Planning Model Research Articles

Evaluation of knowledge-based planning models for male pelvic CBCT-based online adaptive radiotherapy on conventional linear accelerators.

To assess the practicality of employing a commercial knowledge-based planning tool (RapidPlan) to generate adapted intact prostate and prostate bed volumetric modulated arc therapy (VMAT) plans on iterative cone-beam computed tomography (iCBCT) datasets. Intact prostate and prostate bed RapidPlan models were trained utilizing planning data from 50 and 44 clinical cases, respectively. To ensure that refined models were capable of producing adequate clinical plans with a single optimization, models were tested with 50 clinical planning CT datasets by comparing dose-volume histogram (DVH) and plan quality metric (PQM) values between clinical and RapidPlan-generated plans. The RapidPlan tool was then used to retrospectively generate adapted VMAT plans on daily iCBCT images for 20 intact prostate and 15 prostate bed cases. As before, DVH and PQM metrics were utilized to dosimetrically compare scheduled (iCBCT Verify) and adapted (iCBCT RapidPlan) plans. Timing data was collected to further evaluate the feasibility of integrating this approach within an online adaptive radiotherapy workflow. Model testing results confirmed the models were capable of producing VMAT plans within a single optimization that were overall improved upon or dosimetrically comparable to original clinical plans. Direct application of RapidPlan on iCBCT datasets produced satisfactory intact prostate and prostate bed plans with generally improved target volume coverage/conformality and rectal sparing relative to iCBCT Verify plans as indicated by DVH values, though bladder metrics were marginally increased on average. Average PQM values for iCBCT RapidPlans were significantly improved compared to iCBCT Verify plans. The average time required [in mm:ss] to generate adapted plans was 06:09±02:06 (intact) and 07:12±01:04 (bed). This study demonstrated the feasibility of leveraging RapidPlan to expeditiously generate adapted VMAT intact prostate and prostate bed plans on iCBCT datasets. In general, adapted plans were dosimetrically improved relative to scheduled plans, emphasizing the practicality of the proposed approach.

Break Out of the Sea Surface: Genetic Algorithm based Search Path Planning Model for Locating and Searching Submersible Lost in Deep Sea

Deep-sea tourism and exploration, which require regulatory approval due to safety concerns, are burgeoning entertainment activities. Our study introduces a probabilistic model for locating missing submersibles to facilitate these approvals. The model predicts the submersible's location based on Newton's second law, analyzing three potential malfunction scenarios. It incorporates dynamics to account for variations in water flow and terrain, using a normal distribution to handle random location fluctuations. To address the complexities of deep-sea search and rescue, we propose a method that integrates detailed equipment selection, suited to the extreme conditions. Furthermore, we develop a discrete grid-based model for search path planning. This model simplifies path planning into a sorting optimization problem by connecting grid centers and calculating the probability integral for each grid. Our research also discusses the scalability of our positioning and search models, crucial for adapting to various deep-sea environments. We demonstrate the efficacy of our model through simulations and calculations, proving its potential to enhance safety and efficiency in deep-sea tourism projects. This comprehensive approach ensures that our probabilistic model not only predicts the submersible's location but also optimizes the search process, addressing both regulatory and practical challenges in the field of underwater exploration.

Coordinated energy storage and network expansion planning considering the trustworthiness of demand-side response

The enhancement of economic sustainability and the reduction of greenhouse gas (GHG) emissions are becoming more relevant in power system planning. Thus, renewable energy sources (RESs) have been widely used as clean energy for their lower generation costs and environmentally friendly characteristics. However, the strong random uncertainties from both the demand and generation sides make planning an economic, reliable, and ecological power system more complicated. Thus, this paper considers a variety of resources and technologies and presents a coordinated planning model including energy storage systems (ESSs) and grid network expansion, considering the trustworthiness of demand-side response (DR). First, the size of a single ESS was considered as its size has a close effect on maintenance costs and ultimately affects the total operating cost of the system. Second, it evaluates the influence of the trustworthiness of DR. Third, multiple resources and technologies were included in this high-penetration renewable energy integrated power system, such as ESSs, networks, DR technology, and GHG reduction technology. Finally, this model optimizes the decision variables such as the single size and location of ESSs and the operation parameters such as thermal generation costs, loss load costs, renewable energy curtailment costs, and GHG emission costs. Since the problem scale is very large not only due to the presence of various devices but also both binary and continuous variables considered simultaneously, we reformulate this model by decomposition. Then, we transform it into a master problem (MP) and a dual sub-problem (SP). Finally, the proposed method is applied to a modified IEEE 24-bus test system. The results show computational effectiveness and provide a helpful method in planning low-carbon electricity power systems.

Characteristics of Project-Based Learning Models on the Project to Strengthening the Pancasila Student Profiles at Muhammadiyah School

The Project for Strengthening the Pancasila Student Profile utilized a Project-based Learning (PjBL) approach, distinguishing it from intracurricular PjBL programs. The implementation of this project in schools remains complex due to its novelty and the ongoing search for an effective model for planning, implementation, and evaluation. The objectives of this study were as follows: (1) to describe the implementation of the PjBL model in the Project for Strengthening the Pancasila Student Profile at a Muhammadiyah junior high school in Batu City, (2) to describe the development of the Pancasila Student Profile after the implementation of the PjBL model in the Project for Strengthening the Pancasila Student Profile, and (3) to outline the challenges faced by the school and their corresponding solutions in implementing the PjBL model in the Project for Strengthening the Pancasila Student Profile. This research adopted a descriptive and qualitative approach. Data collection techniques encompassed in-depth interviews, observations, and documentation studies. The findings revealed that: (1) the implementation of the PjBL model in the Project for Strengthening the Pancasila Student Profile commenced with material mastery, followed by project execution, and concluded with a celebration, (2) the students demonstrated good character development in alignment with the Pancasila Student Profile, which consists of six competencies formulated as key dimensions, and (3) the encountered challenges in implementing the PjBL model in the Project for Strengthening the Pancasila Student Profile included difficulties in determining the appropriate time for implementing the P5 Project due to the teachers' busy schedules. In conclusion, the activities of the Project for Strengthening the Pancasila Student Profile, utilizing the PjBL approach, have been successfully carried out and have led to the formation of the Pancasila student profile, although there have been implementation obstacles. The best practices observed at Muhammadiyah Middle School in Batu City can serve as an inspiration for other Muhammadiyah schools and private institutions. Widespread implementation of such practices poses a challenge for future researchers.

The inclusion of improved forest management in strategic forest planning and its impact on timber harvests, carbon and biodiversity conservation

In forestry, although the so-called nature-based climate solutions have usually been focused on the calculation of carbon captured in new afforestation projects, it should be noted that the increase in carbon associated with improvements in their management (Improved Forest Management) can also be computed. This type of carbon is not usually integrated into strategic forest planning models, nor has its possible degree of conflict with other regulation ecosystemic services, like biodiversity conservation, been verified. In this research, those two issues have been approached by calculating a baseline in an emblematic forest with an extensive forestry history. For this purpose, we have designed two scenarios, i.e., one linked to its current management (Business As Usual, BAU) and another justified by the inclusion of Improved Forest Management (IFM). The results reveal a notable conflict between the carbon captured and the values of the indicators used to measure biodiversity. In order to reach a compromise between both scenarios, a multi-criteria model has been proposed that could be more attractive than the above ones. In addition, the carbon profit credits in the first ten years have been computed under the IFM scenario; the latter could be, a priori, an object of transaction in a voluntary carbon market. In conclusion, our model generates feasible solutions that allow the integration of IFM into strategic planning. Besides, those solutions show interesting tradeoffs between carbon and biodiversity. This discord must be distinguished by the current state of the forest and its expected growth, as well as their influence on the values associated with provision ecosystem services, such as the present net value associated with timber harvests.

Multi-constraint improved RS path planning method for unmanned rice direct seeding machine

Path planning is one of the key technologies that determines the efficiency and quality of field operations using autonomous agricultural machinery. To date, there has been extensive research on global coverage path planning for unmanned agricultural machinery within the working area; however, the issue of “encircling and edging” left by the machinery during headland turns is often overlooked. This study focuses on the operational conditions of unmanned agricultural machinery in the rice fields of southern China. The path planning problem is abstracted under physical constraints, such as the space at the field headland, the agricultural environment (e.g., types of field ridges), the turning characteristics of the machinery, turning radius, working width, and minimum safety distance, into mathematical constraints. This yields an optimized path planning model and sequence combination. Based on the improved Reeds–Shepp curve, an en-circling and edging path planning algorithm is designed. The planned path for the unmanned agricultural machinery from start to finish consists only of arcs and straight lines, suitable for the right-angle turning, reversing, and 180° U-turn operations required for rice field machinery, thus significantly improving the coverage of field edges and missed areas at the headland. A rice direct-seeding machine was used as a test subject for encircling and edging field trials, with tests conducted in rectangular, trapezoidal, and irregular quadrilateral rice fields. The results show that, for rectangular plots, the full-field coverage rate of rice direct-seeding operations can reach 96.44%; for trapezoidal plots, the coverage rate is 95.47%; and for irregular quadrilateral fields, the coverage rate is 95.69%. These results are promising, indicating that the encircling and edging path planning based on the improved Reeds–Shepp curve can effectively increase the full-field coverage rate of unmanned agricultural machinery, improving work quality and meeting the needs of modernized, intelligent agricultural machinery operations.

A two-stage distributed stochastic planning method for source-grid-load-storage flexibility resources considering flexible ramp capacity

With rapidly increasing levels of renewable energy penetration, flexibility resources play an ever more critical role in the future power system. This paper describes a two-stage stochastic mixed integer second order cone (MISOC) method for flexibility resource planning (VFRP) considering source-grid-load-storage interactions. Considering renewable energy penetration levels and flexibility resource characteristics, this study quantifies the extent to which the share of renewable energy generation affects cost performance, and assesses the priority and potential of investing in flexibility resources. Moreover, the multi-type flexibility resource portfolio allocation method and energy storage only approach are compared in terms of socio-economic benefits. A multi-cut Benders-based approach is used for decomposing large-scale stochastic expansion planning problems to reduce the computational burden. Numerical simulation tests on the modified energy test systems I39G20 and F213G20 verified the correctness and effectiveness of the proposed flexible resource planning models and solution algorithms. The simulation results show that retrofit of coal-fired units for better flexibility has a higher investment return. Still, energy storage presents a tremendous investment prospect and potential. Finally, the multi-type flexibility resource portfolio allocation method is more cost-effective than an energy storage only approach.

Firefighting Vehicle Dispatch and Route Planning Model Based on Priority Passage Rights

<div>Efficient fire rescue operations in urban environments are critical for saving lives and reducing property damage. By utilizing connected vehicle systems (CVS) for firefighting vehicles planning, we can reduce the response time to fires while lowering the operational costs of fire stations. This research presents an innovative nonlinear mixed-integer programming model to enhance fire rescue operations in urban settings. The model focuses on expediting the movement of firefighting vehicles within intricate traffic networks, effectively tackling the complexities associated with collaborative dispatch decisions and optimal path planning for multiple response units. This method is validated using a small-scale traffic network, providing foundational insights into parameter impacts. A case study in Sioux Falls shows its superiority over traditional “nearest dispatch” methods, optimizing both cost and response time significantly. Sensitivity analyses involving clearance speed, clearance time, minimum rescue force, and fire loss parameters contribute to the enhancement of urban fire rescue operations and the refinement of practical decision support systems.</div>

Multi-period optimal capacity expansion planning scheme of regional integrated energy systems considering multi-time scale uncertainty and generation low-carbon retrofit

With increasingly challenging climate crisis, carbon neutrality has become a necessary path for the whole world. However, there still lacks a comprehensive investigation on the optimal capacity expansion planning for a low-carbon transformation while considering multiple uncertainties. In this paper, a multi-period optimal capacity expansion planning scheme for regional integrated energy systems considering multi-time scale uncertainties and generation low-carbon retrofit is proposed. First, to better describe the short-time scale uncertainty caused by renewable energy and load fluctuations, a multi-dimensional tempo-spatial correlated scenario generation method is proposed to more accurately capture stochastic features with the least amounts of representative scenarios. Second, a multi-period optimal planning model considering generation low-carbon retrofit and short-/long-time scale uncertainties is developed. The proposed model combines information gap decision theory and chance constraints to stress both uncertainties simultaneously, which is further linearized to facilitate the computation. Third, an improved bilinear Benders decomposition (IBBD) method is utilized to efficiently solve the proposed large-scale optimal planning problem. Finally, numerical experiments of a real world test system of WF city show: 1) the maximum errors of PDF and CDF between generated scenarios and historical data are 0.108 and 0.016, validating the effectiveness of the proposed scenario generation method; 2) the low-carbon retrofit reduces system carbon emissions by 14.12 × 107 kg, while the total system cost is $956,411,387 with additional energy coupling units and renewables installed, indicating the reliability of the multi-period planning model; 3) the IBBD algorithm demonstrates applicability and efficiency in solving the proposed multi-period optimal expansion planning problem, reducing computation time by over 80.39 % compared to commercial solvers, such as GUROBI.

Investigating in-performance transitions between mental states in high-level judoka using video-based stimulated recall

The Multi-Action Plan model offers an idiosyncratic, sport-specific, and applied framework categorising two peak (Type 1 & 2) and two non-peak performance types (Type 3 & 4). The purpose of the present study was to examine the transitions between these Performance Types across three competition-simulating training judo fights. After videoing three judo fights per participant, we interviewed six high-level judo practitioners (Mdage = 19 years) using video-stimulated recall. While watching their fights, participants indicated which Performance Types they experienced during each fight and, subsequently, discussed their experience with the lead researcher. Findings indicated that participants spent most time in effortful mental states (Type 2 & 3). Additionally, they identified currently not defined states ‘between’ current typologies, e.g., T2.5. Overall, participants reported more down- than upregulations. Specifically, they described downregulations as mostly uncontrolled and related to fatigue, technical-tactical, or cognitive-emotional transition cues. In contrast, they characterised upregulations as deliberate and proactive mental resets, utilising strategies such as self-talk. Lastly, we discussed our findings in relation to existing literature and offered implications for research and practice.

A districting problem with data reliability constraints for equity analysis

While data plays an important role in transportation research, sampled data is not always reliable. Data reliability issue is significant especially for minority groups. In this study, a districting approach is proposed which improves data reliability through aggregation of basic spatial units (BSU), adapted from a max-p-regions problem. The model generates as many aggregated zones as possible that minimize intrazonal heterogeneity while minimizing data margin of error (MOE) of all aggregated zones using a controlling MOE threshold. The problem is first formulated as an integer programming which selects optimal set of zones from a pre-generated set of candidate zones. The difficulty of solving the formulation lies in the generation of the candidate set, so a heuristic solution algorithm is proposed. Two case studies are provided to illustrate the method and validate its performance by evaluating the resulting data quality in an example subsequent planning model. First is an area in Downtown Manhattan with 62 census tracts, comparing the aggregated zones with Neighborhood Tabulation Areas (NTAs) and Taxi Zones. Second is the generation of the New York City Equitable Zoning (NYCEZ), which generated 574 Equitable Zones that reduce the average MOE% of demographic data by 48% for seniors, 75% for low-income population, and 46% for long commuters, all with a district number that is higher than NTAs (221) and Taxi Zones (263). NYCEZ and census tracts are then compared in a subsequent model, synthetic population generation, showing an improvement of 6.2% in standard deviation across simulated populations under the proposed zone design. NYCEZ showed smaller variation in the generated population data. The algorithm can help the decision making of public agencies and the service design of mobility providers by producing reliable and equitable data. The algorithm can also be applied to data-sharing between mobility providers and agencies to alleviate privacy concerns.

Automated building layout generation: Implementation and comparison of STREAMER Early Design Configurator and SDaC Layout Designer

When designing new buildings, various constraints must be taken into account. These constraints encompass factors such as the overall building size, the number, function, and size of required spaces, and even the surrounding neighborhood's existing buildings, infrastructure, and natural environment. Particularly the requirements of interior layout design are usually coupled with each other, making the design process more complex and time-consuming. This paper proposes a novel manner to consider the requirements, aiming to facilitate the generation process of building's interior layout during the early design phase. Besides, this paper aims to generate vectored output, which is more applicable to export BIM model, which also benefits the subsequent design and construct steps. This paper introduces STREAMER Early Design Configurator (EDC) and SDaC Layout Designer, both of which formats the user's requirements, semi-automatically generates interior layouts and exports IFC models of the floor plans. STREAMER EDC is used to discover the potential layouts of large-scale buildings with many rooms such as hospitals, while SDaC Layout Designer focuses on residential houses with comparatively fewer rooms. These drafts are enriched with additional data, including placement information, volume details, and space utilization. Ultimately, the floor plans are exported into three-dimensional objects and exported in the IFC format. This comprehensive step paves the way for more efficient and informed building design, promoting greater flexibility and adaptability in the early stages of the architectural process.

A Cost-Affordable Methodology of 3D Printing of Bone Fractures Using DICOM Files in Traumatology

Three-dimensional (3D) printing has gained popularity across various domains but remains less integrated into medical surgery due to its complexity. Existing literature primarily discusses specific applications, with limited detailed guidance on the entire process. The methodological details of converting Computed Tomography (CT) images into 3D models are often found in amateur 3D printing forums rather than scientific literature. To address this gap, we present a comprehensive methodology for converting CT images of bone fractures into 3D-printed models. This involves transferring files in Digital Imaging and Communications in Medicine (DICOM) format to stereolithography format, processing the 3D model, and preparing it for printing. Our methodology outlines step-by-step guidelines, time estimates, and software recommendations, prioritizing free open-source tools. We also share our practical experience and outcomes, including the successful creation of 72 models for surgical planning, patient education, and teaching. Although there are challenges associated with utilizing 3D printing in surgery, such as the requirement for specialized expertise and equipment, the advantages in surgical planning, patient education, and improved outcomes are evident. Further studies are warranted to refine and standardize these methodologies for broader adoption in medical practice.

Human navigation strategies and their errors result from dynamic interactions of spatial uncertainties

Goal-directed navigation requires continuously integrating uncertain self-motion and landmark cues into an internal sense of location and direction, concurrently planning future paths, and sequentially executing motor actions. Here, we provide a unified account of these processes with a computational model of probabilistic path planning in the framework of optimal feedback control under uncertainty. This model gives rise to diverse human navigational strategies previously believed to be distinct behaviors and predicts quantitatively both the errors and the variability of navigation across numerous experiments. This furthermore explains how sequential egocentric landmark observations form an uncertain allocentric cognitive map, how this internal map is used both in route planning and during execution of movements, and reconciles seemingly contradictory results about cue-integration behavior in navigation. Taken together, the present work provides a parsimonious explanation of how patterns of human goal-directed navigation behavior arise from the continuous and dynamic interactions of spatial uncertainties in perception, cognition, and action.

Utility of do-not-resuscitate orders for critically ill infants in the NICU.

To better understand the value of DNR orders for critically ill infants in the NICU. A prospective mixed-methods approach was utilized including chart review of infants who died in a regional NICU over a twenty-six-month period and surveys of their neonatologists, neonatal fellows, and nurses. 40 infants died during the study period and 120 staff surveys were completed. Infants with DNR orders were of a higher gestational age at birth and a higher chronological age at death. Nurses were more likely to perceive benefit from DNR orders than physicians. Medical staff recollection of the existence of DNR orders was not always accurate. Time and fear of adding unnecessary emotional burden to parents were identified as barriers to DNR order implementation. An advanced care planning model built on open communication instead of DNR order documentation was deemed the best approach. Though DNR orders are beneficial for a subset of infants, DNR orders are likely not applicable for all infants who die in the NICU. More important is supportive, individualized communication between families and the medical team to ensure quality end-of-life care. In the adult and pediatric ICU literature, DNR orders are associated with improved qualitative "good death" assessments and decreased familial decision regret. In the NICU, rates of DNR usage aren't well reported and their overall utility is unclear. Though DNR orders can help guide clinical decision making in the NICU and may be associated with higher quality ethical discussion, our data suggest that they are not applicable in all patient cases. We hope that this work will help guide approaches to end-of-life care in the NICU and underscore the importance of frequent, open communication between families and their medical team.

Joint modeling of choices and reaction times based on Bayesian contextual behavioral control.

In cognitive neuroscience and psychology, reaction times are an important behavioral measure. However, in instrumental learning and goal-directed decision making experiments, findings often rely only on choice probabilities from a value-based model, instead of reaction times. Recent advancements have shown that it is possible to connect value-based decision models with reaction time models. However, typically these models do not provide an integrated account of both value-based choices and reaction times, but simply link two types of models. Here, we propose a novel integrative joint model of both choices and reaction times by combining a computational account of Bayesian sequential decision making with a sampling procedure. This allows us to describe how internal uncertainty in the planning process shapes reaction time distributions. Specifically, we use a recent context-specific Bayesian forward planning model which we extend by a Markov chain Monte Carlo (MCMC) sampler to obtain both choices and reaction times. As we will show this makes the sampler an integral part of the decision making process and enables us to reproduce, using simulations, well-known experimental findings in value based-decision making as well as classical inhibition and switching tasks. Specifically, we use the proposed model to explain both choice behavior and reaction times in instrumental learning and automatized behavior, in the Eriksen flanker task and in task switching. These findings show that the proposed joint behavioral model may describe common underlying processes in these different decision making paradigms.

Robust Trajectory Planning of Gliding-Guided Projectiles with Weak Maneuverability

Due to constraints in launch platforms and cost, the maneuverability of gliding-guided projectiles is limited, necessitating a rational design of their trajectory schemes. To reduce the sensitivity of trajectory schemes to uncertainties while ensuring compatibility between flight schemes and guidance control systems and fully exploiting the control capability of the projectile, a closed-loop robust trajectory planning method is proposed. Models of major uncertain factors and state deviation at the control start point are established. Based on the NIPCE method, the stochastic dynamic model is transformed into a high-dimensional deterministic model with PCE coefficients as state variables, and the uncertainty propagation law is obtained. A PID algorithm is employed to design a tracking guidance law based on position error feedback, and open-loop and closed-loop robust trajectory planning models are established accordingly. The optimal control problem is solved by transforming it into a nonlinear programming problem using the direct shooting method. Our simulation results indicate that the NIPCE method can significantly improve the computational efficiency of uncertainty propagation while ensuring accuracy; compared with parallel MCS, the computation time is reduced by 96.8%. Open-loop robust planning can effectively mitigate the sensitivity of gliding trajectories to uncertainties (the standard deviations of terminal altitude and lateral deviations are reduced by 23.6% and 35.3%, respectively, compared to deterministic planning) but cannot completely eliminate terminal dispersion. Closed-loop robust planning effectively improves control effort consumption on the basis of open-loop planning.

Teacher education for mathematical modelling: exploring the experiences of secondary school teachers in two courses

This paper focuses on in-service teacher education as a crucial agent in driving educational paradigm shifts for the teaching and learning of mathematical modelling. Our paper presents empirical research based on two case studies, examining training courses for in-service secondary school mathematics teachers. The first course integrates different modelling approaches, while the second one is based on the anthropological theory of the didactic and uses the proposal of the study and research paths for teacher education. Both experiences conclude with teachers working on the design of modelling tasks to be implemented in secondary schools. Both courses are analysed through the lenses of how teachers progress on the collective identification of conditions and constraints for modelling, when teachers deal with the design of modelling tasks and analyse their implementations. First, the results show the kind of modelling tasks teachers design and the level of disciplinary specificity at which they plan modelling to be implemented. Second, we analyse how teachers address the “ecological analysis”, that is, the identification of conditions and constraints that facilitate or hinder the integration of modelling in secondary school classrooms after their experiences.

Location Selection Methods for Urban Terminal Co-Distribution Centers with Air–Land Collaboration

Urban terminal logistics and distribution enterprises face the problems of duplicated network layouts, high costs, and inefficient urban environments. Recently, collaborative distribution using unmanned aerial vehicles (UAVs) and ground vehicles has been considered as a means of reducing costs and enhancing efficiency, thus overcoming the issues created by the high-density layout of enterprises’ relatively independent networks. This essentially involves constructing an air–ground collaborative common distribution network. To optimize the economic cost and distribution time of network operations, we established a site selection planning model for air–ground cooperative urban co-distribution centers and designed a solution method based on gray wolf optimization with K-means clustering. Taking the Wangsheren area of Jinan City, China, as an example, 15 UAV co-distribution centers and 13 vehicle co-distribution centers were identified. Although the average distribution cost of the network rose by 35–50% compared to traditional terminal distribution, the time saving was 80–85%, greatly improving the high-value-added service capacity. The end-distribution efficiency and customer satisfaction were also enhanced, which fully verifies the feasibility, validity, and applicability of the proposed model. Our approach can be applied to landing sites and the planning and optimization of large-scale commercial operations using logistics UAVs in urban areas.

A self-adaptive agent for flexible posture planning in robotic milling system

In recent years, industrial robots are widely used in the milling processes of the fundamental components such as aeronautic parts, aerospace cabins and blades on the marine propellers of the worships, because of their flexible structure, large operating space, and robust capacity of rapid reconfiguration. Along with the robotic machining process, multiple types of geometrical and physical constraints display the time-varying characteristics, which are difficult to be considered simultaneously by the traditional static planning methods on the robotic milling posture. Therefore, a deep reinforcement learning (DRL) enhanced virtual repulsive potential field flexible model is proposed for the robotic milling posture dynamic planning. The preliminary planning of static milling posture is realized based on the fixed setting of the virtual modal parameters in the posture planning model, which is treated as a theory preparation for training the deep reinforcement learning agent. To develop the static planning model, multiple constraints are established by considering the performances of geometric, kinematic and machining precision simultaneously. Furthermore, a reward function is constructed for the dynamic agent, comprehensively combining the long and short reward benefits in nonlinear correlation with virtual repulsive forces. By taking the virtual modal parameters as the action space of the dynamic agent, a DRL enhanced agent VRPF-SAC is created and trained under the dynamic milling environment from virtual repulsive planning field. Four tasks of large size robotic milling simulations and experiments are designed and developed to validate the effectiveness of the flexible planning model. In comparison with the static model, the flexible planning model displays the excellent global effects covering the kinematic, and precision performance, with 65.78 %, 72.04 %, and 70.25 % reduction in velocity, acceleration, and jerk of robotic joints, and ensuring the effective precision performance from −0.365 to 0.283 mm of large size workpiece with large curvature changes. The proposed flexible posture planning architecture can provide a basic for robotic dynamic milling of core parts with large size, narrow space and sharp curvatures of the aeronautic parts, aerospace cabins and worship propellers.