shortest possible time, many trajectory algorithms use the constraint objective of minimizing motion time. This can lead to joint constraint saturation and non-smooth motion due to discontinuous acceleration or excessive jitter, resulting in rapid actuator wear, inducing vibration, and reducing tracking accuracy. Therefore, such time-optimal trajectories result in oscillating motion behavior. A common remedy is to constrain twitching by adding a term to the cost function to penalize it, which minimizes oscillating behavior and improves the motion trajectory.

[0017] Minimizing the maximum jerk can reduce errors in trajectory tracking, decrease stress on actuator and manipulator structures, and limit the excitation of robot resonant frequencies, resulting in highly coordinated and natural robot motion. Limiting jerk is a fundamental requirement for avoiding mechanical resonance in robotic arms and improving trajectory accuracy; currently, most of the latest trajectory planning algorithms constrain jerk levels.

[0018] In summary, the main difficulties of existing technologies lie in:

[0019] 1) The forearm (China's space robotic arm) uses a 5th-order polynomial to generate its trajectory. In actual missions, a complete mission trajectory is generated by sequentially connecting several intermediate configurations. During the small-scale approach phase of the space payload operation mission, to ensure the safety of the payload, robotic arm, and space station module, there are strict constraints on the trajectory of the robotic arm's end effector, which is usually a straight Cartesian trajectory. The planning problem of the 5th-order polynomial trajectory is an NP-hard problem, and the straight-line constraint on the end effector trajectory places even stricter requirements on the trajectory planning algorithm.

[0020] 2) There are many types of constraints for robotic arm trajectory planning, but the constraint model can only consider a maximum of three. More constraints will have significant adverse effects on each other. At the same time, the common linear constraint model based on Euclidean distance is difficult to describe the vector difference between the end trajectory and the straight line. More accurate constraint models need to be designed to ensure that the final trajectory meets the requirements of various aspects. Summary of the Invention

[0021] To address the shortcomings of the prior art, this invention provides a linear trajectory planning method for space robotic arm load operation tasks. By designing a mathematical encoding method for a fifth-order polynomial trajectory, designing a linear trajectory planner framework based on a sampling algorithm, and designing a straightness vector constraint model, it can generate an optimal trajectory that meets the constraint requirements.

[0022] To achieve the above objectives, the present invention adopts the following technical solution: a linear trajectory planning method for space robotic arm payload operation tasks, comprising the following steps:

[0023] Design a multi-objective optimization model:

[0024] (1)

[0025]

[0026] The optimization objectives include a linearity vector optimization model, an obstacle avoidance optimization model, and a jerk optimization model, which are represented as follows:

[0027] Straightness vector optimization model:

[0028]

[0029]

[0030] Obstacle avoidance optimization model:

[0031]

[0032]

[0033] Boost Optimization Model:

[0034]

[0035] In the formula, t represents a certain moment during joint movement. T represents the complete time of the joint movement. , Let be the joint position of the i-th joint at time t, where i = 1, 2, ..., 7. This represents the motion vector of the terminal trajectory at time t. The direction vector representing the target line is used to obtain the target's Cartesian space trajectory. , and These represent the upper and lower limits of the joint, respectively. For time t The collision distance between the configured robotic arm and its surroundings. For a safe distance, This is the critical distance. , , Optimize the weights for the three objectives;

[0036] Design a trajectory planner:

[0037] The trajectory planner searches for individuals with intermediate node configurations x of a quintic polynomial trajectory, x = [x 1 ,x 2 ,...,x 7 ], x i The position of the i-th joint is represented using quantum state encoding, where the quantum state is represented as: , For the amplitude of the quantum, For quantum superposition states, α and β are the amplitudes of the two states, α 2 +β 2 =1, the encoding method is as follows:

[0038] (2)

[0039] In the formula, The encoding representing the position of the i-th joint. Indicating the initial search range, the encoding of the robotic arm configuration is c=[c 1 ,c 2 ,...,c 7 ];

[0040] Based on the BSOA algorithm, the QBSO algorithm is proposed. The complete trajectory of the robotic arm is formed by sequentially connecting several intermediate node configurations. Each time, the QBSO algorithm searches for the next node configuration based on the current configuration position and the target trajectory, ultimately forming a joint trajectory composed of n intermediate node configurations connected according to a fifth-degree polynomial equation, where:

[0041] The search range during the k-th iteration is represented as follows:

[0042] (3)

[0043] In the formula, rd is a random parameter. Let be the decay parameter for the k-th iteration, and be... k to the power of These are the initial parameters;

[0044] Based on the quantum-based Logistic equation, the iterative formula for generating new samples is expressed as follows:

[0045] (4)

[0046] In the formula, For the result of the k-th iteration search, Let m be the number of newly generated search samples in the (k+1)th iteration, and u be the chaos parameter.

[0047] Mapping the sample encoding of round k+1 to the joint position is represented as follows:

[0048] (5)

[0049] In the formula, This represents the joint position corresponding to the w-th new sample. This represents the result of the k-th iteration search;

[0050] Based on a multi-objective optimization model, the fitness of w particles in the (k+1)th round is compared, and the particle with the highest fitness is selected as the iteration result of the (k+1)th round, expressed as: .

[0051] Furthermore, the aforementioned The collision distance is obtained using the GJK algorithm.

[0052] Furthermore, the linear trajectory planning method is based on a multi-objective optimization model and a trajectory planner design, and the process is as follows:

[0053] S1, Input: Target Cartesian space trajectory Three-dimensional models and kinematic models of obstacles and robotic arms, initial configuration Target configuration The upper and lower limits of the joint and Optimize weights , and Set the number of intermediate configurations n, the number of newly generated samples m, and the iteration limit;

[0054] S2. Encode the previous node configuration according to formula (2). The first node configuration is the initial configuration. ;

[0055] S3. Update the search range according to formula (3);

[0056] S4. According to formula (4), search for the number of m newly generated samples;

[0057] S5. Map the newly generated sample to the joint position according to formula (5);

[0058] S6. Using the previous node configuration as the starting configuration and the newly generated joint configuration as the ending configuration, generate a fifth-degree polynomial trajectory.

[0059] S7. Calculate the fitness of the new trajectory based on the multi-objective optimization model of formula (1), and select the sample with the highest fitness as the result of this iteration.

[0060] S8. Iterate with iteration number k = k + 1, and check if k is less than or equal to the iteration limit. If yes, return to S3 to continue updating the search range. If no, increment the number of intermediate configurations by 1, store the current search result as a new node configuration, and check if the number of intermediate configurations is less than n. If yes, return to S2 to continue encoding. If no, change the initial configuration. Intermediate configuration and target configuration A fifth-order polynomial connection is used to generate a complete joint trajectory.

[0061] Furthermore, in trajectory planning, the positions of the node configurations are first normalized.

[0062] Compared with existing technologies, the advantages of this invention are as follows: This invention proposes a quantum state-based beetle swarm optimization (QBSO) algorithm to design a trajectory planner for a space robotic arm. It successfully achieves accurate tracking of straight-line trajectories in Cartesian space and can generate joint trajectories that meet the requirements of fifth-order polynomial trajectories. Simulation and practical verification experiments demonstrate superior convergence speed and global optimization capabilities. Results show that, compared with traditional sampling and optimization algorithms, the QBSO algorithm achieves the task objective of tracking the end effector's straight-line trajectory based on fifth-order polynomial joint trajectories while meeting the safe obstacle avoidance distance requirement. Furthermore, it also considers the smoothness of joint motion and the uniformity of velocity, thereby reducing internal stress in the robotic arm and improving the motion accuracy and stability of the end effector. Attached Figure Description

[0063] Figure 1 This is a flowchart of the planning method of the present invention;

[0064] Figure 2 This is a schematic diagram of the DH coordinate system of the robotic arm in the embodiment;

[0065] Figure 3 This is the motion trajectory of the robotic arm in the simulation experiment of the embodiment;

[0066] Figure 4 These are the convergence curves of the QBSO algorithm and the comparison algorithm in the simulation experiment of the embodiment;

[0067] Figure 5 These are the joint position curves under the QBSO algorithm in the simulation experiment of the embodiment;

[0068] Figure 6 These are the joint velocity curves under the QBSO algorithm in the simulation experiment of the embodiment;

[0069] Figure 7 This is the motion trajectory of the robotic arm in the verification experiment of the embodiment;

[0070] Figure 8 These are the joint position curves under the QBSO algorithm in the verification experiment of the embodiment;

[0071] Figure 9 These are the joint velocity curves under the QBSO algorithm in the verification experiment of the embodiment;

[0072] Figure 10 This is the trajectory characteristic curve of the robotic arm in the verification experiment of the embodiment. Detailed Implementation

[0073] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the invention, not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0074] A linear trajectory planning method for payload manipulation tasks of a space robotic arm includes the following steps:

[0075] Optimize model design, including:

[0076] 1. Straightness Vector Optimization Model

[0077] For a robotic arm with seven joints, its Cartesian trajectory is a smooth free curve. We use several intermediate points to connect the fifth-order polynomial trajectory to achieve an effect that approximates a straight Cartesian spatial trajectory.

[0078] The straightness optimization model is represented as follows:

[0079]

[0080] In the formula, t represents a certain moment during joint movement. T represents the complete time of the joint movement. , Let be the joint position of the i-th joint at time t, where i = 1, 2, ..., 7. Let be the position vectors of the seven joints at time t, then Corresponding to the initial configuration, Corresponding to the target configuration, This represents the motion vector of the terminal trajectory at time t. This represents the direction vector of the target straight line. Since it involves straight line trajectory planning, it is achieved through... The target's Cartesian space trajectory can then be obtained. .

[0081] The straightness vector optimization model is then expressed as follows:

[0082]

[0083]

[0084] In the formula, This represents the vector sum of the areas between the terminal trajectory and the target trajectory. and These represent the upper and lower limit positions of the joint, respectively.

[0085] 2. Obstacle Avoidance Optimization Model

[0086] The obstacle avoidance function is implemented on a simulation platform for the space robotic arm, which includes 3D and kinematic models of both the obstacle and the robotic arm. Our primary goal in trajectory planning is to maintain a safe distance between the robotic arm and the obstacle, ensuring the safety of the robotic arm's structure and surrounding equipment. However, once the robotic arm is already within the safe zone, excessively increasing the collision distance becomes meaningless and negatively impacts the optimization of other metrics. A reasonable obstacle avoidance scheme should avoid overemphasizing the collision distance, rather than increasing it after obstacle avoidance has been achieved.

[0087] The obstacle avoidance optimization model is represented as follows:

[0088]

[0089]

[0090]

[0091] In the formula, This indicates the distance between the robotic arm and the obstacle during its complete movement; a higher value indicates a safer robotic arm. For time t The collision distance between the robotic arm and its surroundings was determined using the GJK algorithm. For a safe distance, This is the critical distance.

[0092] 3. Acceleration Optimization Model

[0093] Limiting the jerk of the joints can reduce the internal stress of the joints and the end effector, resulting in a very coordinated and natural robotic arm motion trajectory, which is very beneficial for improving the motion accuracy of the end effector.

[0094] The design jerk optimization model is represented as follows:

[0095]

[0096]

[0097] In the formula, This represents the maximum value of the Euclidean norm of the jerk in the trajectory of the i-th joint.

[0098] 4. Multi-objective optimization model

[0099] Based on the three optimization objectives of straightness vector, obstacle avoidance, and jerk, a multi-objective optimization model is designed as follows:

[0100] (1)

[0101]

[0102] In the formula, , , These are the intrinsic parameters used to adjust the optimization weights for the three objectives.

[0103] The trajectory planner design includes:

[0104] 1. Quantum state encoding method

[0105] The BSOA algorithm's exploration strategy is similar to other intelligent optimization algorithms, balancing the completeness of search probabilities and the accuracy of optimization results by controlling the search step size. However, this balancing effect is weak, and premature convergence leads to a loss of diversity. Therefore, the optimization performance of the BSOA algorithm is significantly reduced when dealing with high-dimensional problems. Here, we propose a quantum-based beetle swarm optimization algorithm (QBSO) to balance population exploration ability and algorithm speed.

[0106] In this invention, the trajectory planner searches for individuals that are intermediate node configurations x of a fifth-degree polynomial trajectory, x = [x 1 ,x 2 ,...,x 7 ], x i Let represent the position of the i-th joint. Inspired by quantum evolution, the QBSO algorithm represents the joint variables in the search individual as a linear superposition of the upper and lower limit positions of the joints, with the quantum state representation as follows:

[0107]

[0108] In the formula, For the amplitude of the quantum, For quantum superposition states, α and β are the amplitudes of the two states, α 2 +β 2 =1.

[0109] The encoding method is represented as follows:

[0110] (2)

[0111] In the formula, The encoding representing the position of the i-th joint. This represents the initial search range. The encoding combination of the 7 joint positions is the encoding c of the robotic arm configuration, c = [c...]. 1 ,c 2 ,...,c 7 ].

[0112] This encoding method normalizes the searched particles and separates the quantum amplitude. Similarly, in trajectory planning, the positions of the node configurations are first normalized.

[0113] 2. Generate new search samples

[0114] The Beetle Antennae Olfactory Algorithm (BAOA) mimics the foraging behavior of beetles. Researchers have improved upon this by proposing the Beetle Swarm Optimization Algorithm (BSOA), which expands the number of individual beetles and enhances the algorithm's ability to escape local optima. This invention improves upon the BSOA algorithm, enhancing its optimization performance in high-dimensional spaces and increasing its search efficiency. The complete trajectory of the robotic arm consists of several intermediate node configurations connected sequentially. Each time, the algorithm searches for the next node configuration based on the current configuration position and the target trajectory, ultimately forming a joint trajectory composed of n intermediate configurations connected by a fifth-degree polynomial equation. The search process is a Markov process, meaning the search result depends only on the current state and is independent of the initial state or previous node configurations.

[0115] The beetle's search range adaptively adjusts with each iteration. Initially, the initial position is far from the target position, resulting in the largest search range. As the beetle searches, it gets closer to the target position, and the search range gradually decreases.

[0116] The search range during the k-th iteration is represented as follows:

[0117] (3)

[0118] In the formula, rd is a random parameter. Let be the decay parameter for the k-th iteration, and be... k to the power of These are the initial parameters.

[0119] Based on the quantum-based Logistic equation, the iterative formula for generating new samples is expressed as follows:

[0120] (4)

[0121] In the formula, For the result of the k-th iteration search, Let m be the number of newly generated search samples in the (k+1)th iteration, and u be the chaos parameter. An adaptive search range is used to balance search efficiency while improving the completeness of the search probability.

[0122] 3. Select a new search result

[0123] Mapping the sample encoding of round k+1 to the joint position is represented as follows:

[0124] (5)

[0125] In the formula, This represents the joint position corresponding to the w-th new sample. This represents the result of the k-th iteration search. Based on the multi-objective optimization model, the fitness of w particles in the (k+1)-th round is compared, and the particle with the highest fitness is selected as the iteration result of the (k+1)-th round, expressed as: .

[0126] Based on the above design, the specific process of the linear trajectory planning method of the present invention is combined with... Figure 1 As shown, it includes the following steps:

[0127] S1, Input: Target Cartesian space trajectory Three-dimensional models and kinematic models of obstacles and robotic arms, initial configuration Target configuration The upper and lower limits of the joint and Optimize weights , and Set the number of intermediate configurations n, the number of newly generated samples m, and the iteration limit.

[0128] S2. Encode the previous node configuration according to formula (2). The first node configuration is the initial configuration.

[0129] S3. Update the search range according to formula (3).

[0130] S4. Based on formula (4), search for the number of m newly generated samples.

[0131] S5. Map the newly generated samples to joint positions according to formula (5).

[0132] S6. Using the previous node configuration as the starting configuration and the newly generated joint configuration as the ending configuration, generate a fifth-degree polynomial trajectory.

[0133] S7. Calculate the fitness of the new trajectory based on the multi-objective optimization model of formula (1), and select the sample with the highest fitness as the result of this iteration.

[0134] S8. Iterate with iteration number k = k + 1, and check if k is less than or equal to the iteration limit. If yes, return to S3 to continue updating the search range. If no, increment the number of intermediate configurations by 1, store the current search result as a new node configuration, and check if the number of intermediate configurations is less than n. If yes, return to S2 to continue encoding. If no, change the initial configuration. Intermediate configuration and target configuration A fifth-order polynomial connection is used to generate a complete joint trajectory.

[0135] Example

[0136] To demonstrate the effectiveness of the proposed QBSO algorithm, it was validated using the EMM simulation platform and compared with other existing sampling algorithms. Since EMM cannot perform seven-DOF motion experiments on the ground, the FrankaEmika Panda robotic arm was used to verify the algorithm's application in real-world tasks.

[0137] Simulation Experiment

[0138] Based on the operational tasks of EMM and the characteristics of the extravehicular working environment of the space station, we defined the initial and target configurations and planned the motion trajectory of the robotic arm's end effector. The initial configuration is [-1.565, 1.932, 1.421, -1.769, -3.111, 2.781, -3.158] (rad), and the target configuration is [-1.288, 0.249, 1.178, -1.831, -2.982, 1.332, -0.071] (rad). To demonstrate the superiority of the QBSO algorithm, we conducted comparative simulations with six existing algorithms. The sample population for both the QBSO algorithm and all comparison algorithms was 20, and the iterations were 1000. We compared the convergence speed and results of these algorithms in the EMM planning task and presented the result curves of the QBSO algorithm.

[0139] The EMM uses a RYPPPYR configuration and the DH method is used to model the robotic arm, combined with... Figure 2 The coordinate system for each joint is shown in Table 1. The DH parameters are shown in Table 1.

[0140] Table 1 DH Parameter Table

[0141]

[0142] Combination Figure 3 As shown, the motion trajectory planned by the QBSO algorithm for the EMM is illustrated. The EMM has an arm length of over 5 meters, and the tracking accuracy at the end of the robotic arm is excellent on a macroscopic scale, while also effectively avoiding obstacles.

[0143] Combination Figure 4 As shown, the convergence curves of the QBSO algorithm and six other comparison algorithms are displayed. It can be observed that the QBSO algorithm exhibits excellent convergence, quickly converging to the vicinity of the optimal solution, and the convergence result is very close to the optimal result.

[0144] Combination Figure 5 and Figure 6 As shown, the joint position and velocity curves of the EMM in dialogue mode under the QBSO algorithm are displayed. It can be seen that due to the addition of the jerk optimization model, the joint position changes are smooth, the maximum values ​​of the velocities of each trajectory segment are close, and the velocity changes are uniform. This will greatly reduce the internal stress of the joint actuators and improve the tracking accuracy of the robotic arm.

[0145] Table 2 shows a comparison of the simulation results of the QBSO algorithm with six other algorithms:

[0146] Table 2 Simulation Results Data

[0147] algorithm Collision distance (m) Maximum tracking error (mm) OMA 0.0735 51.6323 COA 0.0671 48.0326 SAO 0.0652 59.0354 RIME 0.0629 60.6851 GRO 0.0715 53.6546 GMO 0.0826 39.2614 QBSO 0.0832 40.1356

[0148] Verification Experiment

[0149] Since it is difficult to conduct 7-DOF verification tests on the ground, we used the Franka Emika Panda for verification. The initial configuration of the robotic arm was [0.443, 0.526, 0.500, -1.015, -0.039, 1.728, -1.500] (rad), and the final configuration was [-1.346, 0.665, 0.781, -1.383, -0.470, 1.858, -2.897] (rad). The tracked target trajectory was a straight line from the end point of the initial configuration [0.5, -0.5, 0.4] (m) to the end point of the final configuration [0.5, 0.5, 0.6] (m).

[0150] Combination Figure 7 As shown, the initial configuration, intermediate configuration, and target configuration of the robotic arm's movement are illustrated.

[0151] Combination Figure 8 and Figure 9 As shown, the joint position and velocity curves of the EMM in the dialogue under the QBSO algorithm are displayed, with noise filtered out using a Savitzky-Golay filter. It can be seen that the joint position changes are smooth, and the velocity does not change abruptly.

[0152] Combination Figure 10 As shown, the changes in tracking error and collision distance are illustrated. The change in collision distance is relatively small because the obstacle is very close to the first link of the robotic arm. Link 1's movement is relatively small, so the collision distance remains essentially unchanged. The maximum error from the straight trajectory is 22.1 mm, which meets the requirements for the robotic arm to track a predetermined trajectory for large-scale transfer tasks.

[0153] The references for the comparison algorithms are as follows:

[0154] [1]K. Zolfi, “Gold rush optimizer: A new population-basedmetaheuristic algorithm,” Operations Research and Decisions, vol. 33, no. 1,2023, doi: 10.37190 / ord230108.

[0155] [2]F. Rezaei, H. R. Safavi, M. Abd Elaziz, and S. Mirjalili, “GMO:geometric mean optimizer for solving engineering problems,” Soft Comput.,vol. 27, no. 15, pp. 10571–10606, Aug. 2023, doi: 10.1007 / s00500-023-08202-z.

[0156] [3]M.-Y. Cheng and M. N. Sholeh, “Optical microscope algorithm: A newmetaheuristic inspired by microscope magnification for solving engineeringoptimization problems,” Knowledge-Based Systems, vol. 279, p. 110939, Nov.2023, doi: 10.1016 / j.knosys.2023.110939.

[0157] [4]L. Deng and S. Liu, “Snow ablation optimizer: A novelmetaheuristic technique for numerical optimization and engineering design,”Expert Systems with Applications, vol. 225, p. 120069, Sep. 2023, doi:10.1016 / j.eswa.2023.120069.

[0158] [5]H. Jia, H. Rao, C. Wen, and S. Mirjalili, “Crayfish optimizationalgorithm,” Artif Intell Rev, vol. 56, no. 2, pp. 1919–1979, Nov. 2023, doi:https: / / doi.org / 10.1007 / s10462-023-10567-4.

[0159] [6]H. Su et al., “RIME: A physics-based optimization,” Neurocomputing, vol. 532, pp. 183–214, May 2023, doi: 10.1016 / j.neucom.2023.02.010.

[0160] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of the equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0161] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A linear trajectory planning method for payload operation tasks of a space robotic arm, characterized in that: Includes the following steps: Design a multi-objective optimization model: （1） The optimization objectives include a linearity vector optimization model, an obstacle avoidance optimization model, and a jerk optimization model, which are represented as follows: Straightness vector optimization model: Obstacle avoidance optimization model: Boost Optimization Model: In the formula, t represents a certain moment during joint movement. T represents the complete time of the joint movement. , Let be the joint position of the i-th joint at time t, where i = 1, 2, ..., 7. This represents the motion vector of the terminal trajectory at time t. The direction vector representing the target line is used to obtain the target's Cartesian space trajectory. , and These represent the upper and lower limits of the joint, respectively. At time t The collision distance between the configured robotic arm and its surroundings. For a safe distance, This is the critical distance. , , Optimize the weights for the three objectives; Design a trajectory planner: The trajectory planner searches for individuals with intermediate node configurations x of a quintic polynomial trajectory, x = [x 1 ,x 2 ,...,x 7 ], x i The position of the i-th joint is represented using quantum state encoding, where the quantum state is represented as: , For the amplitude of the quantum, For quantum superposition states, α and β are the amplitudes of the two states, α 2 +β 2 =1, the encoding method is as follows: （2） In the formula, The encoding representing the position of the i-th joint. Indicating the initial search range, the encoding of the robotic arm configuration is c = [c 1 ,c 2 ,...,c 7 ]; Based on the BSOA algorithm, the QBSO algorithm is proposed. The complete trajectory of the robotic arm is formed by sequentially connecting several intermediate node configurations. Each time, the QBSO algorithm searches for the next node configuration based on the current configuration position and the target trajectory, ultimately forming a joint trajectory composed of n intermediate node configurations connected according to a fifth-degree polynomial equation, where: The search range during the k-th iteration is represented as follows: （3） In the formula, rd is a random parameter. Let be the decay parameter for the k-th iteration, and be... k to the power of These are the initial parameters; Based on the quantum-based Logistic equation, the iterative formula for generating new samples is expressed as follows: （4） In the formula, For the result of the k-th iteration search, Let m be the number of newly generated search samples in the (k+1)th iteration, and u be the chaos parameter. Mapping the sample encoding of round k+1 to the joint position is represented as follows: （5） In the formula, This represents the joint position corresponding to the w-th new sample. This represents the result of the k-th iteration search; Based on a multi-objective optimization model, the fitness of w particles in the (k+1)th round is compared, and the particle with the highest fitness is selected as the iteration result of the (k+1)th round, expressed as: .

2. The linear trajectory planning method for space robotic arm load operation tasks according to claim 1, characterized in that: The The collision distance is obtained using the GJK algorithm.

3. A linear trajectory planning method for a space robotic arm's payload operation task according to claim 1 or 2, characterized in that: The linear trajectory planning method is based on a multi-objective optimization model and a trajectory planner design, and the process is as follows: S1, Input: Target Cartesian space trajectory Three-dimensional models and kinematic models of obstacles and robotic arms, initial configuration Target configuration The upper and lower limits of the joint and Optimize weights , and Set the number of intermediate configurations n, the number of newly generated samples m, and the iteration limit; S2. Encode the previous node configuration according to formula (2). The first node configuration is the initial configuration. ; S3. Update the search range according to formula (3); S4. According to formula (4), search for the number of m newly generated samples; S5. Map the newly generated sample to the joint position according to formula (5); S6. Using the previous node configuration as the starting configuration and the newly generated joint configuration as the ending configuration, generate a fifth-degree polynomial trajectory. S7. Calculate the fitness of the new trajectory based on the multi-objective optimization model of formula (1), and select the sample with the highest fitness as the result of this iteration. S8. Iterate with iteration number k = k + 1, and check if k is less than or equal to the iteration limit. If yes, return to S3 to continue updating the search range. If no, increment the number of intermediate configurations by 1, store the current search result as a new node configuration, and check if the number of intermediate configurations is less than n. If yes, return to S2 to continue encoding. If no, change the initial configuration. Intermediate configuration and target configuration A fifth-order polynomial connection is used to generate a complete joint trajectory.

4. The linear trajectory planning method for space robotic arm load operation tasks according to claim 3, characterized in that: In trajectory planning, the positions of node configurations are first normalized.

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