0 Introduction
Safflower (Carthamus tinctorius L.), a distinctive economic crop with medicinal, culinary, and industrial value, has witnessed a significant increase in its market value[1-3]. As one of the primary producers of safflower, China, particularly the Xinjiang Uygur Autonomous Region(Xinjiang region), has emerged as a core supply center[4,5]. To enable efficient picking within the plant's growth cycle, mechanized picking has become a prominent focus of research[6-8]. In particular, the application of robotic technologies offers promising solutions for the automated picking of safflower filament[9].
To address the sequencing problem encountered in the picking point planning process of safflower picking robots, it is essential to recognize its inherent similarity to the Traveling Salesman Problem (TSP). The TSP aims to determine the shortest path that visits a set of designated locations exactly once before returning to the starting point[10-12]. Drawing on this principle, a combinatorial optimization model based on the three-dimensional traveling salesman problem (3D TSP) was developed for safflower picking. Traditionally, swarm intelligence algorithms have been widely employed to solve TSP-related problems[13,14]. Utamima and Reiners[15] proposed a hybrid algorithm combining aenetic algorithm (GA), Tabu Search (TS), and ant colony optimization (ACO), which effectively addressed the path planning problem in multi-field and multi-machine agricultural scenarios. The method reduced travel distance by an average of 16.21% compared to traditional approaches and significantly shortened computation time. Gao et al.[16] proposed an improved PSO for apple picking robot path planning, which enhances obstacle avoidance and significantly improves picking efficiency. Shuping et al.[17] proposed a spraying path planning method based on the Vector Modeling Method, which effectively ensures full boundary coverage while minimizing redundant overlaps and turning points. This approach significantly improves the operational efficiency and coverage precision of unmanned helicopter pesticide spraying tasks. These algorithms simulate the collective behavior mechanisms observed in nature, enabling them to find near optimal solutions. However, as the number of individuals increases, swarm intelligence algorithms must recompute the path from scratch for each iteration. This leads to low computational efficiency in dynamic environments, rendering them less suitable for safflower picking tasks.
In contrast, reinforcement learning (RL) offers the advantage of offline learning[18,19]. By training on simulated data, RL models can acquire efficient path planning strategies[20]. In the context of safflower picking, RL models can rapidly adapt to changes in the number of target flowers, thereby enhancing picking efficiency, flexibility, and robustness. For example, Zhang et al.[21] proposed a model-based Temporal Proximity Soft Actor-Critic algorithm, integrating a long short-term memory (LSTM) model to optimize the maize threshing process by enhancing threshing quality and reducing damage rates. Yang et al.[22] proposed a path planning method for agricultural robots based on an improved RL approach. By integrating a residual network structure with a multi-step temporal difference error mechanism, the method significantly improved real-time decision-making capabilities in dynamic environments. However, its collaborative optimization of perception and obstacle avoidance in three-dimensional complex terrains, such as densely planted crop areas—requires further investigation. Lin et al. [23] developed a path planning framework based on recurrent deep deterministic policy gradient, in which a LSTM structure was used to retain historical state information, and continuous action outputs enabled collision free path generation. This method demonstrated superior obstacle avoidance and path stability under dynamic conditions, although its computational complexity remains relatively high, leaving room for optimization in large-scale picking scenarios. Despite progress in applying deep reinforcement learning to agricultural path planning, several challenges persist in handling complex and dynamic environments, including inadequate state representation, insufficient real time responsiveness, and low training efficiency.
To address these issues, researchers have recently begun integrating pointer network architectures with RL[24]. The RL pointer network processes input sequences directly and outputs optimized decision sequences. This not only improves state representation but also leverages offline learning to reduce computational costs during online inference. Bello et al.[25] were the first to introduce RL via policy gradient methods into pointer networks to tackle the Traveling Salesman Problem (TSP) in an end-to-end, unsupervised learning setting. Gu and Yang[26] proposed a deep learning framework that combined pointer networks with a hybrid learning strategy—supervised learning with RL, which demonstrated strong generalization ability in solving Non-deterministic Polynomial-time hard problems such as Max-Cut, achieving over 92% accuracy on high-dimensional dynamic data. However, applying such models directly to safflower picking where target distributions change rapidly still suffers from suboptimal real-time decision making efficiency, primarily due to excessive search space and the resulting computational latency. To address this, Lin et al.[27] proposed an enhanced RL pointer network structure with a refined sequence planning strategy, which effectively reduced the computational burden in high-density environments and improved the rationality of picking sequences. Compared to traditional optimization methods, their approach reduced the average path length by 11.3% and achieved a 2.4× improvement in inference speed, highlighting the efficiency advantages of reinforcement learning in complex agricultural scenarios. Nevertheless, due to the unique growth patterns and picking requirements of safflower, real-world applications still face challenges such as dynamically changing flower distributions and complex picking paths. Although the aforementioned studies have progressively enhanced the performance of RL-based pointer networks in combinatorial optimization tasks, key limitations remain: excessive path redundancy in dynamic environments, limited spatial search capacity of conventional pointer networks, reduced decision-making efficiency, and prolonged inference time. These issues are particularly critical in robotic safflower picking, where the spatial layout of targets is non-uniform and decision latency directly impacts task success. Moreover, insufficient coordination between the actor and critic networks can lead to unstable training and suboptimal policy convergence.
To address the aforementioned challenges, an Actor–Critic reinforcement learning pointer network algorithm (AC-RL-PtrNet) was developed for safflower picking scenarios. In this framework, three main enhancements were designed. First, an enhanced dynamic exponential moving average (DEMA)-based attention module with distance encoding was introduced, enabling more effective modeling of both local and global spatial structures among safflower targets. Second, a structured pruning strategy was applied to LSTM gates and dense layers to reduce network redundancy and inference latency, while preserving decision performance under dense or dynamically changing picking configurations. Third, the Critic network was restructured with input normalization, compact non-linear layers, and residual connections, allowing more stable value estimation and improved Actor–Critic optimization during policy learning in complex field environments.
1 Materials and methods
1.1 Data preparation
1.1.1 Safflower picking robot and working principle
In this study, a safflower picking robot based on a parallel robotic arm was employed. The system consists of a high-clearance mobile chassis, a parallel robotic arm, an end Effector, a negative pressure safflower filament collection module, a visual recognition system, and a control system. The overall dimensions of the robot are 1 600 mm×1 280 mm×1 400 mm (length×width×height), and the operational workspace of the parallel robotic arm is defined by a cylindrical volume with a radius of 300 mm and a height of 300 mm. The working principle of the parallel safflower picking robot is illustrated in Fig. 1. During each picking task, the robot first identifies and localizes the safflower filament using its vision system and image processing algorithms[28]. The detected coordinates are then transformed from the camera coordinate frame to the robotic arm coordinate frame. Subsequently, the optimal sequence is determined using a path planning algorithm. Finally, as shown in Fig. 1c and Fig. 1d, the robotic arm follows the planned trajectory under the control of the onboard system. The end effector, in conjunction with the negative pressure safflower filament collection module, performs the picking and collection of the safflower filament.
Fig. 1 Flowchart of safflower picking by parallel robot |
1.1.2 Safflower data
During the safflower picking season from July to September, a field survey was conducted in Jimusaer county, Xinjiang. The investigation revealed that safflower is cultivated in rigid rows, with an inter-row spacing of 600 mm and an intra-row plant spacing of 150 mm. respectively. Within the reachable workspace of a single robotic arm, the number of safflower capitula was statistically found to range between 31 and 50. Based on this, 40 flower heads were chosen as a representative reference for training and evaluation.
Table 1~ Table 3 present the spatial distributions and corresponding coordinate points of 25, 31, and 43 safflower targets, respectively. To construct the dataset, a binocular stereo vision system mounted on an actual safflower-picking robot was employed. As illustrated in Fig. 2, the system first captured RGB images of safflower plants under field conditions. These included scenarios with both occluded and non-occluded safflower heads. The image recognition and localization algorithm then processed the images and computed the corresponding 3D coordinates of each detected safflower head. The recorded values represent the three-dimensional positions (X, Y, Z) of the safflower heads relative to the stereo camera's reference frame. To enhance computational efficiency and enable more stable learning during model training and inference, all spatial coordinates were further normalized to a [0,1] range after acquisition. This normalization ensures consistent input scaling and facilitates the decision-making process of the reinforcement learning model. The resulting dataset serves as a real-world test set that simulates irregularly distributed picking targets, providing a robust benchmark for evaluating the proposed path planning algorithm under complex spatial conditions.
Table 1 Spatial distribution and 3D coordinates of 25 safflower targets |
| Spatial distribution | Lable | Coordinate points | Lable | Coordinate points |
|---|---|---|---|---|
 | 1 | （0.370 85， 0.225 16， 0.845 60） | 14 | （0.107 30， 0.718 10， 0.351 90） |
| 2 | （0.2607 1， 0.3415 2， 0.684 10） | 15 | （0.444 20， 0.735 80， 0.791 80） | |
| 3 | （0.150 57， 0.274 46， 0.719 60） | 16 | （0.668 30， 0.909 50， 0.713 80） | |
| 4 | （0.083 69， 0.296 23， 0.402 10） | 17 | （0.829 70， 0.785 10， 0.691 60） | |
| 5 | （0.091 51， 0.540 71， 0.899 40） | 18 | （0.773 30， 0.714 30， 0.719 50） | |
| 6 | （0.407 40， 0.517 10， 0.910 40） | 19 | （0.794 20， 0.560 00， 0.591 80） | |
| 7 | （0.549 00， 0.278 40， 0.820 40） | 20 | （0.896 50， 0.643 30， 0.628 80） | |
| 8 | （0.608 00， 0.065 50， 0.524 90） | 21 | （0.942 30， 0.594 00， 0.613 50） | |
| 9 | （0.820 50， 0.177 80， 0.694 80） | 22 | （0.938 50， 0.692 60， 0.634 90） | |
| 10 | （0.619 90， 0.457 80， 0.710 90） | 23 | （0.968 60， 0.824 70， 0.490 60） | |
| 11 | （0.551 69， 0.434 36， 0.694 90） | 24 | （0.841 50， 0.897 50， 0.391 80） | |
| 12 | （0.529 40， 0.564 48， 0.701 90） | 25 | （0.801 60， 0.962 40， 0.361 80） | |
| 13 | （0.284 33， 0.649 31， 0.872 60） |
Table 3 Spatial distribution and 3D coordinates of 43 safflower targets |
| Spatial distribution | Lable | Coordinate points | Lable | Coordinate points |
|---|---|---|---|---|
| | 1 | （0.066 90， 0.944 80， 0.220 69） | 23 | （0.958 28， 0.501 20， 0.077 57） |
| 2 | （0.272 09， 0.007 86， 0.789 90） | 24 | （0.978 76， 0.869 70， 0.144 32） | |
| 3 | （0.291 00， 0.675 90， 0.498 20） | 25 | （0.413 78， 0.755 43， 0.050 40） | |
| 4 | （0.274 50， 0.580 01， 0.828 09） | 26 | （0.280 54， 0.011 32， 0.336 20） | |
| 5 | （0.387 98， 0.546 18， 0.486 30） | 27 | （0.236 89， 0.745 04， 0.409 20） | |
| 6 | （0.026 03， 0.840 90， 0.239 20） | 28 | （0.970 50， 0.141 88， 0.509 40） | |
| 7 | （0.017 18， 0.414 45， 0.101 10） | 29 | （0.881 24， 0.569 85， 0.649 90） | |
| 8 | （0.927 67， 0.631 05， 0.318 80） | 30 | （0.582 91， 0.902 41， 0.734 50） | |
| 9 | （0.371 76， 0.72219， 0.901 90） | 31 | （0.662 84， 0.021 60， 0.092 40） | |
| 10 | （0.269 97， 0.768 43， 0.741 02） | 32 | （0.204 40， 0.369 01， 0.800 06） | |
| 11 | （0.725 02， 0.085 77， 0.862 82） | 33 | （0.169 60， 0.898 20， 0.854 90） | |
| 12 | （0.559 95， 0.614 29， 0.183 17） | 34 | （0.839 21， 0.173 10， 0.265 33） | |
| 13 | （0.884 94， 0.752 67， 0.490 53） | 35 | （0.513 48， 0.998 80， 0.585 30） | |
| 14 | （0.783 94， 0.016 53， 0.096 84） | 36 | （0.033 25， 0.672 79， 0.615 30） | |
| 15 | （0.787 99， 0.435 66， 0.371 51） | 37 | （0.549 80， 0.890 58， 0.660 40） | |
| 16 | （0.122 35， 0.477 45， 0.504 56） | 38 | （0.298 60， 0.111 27， 0.308 30） | |
| 17 | （0.297 22， 0.291 65， 0.551 51） | 39 | （0.636 40， 0.499 50， 0.296 30） | |
| 18 | （0.321 45， 0.471 07， 0.879 74） | 40 | （0.824 54， 0.998 80， 0.981 20） | |
| 19 | （0.831 73， 0.542 33， 0.048 44） | 41 | （0.971 44， 0.608 50， 0.847 90） | |
| 20 | （0.105 04， 0.866 72， 0.470 37） | 42 | （0.372 60， 0.688 90， 0.952 72） | |
| 21 | （0.048 52， 0.678 90， 0.475 20） | 43 | （0.611 60， 0.412 78， 0.091 30） | |
| 22 | （0.344 70， 0.201 90， 0.167 13） |
Fig. 2 Workflow of vision-based safflower recognition and localization system |
Table 2 Spatial distribution and 3D coordinates of 31 safflower targets |
| Spatial distribution | Lable | Coordinate points | Lable | Coordinate points |
|---|---|---|---|---|
| | 1 | （0.031 29， 0.153 36， 0.352 20） | 17 | （0.670 69， 0.953 60， 0.498 40） |
| 2 | （0.195 88， 0.113 25， 0.634 10） | 18 | （0.676 65， 0.848 85， 0.684 30） | |
| 3 | （0.345 74， 0.266 43， 0.769 10） | 19 | （0.701 89， 0.865 28， 0.642 40） | |
| 4 | （0.417 69， 0.398 49， 0.586 40） | 20 | （0.797 98， 0.896 00， 0.891 50） | |
| 5 | （0.170 80， 0.548 25， 0.781 10） | 21 | （0.766 78， 0.708 47， 0.688 10） | |
| 6 | （0.273 79， 0.629 54， 0.697 40） | 22 | （0.812 71， 0.784 00， 0.581 70） | |
| 7 | （0.100 57， 0.739 19， 0.826 40） | 23 | （0.853 47， 0.841 81， 0.724 50） | |
| 8 | （0.024 39， 0.693 11， 0.597 60） | 24 | （0.944 39， 0.759 25， 0.573 90） | |
| 9 | （0.092 73， 0.861 65， 0.837 10） | 25 | （0.919 31， 0.683 73， 0.649 20） | |
| 10 | （0.051 98， 0.953 60， 0.887 40） | 26 | （0.968 68， 0.692 05， 0.637 40） | |
| 11 | （0.187 26， 0.958 50， 0.682 74） | 27 | （0.878 55， 0.613 11， 0.695 20） | |
| 12 | （0.264 38， 0.914 77， 0.599 40） | 28 | （0.852 53， 0.497 48， 0.673 30） | |
| 13 | （0.473 02， 0.967 90， 0.726 40） | 29 | （0.971 19， 0.255 98， 0.488 40） | |
| 14 | （0.527 73， 0.798 08， 0.822 40） | 30 | （0.812 71， 0.277 10， 0.683 30） | |
| 15 | （0.582 28， 0.953 60， 0.742 70） | 31 | （0.730 42， 0.069 73， 0.268 40） | |
| 16 | （0.599 52， 0.966 62， 0.705 60） |
1.2 Combinatorial optimization problem formulation
Input definition: For the three-dimensional traveling salesman problem (3D-TSP), the input is defined as a set of 3D coordinates representing the positions of safflower filament, denoted as , where indicates the spatial location of the i-th safflowers.
Output definition: The model aims to output a visiting sequence , which satisfies the Hamiltonian circuit constraint, that is, each point is visited exactly once and minimizes the total tour length, defined as Equation (1) :
Where, denotes the total tour length, and is the total number of points.
Fig. 3 provides a detailed illustration of the process in which the safflower data, serving as the problem input, is processed by a RL pointer network model based on the Actor-Critic architecture, ultimately resulting in the output of the picking sequence.
Fig. 3 The process of modelling input to output of AC-RL-PrtNet |
1.3 Overview of the RL pointer network based on the Actor-Critic architecture
In solving combinatorial optimization problems, the integration of RL with pointer networks has demonstrated powerful modeling and decision-making capabilities. This approach adopts an end-to-end learning paradigm, enabling the autonomous exploration of high-quality path planning strategies in unknown environments. This section sequentially presents the long short-term memory (LSTM) based encoder-decoder architecture, the formulation of the markov decision process (MDP), the policy gradient method, and the specific implementation of the Actor-Critic dual network collaborative optimization within this framework.
1.3.1 Encoder-decoder architecture
1) Encoder: Spatiotemporal Feature Extraction with LSTM Traditional sequence modeling methods struggle to capture complex spatial relationships in three-dimensional space. In this study, a LSTM network is employed to process the input state sequence. Leveraging its recurrent structure, the LSTM can progressively integrate spatial neighborhood information across layers[29]. Given an input sequence , the encoder generates a sequence representation by recursively computing the hidden states, as shown in Equation (2) :
Where, denotes the hidden state corresponding to the t-th coordinate, which captures the contextual information of all picking points from the beginning up to the current step. After processing by the encoder, all hidden states are aggregated into a matrix, which serves as the input for the subsequent attention mechanism and decoding process. The initial hidden state is set to a zero vector. To determine an appropriate hidden layer dimension, an ablation study was conducted with three configurations: 64, 128 and 256. The models were evaluated based on total training time, best path length achieved, and model size. As shown in Table 4, the configuration with 128 hidden units achieved the best trade-off between optimization quality and computational cost. Therefore, a hidden size of 128 was adopted in the final model design.
Table 4 Ablation results for hidden state dimension |
| Hidden dim | Training time/s | Best path | Model size/MB |
|---|---|---|---|
| 64 | 1 672 | 11.856 | 4.251 |
| 128 | 1 998 | 11.414 | 4.462 |
| 256 | 2 920 | 11.186 | 5.282 |
2) Decoder: The decoder adopts an attention-driven LSTM structure, which takes as input the output from the previous time step and utilizes the contextual information produced by the encoder to generate an action probability distribution. The initial hidden state of the decoder, , is set to the final hidden state of the encoder. The decoding process at time step t involves the following steps:
(a) Attention weight calculation is shown in Equation (3) :
Where, , are learnable parameters; denotes the hidden state of the encoder at position; and d denotes the hidden layer dimension.
(b) Probability distribution generation is shown in Equation (4) :
Where, denotes the probability of selecting node at step , conditioned on the previously visited sequence and the input feature set .
(c) State update is shown in Equation (5) :
Where, denotes the long short-term memory network used to update the decoder state, represents the hidden state of the decoder at the previous time step, and maps the index of the selected node to an embedding vector. To prevent repeated visits, a masking mechanism is employed during the calculation of , where the logits corresponding to already visited nodes are assigned a value of , thereby ensuring that only feasible paths are generated.
1.3.2 MDPmodeling
RL enables agents to interact with their environment to learn optimal strategies. In the context of the TSP, the problem solving process can be formulated as a MDP. Specifically, the state space is defined as the set of unvisited safflower coordinates at each step. For example, the state at time step t is defined as: indicating the set of nodes not yet visited up to step t. Transitions between states correspond to selecting an unvisited node to visit next. For instance, given the current state , executing an action (selecting a new target node ) results in the next state: .
In the reinforcement learning framework, the reward function is defined based on the negative Euclidean distance between consecutive nodes, as shown in Equation (6) :
Where, represents the return to the starting node. The immediate reward denotes the negative squared Euclidean distance between two consecutive nodes. The total return is the negative sum of travel distances along the path as Equation (7) :
Where denotes the length of the current path under policy .
To guide the agent's behavior, a neural network based on parameterized stochastic policy function is adopted as Equation (8) :
Where, X represents the set of all safflower coordinates, and denotes the stochastic policy parameterized by , which gives the probability of selecting action under the current state . The policy outputs a probability distribution over the available actions (unvisited nodes) and determines the likelihood of selecting each one at the current step.
By combining the policy network with a value function estimator, the training is performed using the advantage Actor-Critic algorithm, which allows for efficient gradient based policy optimization.
1.3.3 Policy gradient method
The policy gradient method optimizes the policy parameters directly to maximize the expected cumulative reward. The core idea is to increase the probability of actions leading to high-return trajectories, while suppressing those associated with lower returns. The objective function is defined as the expected return, as shown in Equation (9) :
Where, denotes the expected cumulative reward under policy , and represents the learnable parameters of the policy network.
According to the policy gradient theorem[30], the gradient can be written as shown in Equation (10) :
Where, denotes the action-value function under policy , representing the expected return after taking action in state . Since directly computing requires trajectory rollout, which is computationally expensive, it is often approximated by the empirical return, as shown in Equation (11) :
Thus, the gradient update can be simplified as shown in Equation (12) :
Where, B is the batch size. However, this estimation often suffers from high variance, which may hinder stable convergence. To mitigate this issue, a baseline function was introduced to reduce variance without biasing the gradient, as expressed in Equation (13) :
1.3.4 Actor-Critic architecture and policy
To address the complex of 3D safflower picking, this study adopts a collaborative optimization framework based on the Actor-Critic architecture. The agent interacts with the environment to continuously improve its policy without requiring accurately labeled data. The overall interaction between the environment, the Actor network, and the Critic network is illustrated in Fig. 4, which demonstrates the flow of information, decision making, and policy update processes involved in this reinforcement learning framework.
Fig. 4 An interactive Actor-Critic decision framework for 3D safflower picking tasks |
The Actor network is implemented using a pointer network, essentially serving as a parameterized policy function responsible for generating the probability distribution over actions for dynamic path planning (as in Equation (4) ). In the context of the 3D TSP, the actor leverages the attention mechanism in the decoder (as described in Equation (3) ) to capture global spatial features extracted by the encoder. It then combines these features with the current state to produce a prioritized ranking of candidate nodes. Unlike traditional greedy algorithms, the Actor selects the next node through probabilistic sampling. For example, during training, a multinomial distribution is used to sample actions, ensuring sufficient exploration of the solution space. The policy gradient signal in reinforcement learning (as defined in Equation Eq. (12) ) directly influences this probability distribution, increasing the likelihood of actions associated with high-reward trajectories while suppressing the generation of inefficient paths.
The Critic network functions as an independent evaluation module, responsible for estimating the expected return under the current state and policy . Structurally, it resembles the encoder, but employs a parameter separated LSTM network (nonshared with the Actor encoder). By aggregating the hidden representations of unvisited nodes (as in Equation (2) ), the Critic produces a global value representation. A key role of the Critic is to provide a dynamic baseline (Equation (3) ), which transforms the original Monte Carlo return into the advantage function, as shown in Equation (14) :
Where, denotes the advantage of taking action at state under policy , and represents the Critic's estimate of the expected return from state with parameters , This formulation effectively reduces the variance of gradient estimation and enhances the stability of policy optimization.
The Critic loss function aims to minimize the mean squared error between the predicted value function and the actual expected return, thereby driving to approximate the expected return more accurately, as defined in Equation (5) :
Where, denotes the batch size, is the total return of the -th sampled trajectory.
The Actor loss function maximizes the advantage weighted log probability (Equation (6) ), adjusting the policy optimization direction based on the advantage value:
Where, denotes the advantage function of the -th trajectory; the operator refers to the natural logarithm applied to the policy probability, which is used to compute the policy gradient in the actor-critic framework.
2 Algorithm improvement
In the original RL based pointer network for path planning, the attention mechanism adopts a classical singlehead linear transformation structure. However, this design suffers from the following issues:
(1) Static weight allocation: All safflower positions share the same attention computation logic, making the model prone to focusing on local optima rather than the global optimal path.
(2) Limited representational capacity: A single attention head struggles to simultaneously capture efficient traversal patterns in dense regions and the priority features of edge positioned flowers. When the flower density varies significantly in the central region, the traditional mechanism often produces intersecting paths with repeated coverage rates as high as 15%~20%[31].
(3) Slow inference and decision making: The model exhibits latency during path generation.
To address these issues, this chapter replaces the original attention mechanism with a DEMA attention, which enhances the model's ability to capture spatial information. Additionally, pruning techniques are applied to the LSTM network to further improve inference efficiency and overall model performance.
2.1 Dynamic exponential moving average attention mechanism
The introduction of the EMA-based attention mechanism enables the model to balance current observations with historical attention trends, thereby enhancing temporal stability, smoothing attention distributions, and improving robustness in dynamic spatial environments[32]. As illustrated in Fig. 5 for the improved DEMA, to improve spatial sensitivity, the enhanced DEMA attention mechanism incorporates distance encoding directly into the computation process. Initially, the input undergoes multi-head partitioning, during which spatial distance information is embedded to enrich feature representation. This is followed by an adaptive reweighting phase driven by dynamic exponential moving average calculations. Subsequently, a nonlinear projection layer refines the aggregated context into the final attention output. Through the integration of present contextual cues, temporal dynamics, and spatial layout, the module is better equipped to model inter-flower relationships and generate more precise path planning outcomes. The key components of this improved attention pipeline are elaborated in the subsequent subsections.
Fig. 5 Computational flow of the DEMA attention mechanism |
2.1.1 Redefinition of multi head self attention
The improved attention module divides the embedding dimensions into multiple subspaces, enabling the model to capture diverse environmental features in parallel, such as sharp distributional changes and local density variations. Meanwhile, a dynamic decay parameter is initialized and constrained within a predefined range to balance the influence of the current attention with that of the historical global average attention.
2.1.2 Incorporation of distance encoding
To incorporate spatial topology information into the attention mechanism, a distance-encoding module is introduced. Specifically, the Euclidean distances between flower positions are used as additional inputs, transformed into vector representations through a linear projection, and then fused with the query vectors to compute the attention scores. It is as follows Equation (7) :
Where, denotes the Euclidean distance between the -th and -th safflower positions, represents the learnable projection weight matrix, is the corresponding bias vector.
This design enables the attention weights to reflect not only semantic similarity but also spatial distance, thereby enhancing the model's ability to capture relative positional relationships between flowers in path planning.
2.1.3 Adaptive EMA weight adjustment
Traditional attention mechanisms typically rely solely on the current state to compute attention scores, without incorporating historical statistical information. To address this, an adaptive EMA weight adjustment strategy is introduced, defined as in Equation (18) :
where, is a dynamic decay factor, and represents the attention scores at the current step. Specifically, represents the attention scores from the previous time step to make responsive to spatial layout variations. It is defined as a function of local target density, as shown in Equation (19) :
Where, represents the spatial density of picking targets around the current query position at time step , and is a tunable scaling parameter. This formulation allows the model to emphasize past attention in high-density regions (smaller ) while prioritizing current observations in sparse areas (larger ), thereby enhancing stability and adaptability in dynamic environments. This EMA-based adjustment balances the current state with past attention trends, enabling the model to adaptively respond to abrupt environmental changes, maintaining a more stable and globally aware attention distribution. This leads to smoother and more effective path planning.
2.1.4 Nonlinear transformation of output
The EMA-adjusted attention scores are used to compute a weighted sum of the value vectors, producing the attention context, as shown in Equation (20) :
Where represents the attention context at time step , denotes the EMA-adjusted attention weights, and refers to the value vectors associated with each input.
The resulting context vector is then passed through a nonlinear transformation using a ReLU activation to enhance feature representation, as shown in Equation (21) :
The terms and denote the weights and biases of the first and second fully connected layers, respectively. This nonlinear transformation further enhances the feature composition capability, enabling the network to better capture complex inter object relationships in the picking task.
2.2 Network pruning
In recent years, the increasing complexity and computational cost of Deep Neural Network models have become major challenges. To reduce the consumption of computational resources without significantly compromising model performance, network pruning techniques have been extensively studied[33,34]. Among them, structured pruning has attracted considerable attention due to its ability to directly eliminate redundant structures in the computational graph, thereby facilitating hardware acceleration[35-37]. In this work, a structured pruning method is proposed for the gated architecture of LSTM networks, focusing on pruning the input and output gates. Additionally, L1-based pruning is applied to the fully connected layers, aiming to reduce model parameters and accelerate inference.
2.2.1 LSTM gate importance based pruning strategy
Given the structural characteristics of LSTM components in recurrent neural networks, this pruning strategy selectively targets the input and output gates, where parameter redundancy is notably more prevalent. This decision is grounded in the following theoretical considerations:
(1) Parameter distribution analysis: Examination of the gate weight matrices indicates a heavy-tailed distribution, particularly within the input and output gates, suggesting that many weights contribute minimally to the model's expressive capacity.
(2) Criticality of the forget gate: Empirical evidence from initial tests shows that even small perturbations in the forget gate's parameters can lead to a marked drop in performance, implying that its preservation is essential for maintaining temporal stability.
(3) Functional complementarity: The input and output gates are responsible for encoding and exposing temporal information, respectively. Their interdependent functions permit synchronized pruning without compromising the LSTM's representational capability.
2.2.2 Structured pruning implementation for gate structures
For a given weight matrix (i.e., or ) and the selected gate indices , the pruning procedure is carried out as follows. First, determine the range of gate indices for the input gate and the output gate .
Next, the pruning threshold is computed. For the selected gate, let denote the corresponding weight parameter vector, and define the pruning ratio. The number of parameters to be pruned is given by Equation (22) :
Where, is the number of pruned parameters, and represents the pruning ratio that determines the overall sparsity level.
The pruning threshold is computed as the maximum among the smallest absolute weight values, as shown in Equation (23) :
Based on a pruning mask is generated as follows, as shown in Equation (24) :
Only the parameters within the target gate indices are pruned, while weights outside this scope remain unchanged.
Finally, the weight matrix is updated by applying the pruning mask, so that the pruned weight matrix is expressed as:
Where, denotes the concatenation of the unpruned segments, and denotes element wise multiplication.
The pruning operation is applied separately to the input and output gates for both and . Experimental validation shows that the encoder adopts a pruning ratio of 35% for both its input and output gates, while the decoder uses a pruning ratio of 25% for these gates.
2.3 Structural enhancements of the critic network
To further improve the value estimation capability for planned paths, this work introduces structural-level enhancements within the Critic network. Although these enhancements do not directly impact the decoder's decision-making process, they play a vital role in supplying more stable, structure-aware prediction signals. This indirectly boosts the learning efficiency of the Actor module and enhances the overall synergy of the Actor-Critic framework.
2.3.1 Enhanced input embedding with normalization mechanisms
To increase the expressive power of the original spatial coordinates in high-dimensional latent space, the Critic integrates a normalization-augmented embedding layer at the input stage. Specifically, Batch Normalization is applied to raw inputs, followed by two fully connected layers with ReLU activations. This is further regularized by Layer Normalization and Dropout to improve discriminative power and generalization under spatial variability. The embedding process is formulated as follows, as shown in Equation (26) :
Where, represents the raw coordinate of the node, is the embedded feature, and are trainable weights. Layer normalization and dropout jointly stabilize the feature distribution and mitigate overfitting.
2.3.2 Contextual aggregation from LSTM encoder
The Critic network adopts the same LSTM encoder as the Actor to generate a sequence of hidden representations for the path, as formulated in Equation (27) :
Where encodes the entire sequence and denotes the final hidden state. This serves as a condensed global representation of the path, which is then used as the query in the subsequent attention-based value refinement module.
2.3.3 Lightweight attention-based context fusion
To enhance the Critic's sensitivity to critical waypoints along the path, a lightweight attention fusion mechanism is introduced to amplify the response to important spatial cues. This module learns to attend selectively to key positions within the LSTM-encoded trajectory. First, the sequence output H is projected using a 1D convolutional layer to produce reference features, as shown in Equation (28) :
Where, represents the learnable convolutional weight matrix that projects the hidden representations into the reference feature space, while is the transposed sequence output obtained from the shared LSTM encoder.
Simultaneously, the query vector is mapped to the same dimensionality, as shown in Equation (29) :
Where, represents the transformed query feature that aligns with the reference feature space, enabling compatibility computation with , denotes the learnable projection matrix used to map the final hidden state into the query space.
A joint compatibility function is then computed via, as expressed in Equation (30) :
Attention weights are derived using a learnable vector , as defined in Equation (31) :
These weights are used to obtain a context vector via weighted aggregation, as described in Equation (32) :
Where, denotes the context vector obtained through weighted aggregation of all hidden representations. The final output for value estimation is obtained by combining the context vector with the original query and feeding it into a prediction MLP, as shown in Equation (33) :
This design allows the Critic to capture both the global structure and local saliency of the path, improving the accuracy of cost prediction and facilitating better guidance for policy updates in the Actor network.
2.4 Algorithm learning method
In light of the aforementioned modifications, this work employs an improved Reinforcement Learning Pointer Network (AC-RL-PtrNet). Each time a path sequence is generated, the DEMA attention mechanism automatically computes the attention scores, thereby yielding more reasonable picking decisions. The pruning operations also improve the training speed while maintaining model performance with minimal loss. Algorithm 1 outlines the pseudocode for the training process.
In the training task, is set to 40. The experiments were conducted on a Windows 1 064-bit machine equipped with an NVIDIA GeForce RTX 4060 Ti GPU, an Intel Core i5-14600KF CPU @ 3.5 GHz, and 32 GB of RAM. The implementation utilizes PyTorch 2.0 with CUDA 12.1 under Python 3.12.7. Training samples are randomly generated from space. To ensure good generalization performance, the model is trained for 2 000 epochs, with each epoch comprising 10 steps. The batch size is set to 256 and the initial learning rate is 0.001, with a decay factor of 0.96 applied every 5 000 steps. Both the Actor and Critic networks are trained via the Adam optimizer to minimize their respective loss functions. To clearly describe the optimization process of the proposed model, the detailed training steps of the actor–critic framework are presented in the below algorithm.
| Training Algorithm |
|---|
| Input： Number of training iterations S， batch size B |
| Output： Optimal path Initialize： （with internal dynamic EMA attention module）， ， Optimizer and learning rate |
| for t= 1 to S do： |
| The Actor network generates B trajectories via a DEMA-based attention mechanism：
|
| Compute reward R（π） and log-probability：
|
| Value estimation using the Critic network：
|
| Compute advantage：
|
| Update Actor： Backpropagate the error through the LSTM-based DEMA module in the Actor network：
|
| Update Critic using mean-squared error loss：
|
| end for： Return to the shortest path |
3 Experiments and results
To validate the effectiveness of the proposed model in addressing the safflower picking sequence planning problem, a simulation-based analysis was conducted. The performance of the model was evaluated using metrics such as path length and average runtime. In this chapter, all safflowers coordinates are normalized to enhance numerical stability and mitigate gradient explosion. In Section 3.5, the actual three-dimensional picking paths are reconstructed to provide a visual representation of the real trajectories.
3.1 Impact of DEMA on the model
To evaluate the influence of the DEMA attention mechanism on model performance, analyses were conducted during both the training and testing phases. The baseline model refers to the original unmodified network. In the training phase, comparative experiments were carried out with the baseline model, graph attention network (GAT), efficient multi-scale attention (EMSA), seer attention mechanism (SeA), DEMA without distance information (NoDist-DEMA), and the DEMA-enhanced model. Fig. 6 illustrates the convergence curves for these models during training. The results indicate that the DEMA-based model achieves superior improvements in terms of path length compared to the other methods. Moreover, it demonstrates faster convergence at approximately 200 epochs and avoids getting trapped in local optima, thereby attaining a better convergence value. It is noted, however, that increasing the number of training epochs necessitates more training time.
Fig. 6 Iterative convergence comparison of various attention mechanisms against the baseline |
Based on the inherent randomness in the number of safflower picks per run, the model was tested with n=20, 28, 37, and 46 (as shown in Table 5). The results indicate that, for n=20 and n=37, the improved SeA attention mechanism yields path lengths comparable to those of the DEMA-enhanced model. However, in terms of average runtime, the SeA mechanism requires 1.5 to 2 times longer than the DEMA model. In comparison to the baseline model, the proposed approach not only significantly reduces the path length but also nearly doubles the average inference speed. Compared to the NoDist-DEMA variant, which excludes distance encoding, the full DEMA model consistently achieves marginally shorter path lengths and faster inference across all test cases. This demonstrates that integrating distance information enhances both spatial perception and planning efficiency, further validating the design of the DEMA attention mechanism.
Table 5 Comparison of results of different architectures under various numbers of safflower points |
| Method | n=20 | n=28 | n=37 | n=46 | ||||
|---|---|---|---|---|---|---|---|---|
| Length /cm | Time/s | Length/cm | Time /s | Length/cm | Time/s | Length /cm | Time/s | |
| baseline | 6.769 | 90.83 | 8.524 | 183.26 | 10.299 | 368.36 | 11.806 | 511.05 |
| GAT | 7.399 | 98.46 | 12.064 | 197.85 | 16.638 | 414.79 | 23.665 | 602.34 |
| EMSA | 8.321 | 126.12 | 11.992 | 254.96 | 15.251 | 496.07 | 19.019 | 582.41 |
| SeA | 6.675 | 63.07 | 8.404 | 185.84 | 9.940 | 327.68 | 11.433 | 510.73 |
| NoDist-DEMA | 6.719 | 59.32 | 8.346 | 123.94 | 10.145 | 231.76 | 11.402 | 304.78 |
| DEMA | 6.674 | 51.01 | 8.302 | 113.74 | 10.058 | 224.29 | 11.398 | 334.62 |
|
As shown in Table 5, the numerical results have demonstrated the performance differences of various attention mechanisms in terms of path length and computation time across multiple test points. To further visualize these differences and highlight the advantages of the proposed method, Fig. 7 presents a color matrix that fully reflects the differences in path planning quality and robustness among various attention mechanisms at different test points. The numerical values in the figure represent the differences in path performance relative to the baseline model, with larger positive values indicating greater improvements. In terms of path length, the DEMA model demonstrates a more substantial enhancement, especially when the number of safflower picking points ranges from 37 to 50—yielding improvements between 0.2 cm and 0.41 cm. Moreover, the DEMA model consistently maintains deeper color values across most test points, indicating its superior performance in path quality. Although the SeA model exhibits performance comparable to the DEMA model in certain scenarios, Table. 5 shows that its runtime is inferior to that of the DEMA approach. These results indicate that the incorporation of the DEMA attention mechanism can significantly enhance both the planning efficiency and the accuracy of safflower picking.
Fig. 7 Path length gap of different models at different test points |
3.2 Impact of pruning on the model
Different pruning strategies based on the importance of the gates were designed and evaluated during both the training and testing phases. In this study, three pruning strategies were compared:
(1) Group A: Both the encoder and decoder input and output gates are pruned by 35%.
(2) Group B: Both the encoder and decoder input and output gates are pruned by 25%.
(3) Group C: The encoder input and output gates are pruned by 35%, while the decoder gates are pruned by 25%.
Table 6 presents the comparative results for these three strategies. Preliminary sensitivity experiments indicated that when the pruning ratio was lower than 25%, the computational benefits were negligible, and when it exceeded 35%, the model experienced severe information loss and degraded performance. Therefore, these three representative configurations were selected for analysis.
Table 6 Comparison of results for different pruning strategies of the proposed model |
| Strategy | Encoder pruning | Decoder pruning | Params | Sparsity/% | Training Time/s | Speedup/% | |||
|---|---|---|---|---|---|---|---|---|---|
| Input gate | Output gate | Input gate | Output gate | Initial （×105） | Modified （×105） | ||||
| Group A | 0.35 | 0.35 | 0.35 | 0.35 | 4.462 | 4.106 | 8 | 161 | —— |
| Group B | 0.25 | 0.25 | 0.25 | 0.25 | 4.265 | 4.44 | 1 747 | 12 | |
| Group C | 0.35 | 0.35 | 0.25 | 0.25 | 4.201 | 5.88 | 1 698 | 15 | |
|
Analysis shows that the model under Group A achieves an offline training duration of less than 3 minutes; however, the excessive pruning applied to the decoder in Group A leads to significant information loss, causing the model to become trapped in local optima. In contrast, Group C adopted in this study yields a parameter sparsity of approximately 5.88%, effectively removing redundant information and enhancing training speed by about 15%, while simultaneously reducing model size and inference overhead. Therefore, implementing pruning operations on the LSTM not only optimizes computational speed but also decreases memory usage.
3.3 Ablation study on model enhancements
To further evaluate the individual and cumulative contributions of each proposed enhancement — including the DEMA attention mechanism, the structured pruning strategy, and the improved Critic network — an ablation study was conducted. Specifically, four configurations were compared: 1) the baseline model without any enhancement, 2) the model with DEMA only, (3) the model with DEMA and pruning, and (4) the full model integrating DEMA, pruning, and the enhanced Critic. To this end, we will validate this ablation experiment on test sets with 25, 31, and 43 safflowers.
As shown in Table 7, although the full model exhibits slightly longer inference time compared to the previous variant under the 25-target scenario, it consistently achieves superior performance across other datasets in terms of path length reduction and inference robustness. These results indicate that the proposed model enhancements are well-suited for sequential path planning in safflower picking tasks.
Table 7 Ablation study on model enhancements |
| baseline | DEMA | Pruning | The enhanced Critic | n=25 | n=31 | n=43 | |||
|---|---|---|---|---|---|---|---|---|---|
| Length/cm | Time/s | Length/cm | Time/s | Length/cm | Time/s | ||||
| √ | 6.674 | 88.08 | 6.749 | 167.35 | 11.426 | 497.50 | |||
| √ | 5.930 | 80.86 | 6.647 | 127.00 | 11.049 | 262.47 | |||
| √ | √ | 5.907 | 63.00 | 6.441 | 125.00 | 11.043 | 244.27 | ||
| √ | √ | √ | 5.826 | 69.79 | 6.356 | 94.90 | 10.784 | 244.50 | |
3.4 Comparison with swarm intelligence algorithms
In this experiment, the performance of the proposed model (before and after improvement) was compared with traditional swarm intelligence algorithms, including particle swarm optimization (PSO), the non-dominated sorting genetic algorithm (NSGA), and ACO, in the task of safflower picking path planning. The evaluation was conducted using two test cases with safflower quantities of n=25 and n=31, focusing on metrics such as path length, computational time, and speed improvement.
As shown in Table 8, swarm intelligence algorithms tend to require significantly longer runtimes in real-world deployment scenarios. Using AC-RL-PtrNet as the baseline for improvement rate comparisons, test cases with n = 25 and n = 31 safflowers were evaluated. The proposed model achieved inference speed improvements ranging from -2.63% to 61.87% for the 25-safflower case and 22.93% to 59.10% for the 31-safflower case, along with path length reductions between 4.24% and 61.47%, compared to traditional swarm intelligence algorithms such as PSO, ACO, and NSGA. Improvement Rate (%) represents the relative time-saving of AC-RL-PtrNet compared to each method, calculated as . A higher value indicates that AC-RL-PtrNet provides a more significant improvement over the other methods. To assess the statistical significance of these improvements, independent two-sample t-tests were performed on 30 repeated runs. The results in Table 8 indicate that this method achieves statistically significant path length reductions over all baselines (p < 0.05), confirming the robustness of the observed gains.
Table 8 Comparison of the proposed AC-RL-PtrNet model with traditional algorithms |
| Method | n=25 | n=31 | ||||||
|---|---|---|---|---|---|---|---|---|
| Length/cm （p-value） | Improvement rate/% | Time/s | Improvement Rate/% | Length /cm （p-value） | Improvement rate/% | Time/s | Improvement Rate/% | |
| Baseline | 6.084（p<0.008 0） | 4.24 | 82.00 | 14.85 | 6.913 0（p<0.005） | 8.07 | 215.0 | 55.86 |
| PSO | 15.123 （p<0.001 0） | 61.47 | 183.00 | 61.87 | 15.437 5 （p<0.001） | 58.82 | 232.0 | 59.10 |
| ACO | 7.09（p<0.001 0） | 17.84 | 104.00 | 32.91 | 6.966 2（p<0.001） | 8.75 | 123.0 | 22.93 |
| NSGA | 6.44（p<0.003 6） | 9.56 | 68.00 | -2.63 | 7.960 0（p<0.001） | 20.17 | 135.0 | 29.70 |
| AC-RL-PtrNet | 5.826 | — | 69.79 | — | 6.356 0 | — | 94.9 | — |
|
In the test case with 25 safflowers, although the NSGA algorithm achieves a shorter runtime than the improved AC-RL-PtrNet model, the latter yields a 9.56% improvement in path optimization, demonstrating a significantly higher planning efficiency. It is important to note that reinforcement learning operates in an offline training and online inference paradigm. This means that as the number of safflower targets increases, this model does not require retraining for each new instance, unlike swarm intelligence algorithms, which need to re-optimize from scratch for different configurations. This advantage makes this approach more suitable for real-time, responsive applications in safflower picking scenarios.
Furthermore, as shown in Table 8, the AC-RL-PtrNet generates shorter paths than swarm intelligence algorithms in both the n=25 and n=31 test cases, with statistically significant improvements. It reduces the path length by 0.258 and 0.557 cm units compared to the baseline, respectively. Notably, the pruning strategy introduced in this model does not result in significant loss of positional information, thereby achieving a desirable balance between path optimization and inference efficiency.
3.5 Field experiment
3.5.1 Field setup and real-world planning examples
To validate the practical feasibility of the proposed method, real-world field experiments were conducted in Jimusaer county, Xinjiang, using this safflower-picking robot in an open agricultural environment. As shown in Fig. 8a, the robot was deployed in a safflower field and executed picking path planning in real time. Two representative test cases involving 25 and 31 safflower blossoms were selected for demonstration, corresponding to different safflower varieties, as illustrated in Fig. 8b and Fig. 8c, respectively. These scenarios provide a practical basis for evaluating the performance of this model under different spatial configurations and picking densities.
Fig. 8 Field experiment setup and example planning results for 25 and 31 safflower blossoms |
3.5.2 Analysis of sequence planning results
To further evaluate the real-world effectiveness of the proposed model, we conducted a comparative analysis against NSGA, the best-performing baseline among the traditional optimization algorithms, across two representative safflower varieties and picking scenarios-25 and 31 blossoms of Yuhong No.1 and Yunhong No.5, respectively. The results, summarized in Table 9, demonstrate that the AC-RL-PtrNet model consistently outperformed NSGA in both path and time efficiency. Specifically, this model achieved reductions of 11.52% and 20.17% in path length, as well as 5.43% and 29.70% in picking time across the two scenarios.
The corresponding sequence planning visualizations are presented in Fig. 9. Fig. 9a and Fig. 9b correspond to the sequence planning results for 25 and 31 safflowers, respectively. Fig. 9(c–f) illustrate the comparison between NSGA and AC-RL-PtrNet under the two scenarios. The visual comparison highlights that the paths generated by the AC-RL-PtrNet model are not only shorter but also more structured and efficient than those produced by the NSGA algorithm, which tends to generate redundant and crossover-prone paths. In contrast, the AC-RL-PtrNet model demonstrates superior balance between global path optimization and local adjustment, producing more regular and structured paths. The node connections are more consistent with the spatial distribution of the targets, revealing a more ideal 3D TSP planning capability, as well as enhanced intelligence and practical applicability. These visual results further confirm that the proposed approach can effectively generate optimal picking sequences even in complex environments characterized by densely clustered or unevenly distributed safflowers.
Fig. 9 Comparison of safflower picking sequence planning on 25 and 31 flowers |
In summary, the improved model exhibits notable advantages in extracting spatial distribution features of safflowers, while the introduced pruning strategy effectively reduces computational redundancy and enhances decision-making efficiency. These strengths make it a robust, stable, and efficient solution for intelligent safflower picking tasks.
4 Conclusion
This study focuses on the task of automatic safflower picking and, by considering the structural characteristics of a parallel picking robot platform, proposes a sequence planning algorithm based on a reinforcement learning pointer network under the Actor-Critic framework. The proposed method is specifically designed for integration into safflower-picking robots, addressing the complex path planning needs encountered in unstructured agricultural environments. To address redundant paths and low time efficiency in traditional methods, we integrate a DEMA attention mechanism with distance encoding into the actor network, enhancing its ability to model spatial relationships among safflowers. A structured pruning strategy is also applied to the LSTM gating units and fully connected layers, effectively reducing model complexity while preserving performance. Furthermore, a novel enhancement to the critic network is introduced. This involves a refined embedding and attention formulation, incorporating input normalization, multi-layer residual connections, and an improved prediction module, significantly improving value estimation accuracy and training stability. The complementary design between actor and critic components ensures more consistent policy optimization during learning. In the experimental section, the sequential safflower picking problem is reformulated as a three-dimensional traveling salesman problem. Ablation studies reveal that each of the three enhancements—DEMA attention, LSTM pruning, and critic refinement—contributes incrementally to overall performance gains in both inference time and path quality. Furthermore, empirical comparisons with established swarm intelligence algorithms—such as PSO, NSGA and ACO—demonstrate that this method consistently delivers shorter traversal routes and improved planning efficiency under different target distributions. In real-world validation involving datasets of 25 and 31 safflowers, the proposed approach surpasses the strongest baseline NSGA, confirming its practical advantages. These results highlight the framework's applicability in real-time field deployment and its effectiveness in improving path planning capabilities of safflower-picking robots. Additionally, due to the generality of the 3D TSP formulation and the modular design of the AC-RL-PtrNet architecture, this method has strong potential for transferability to other agricultural applications such as tomato, strawberry, or pear picking. The DEMA attention and pruning strategies can also be reconfigured to accommodate different spatial complexities, object densities, and environmental conditions, making the proposed framework a promising solution for a wider class of 3D sequence planning tasks in precision agriculture. These findings affirm the robustness and adaptability of the AC-RL-PtrNet framework in complex agricultural environments, emphasizing its potential for enhancing automated safflower picking performance.
