arXiv subjects

Danail Stoyanov

Publications and source records attributed to Danail Stoyanov.

At least 37 records · Page 2Linked to original sources

arXiv2026

TemporalDoRA: Temporal PEFT for Robust Surgical Video Question Answering

Surgical Video Question Answering (VideoQA) requires accurate temporal grounding while remaining robust to natural variation in how clinicians phrase questions, where linguistic bias can arise. Standard Parameter Efficient Fine Tuning (PEFT) methods adapt pretrained projections without explicitly modeling frame-to-frame interactions within the adaptation pathway, limiting their ability to exploit sparse temporal evidence. We introduce TemporalDoRA, a video-specific PEFT formulation that extends Weight-Decomposed Low-Rank Adaptation by (i) inserting lightweight temporal Multi-Head Attention (MHA) inside the low-rank bottleneck of the vision encoder and (ii) selectively applying weight decomposition only to the trainable low-rank branch rather than the full adapted weight. This design enables temporally-aware updates while preserving a frozen backbone and stable scaling. By mixing information across frames within the adaptation subspace, TemporalDoRA steers updates toward temporally consistent visual cues and improves robustness with minimal parameter overhead. To benchmark this setting, we present REAL-Colon-VQA, a colonoscopy VideoQA dataset with 6,424 clip--question pairs, including paired rephrased Out-of-Template questions to evaluate sensitivity to linguistic variation. TemporalDoRA improves Out-of-Template performance, and ablation studies confirm that temporal mixing inside the low-rank branch is the primary driver of these gains. We also validate on EndoVis18-VQA adapted to short clips and observe consistent improvements on the Out-of-Template split. Code and dataset available at~\href{https://anonymous.4open.science/r/TemporalDoRA-BFC8/}{Anonymous GitHub}.

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arXiv2026

Training-free Temporal Object Tracking in Surgical Videos

Purpose: In this paper, we present a novel approach for online object tracking in laparoscopic cholecystectomy (LC) surgical videos, targeting localisation and tracking of critical anatomical structures and instruments. Our method addresses the challenges of costly pixel-level annotations and label inconsistencies inherent in existing datasets. Methods: Leveraging the inherent object localisation capabilities of pre-trained text-to-image diffusion models, we extract representative features from surgical frames without any training or fine-tuning. Our tracking framework uses these features, along with cross-frame interactions via an affinity matrix inspired by query-key-value attention, to ensure temporal continuity in the tracking process. Results: Through a pilot study, we first demonstrate that diffusion features exhibit superior object localisation and consistent semantics across different decoder levels and temporal frames. Later, we perform extensive experiments to validate the effectiveness of our approach, showcasing its superiority over competitors for the task of temporal object tracking. Specifically, we achieve a per-pixel classification accuracy of 79.19%, mean Jaccard Score of 56.20%, and mean F-Score of 79.48% on the publicly available CholeSeg8K dataset. Conclusion: Our work not only introduces a novel application of text-to-image diffusion models but also contributes to advancing the field of surgical video analysis, offering a promising avenue for accurate and cost-effective temporal object tracking in minimally invasive surgery videos.

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arXiv2026

Confidence-aware Monocular Depth Estimation for Minimally Invasive Surgery

Purpose: Monocular depth estimation (MDE) is vital for scene understanding in minimally invasive surgery (MIS). However, endoscopic video sequences are often contaminated by smoke, specular reflections, blur, and occlusions, limiting the accuracy of MDE models. In addition, current MDE models do not output depth confidence, which could be a valuable tool for improving their clinical reliability. Methods: We propose a novel confidence-aware MDE framework featuring three significant contributions: (i) Calibrated confidence targets: an ensemble of fine-tuned stereo matching models is used to capture disparity variance into pixel-wise confidence probabilities; (ii) Confidence-aware loss: Baseline MDE models are optimized with confidence-aware loss functions, utilizing pixel-wise confidence probabilities such that reliable pixels dominate training; and (iii) Inference-time confidence: a confidence estimation head is proposed with two convolution layers to predict per-pixel confidence at inference, enabling assessment of depth reliability. Results: Comprehensive experimental validation across internal and public datasets demonstrates that our framework improves depth estimation accuracy and can robustly quantify the prediction's confidence. On the internal clinical endoscopic dataset (StereoKP), we improve dense depth estimation accuracy by ~8% as compared to the baseline model. Conclusion: Our confidence-aware framework enables improved accuracy of MDE models in MIS, addressing challenges posed by noise and artifacts in pre-clinical and clinical data, and allows MDE models to provide confidence maps that may be used to improve their reliability for clinical applications.

cs.CV↗

arXiv2026

Multi-Modal Monocular Endoscopic Depth and Pose Estimation with Edge-Guided Self-Supervision

Monocular depth and pose estimation play an important role in the development of colonoscopy-assisted navigation, as they enable improved screening by reducing blind spots, minimizing the risk of missed or recurrent lesions, and lowering the likelihood of incomplete examinations. However, this task remains challenging due to the presence of texture-less surfaces, complex illumination patterns, deformation, and a lack of in-vivo datasets with reliable ground truth. In this paper, we propose **PRISM** (Pose-Refinement with Intrinsic Shading and edge Maps), a self-supervised learning framework that leverages anatomical and illumination priors to guide geometric learning. Our approach uniquely incorporates edge detection and luminance decoupling for structural guidance. Specifically, edge maps are derived using a learning-based edge detector (e.g., DexiNed or HED) trained to capture thin and high-frequency boundaries, while luminance decoupling is obtained through an intrinsic decomposition module that separates shading and reflectance, enabling the model to exploit shading cues for depth estimation. Experimental results on multiple real and synthetic datasets demonstrate state-of-the-art performance. We further conduct a thorough ablation study on training data selection to establish best practices for pose and depth estimation in colonoscopy. This analysis yields two practical insights: (1) self-supervised training on real-world data outperforms supervised training on realistic phantom data, underscoring the superiority of domain realism over ground truth availability; and (2) video frame rate is an extremely important factor for model performance, where dataset-specific video frame sampling is necessary for generating high quality training data.

cs.CV↗

arXiv2026

SurgFusion-Net: Diversified Adaptive Multimodal Fusion Network for Surgical Skill Assessment

Robotic-assisted surgery (RAS) is established in clinical practice, and automated surgical skill assessment utilizing multimodal data offers transformative potential for surgical analytics and education. However, developing effective multimodal methods remains challenging due to the task complexity, limited annotated datasets and insufficient techniques for cross-modal information fusion. Existing state-of-the-art relies exclusively on RGB video and only applies on dry-lab settings, failing to address the significant domain gap between controlled simulation and real clinical cases, where the surgical environment together with camera and tissue motion introduce substantial complexities. This work introduces SurgFusion-Net and Divergence Regulated Attention (DRA), an innovative fusion strategy for multimodal surgical skill assessment. We contribute two first-of-their-kind clinical datasets: the RAH-skill dataset containing 279,691 RGB frames from 37 videos of Robot-assisted Hysterectomy (RAH), and the RARP-skill dataset containing 70,661 RGB frames from 33 videos of Robot-Assisted Radical Prostatectomy (RARP). Both datasets include M-GEARS skill annotations, corresponding optical flow and tool segmentation masks. DRA incorporates adaptive dual attention and diversity-promoting multi-head attention to fuse multimodal information, from three modalities, based on surgical context, enhancing assessment accuracy and reliability. Validated on the JIGSAWS benchmark, RAH-skill, and RARP-skill datasets, our approach outperforms recent baselines with SCC improvements of 0.02 in LOSO, 0.04 in LOUO across JIGSAWS tasks, and 0.0538 and 0.0493 gains on RAH-skill and RARP-skill, respectively.

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arXiv2026

Comparative validation of surgical phase recognition, instrument keypoint estimation, and instrument instance segmentation in endoscopy: Results of the PhaKIR 2024 challenge

Reliable recognition and localization of surgical instruments in endoscopic video recordings are foundational for a wide range of applications in computer- and robot-assisted minimally invasive surgery (RAMIS), including surgical training, skill assessment, and autonomous assistance. However, robust performance under real-world conditions remains a significant challenge. Incorporating surgical context - such as the current procedural phase - has emerged as a promising strategy to improve robustness and interpretability. To address these challenges, we organized the Surgical Procedure Phase, Keypoint, and Instrument Recognition (PhaKIR) sub-challenge as part of the Endoscopic Vision (EndoVis) challenge at MICCAI 2024. We introduced a novel, multi-center dataset comprising thirteen full-length laparoscopic cholecystectomy videos collected from three distinct medical institutions, with unified annotations for three interrelated tasks: surgical phase recognition, instrument keypoint estimation, and instrument instance segmentation. Unlike existing datasets, ours enables joint investigation of instrument localization and procedural context within the same data while supporting the integration of temporal information across entire procedures. We report results and findings in accordance with the BIAS guidelines for biomedical image analysis challenges. The PhaKIR sub-challenge advances the field by providing a unique benchmark for developing temporally aware, context-driven methods in RAMIS and offers a high-quality resource to support future research in surgical scene understanding.

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arXiv2025

A multi-centre, multi-device benchmark dataset for landmark-based comprehensive fetal biometry

Accurate fetal growth assessment from ultrasound (US) relies on precise biometry measured by manually identifying anatomical landmarks in standard planes. Manual landmarking is time-consuming, operator-dependent, and sensitive to variability across scanners and sites, limiting the reproducibility of automated approaches. There is a need for multi-source annotated datasets to develop artificial intelligence-assisted fetal growth assessment methods. To address this bottleneck, we present an open, multi-centre, multi-device benchmark dataset of fetal US images with expert anatomical landmark annotations for clinically used fetal biometric measurements. These measurements include head bi-parietal and occipito-frontal diameters, abdominal transverse and antero-posterior diameters, and femoral length. The dataset comprises 4,513 de-identified US images from 1,904 subjects acquired at three clinical sites using seven different US devices. We provide standardised, subject-disjoint train/test splits, evaluation code, and baseline results to enable fair and reproducible comparison of methods. Using an automatic biometry model, we quantify domain shift and demonstrate that training and evaluation confined to a single centre substantially overestimate performance relative to multi-centre testing. To the best of our knowledge, this is the first publicly available multi-centre, multi-device, landmark-annotated dataset that covers all primary fetal biometry measures, providing a robust benchmark for domain adaptation and multi-centre generalisation in fetal biometry and enabling more reliable AI-assisted fetal growth assessment across centres. All data, annotations, training code, and evaluation pipelines are made publicly available.

cs.CV↗

arXiv2025

Graph Neural Networks for Surgical Scene Segmentation

Purpose: Accurate identification of hepatocystic anatomy is critical to preventing surgical complications during laparoscopic cholecystectomy. Deep learning models often struggle with occlusions, long-range dependencies, and capturing the fine-scale geometry of rare structures. This work addresses these challenges by introducing graph-based segmentation approaches that enhance spatial and semantic understanding in surgical scene analyses. Methods: We propose two segmentation models integrating Vision Transformer (ViT) feature encoders with Graph Neural Networks (GNNs) to explicitly model spatial relationships between anatomical regions. (1) A static k Nearest Neighbours (k-NN) graph with a Graph Convolutional Network with Initial Residual and Identity Mapping (GCNII) enables stable long-range information propagation. (2) A dynamic Differentiable Graph Generator (DGG) with a Graph Attention Network (GAT) supports adaptive topology learning. Both models are evaluated on the Endoscapes-Seg50 and CholecSeg8k benchmarks. Results: The proposed approaches achieve up to 7-8% improvement in Mean Intersection over Union (mIoU) and 6% improvement in Mean Dice (mDice) scores over state-of-the-art baselines. It produces anatomically coherent predictions, particularly on thin, rare and safety-critical structures. Conclusion: The proposed graph-based segmentation methods enhance both performance and anatomical consistency in surgical scene segmentation. By combining ViT-based global context with graph-based relational reasoning, the models improve interpretability and reliability, paving the way for safer laparoscopic and robot-assisted surgery through a precise identification of critical anatomical features.

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arXiv2025

Surgical AI Copilot: Energy-Based Fourier Gradient Low-Rank Adaptation for Surgical LLM Agent Reasoning and Planning

Image-guided surgery demands adaptive, real-time decision support, yet static AI models struggle with structured task planning and providing interactive guidance. Large language models (LLMs)-powered agents offer a promising solution by enabling dynamic task planning and predictive decision support. Despite recent advances, the absence of surgical agent datasets and robust parameter-efficient fine-tuning techniques limits the development of LLM agents capable of complex intraoperative reasoning. In this paper, we introduce Surgical AI Copilot, an LLM agent for image-guided pituitary surgery, capable of conversation, planning, and task execution in response to queries involving tasks such as MRI tumor segmentation, endoscope anatomy segmentation, overlaying preoperative imaging with intraoperative views, instrument tracking, and surgical visual question answering (VQA). To enable structured agent planning, we develop the PitAgent dataset, a surgical context-aware planning dataset covering surgical tasks like workflow analysis, instrument localization, anatomical segmentation, and query-based reasoning. Additionally, we propose DEFT-GaLore, a Deterministic Energy-based Fourier Transform (DEFT) gradient projection technique for efficient low-rank adaptation of recent LLMs (e.g., LLaMA 3.2, Qwen 2.5), enabling their use as surgical agent planners. We extensively validate our agent's performance and the proposed adaptation technique against other state-of-the-art low-rank adaptation methods on agent planning and prompt generation tasks, including a zero-shot surgical VQA benchmark, demonstrating the significant potential for truly efficient and scalable surgical LLM agents in real-time operative settings.

cs.CV↗

arXiv2025

Learning from Single Timestamps: Complexity Estimation in Laparoscopic Cholecystectomy

Purpose: Accurate assessment of surgical complexity is essential in Laparoscopic Cholecystectomy (LC), where severe inflammation is associated with longer operative times and increased risk of postoperative complications. The Parkland Grading Scale (PGS) provides a clinically validated framework for stratifying inflammation severity; however, its automation in surgical videos remains largely unexplored, particularly in realistic scenarios where complete videos must be analyzed without prior manual curation. Methods: In this work, we introduce STC-Net, a novel framework for SingleTimestamp-based Complexity estimation in LC via the PGS, designed to operate under weak temporal supervision. Unlike prior methods limited to static images or manually trimmed clips, STC-Net operates directly on full videos. It jointly performs temporal localization and grading through a localization, window proposal, and grading module. We introduce a novel loss formulation combining hard and soft localization objectives and background-aware grading supervision. Results: Evaluated on a private dataset of 1,859 LC videos, STC-Net achieves an accuracy of 62.11% and an F1-score of 61.42%, outperforming non-localized baselines by over 10% in both metrics and highlighting the effectiveness of weak supervision for surgical complexity assessment. Conclusion: STC-Net demonstrates a scalable and effective approach for automated PGS-based surgical complexity estimation from full LC videos, making it promising for post-operative analysis and surgical training.

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arXiv2025

SurgAnt-ViVQA: Learning to Anticipate Surgical Events through GRU-Driven Temporal Cross-Attention

Anticipating forthcoming surgical events is vital for real-time assistance in endonasal transsphenoidal pituitary surgery, where visibility is limited and workflow changes rapidly. Most visual question answering (VQA) systems reason on isolated frames with static vision language alignment, providing little support for forecasting next steps or instrument needs. Existing surgical VQA datasets likewise center on the current scene rather than the near future. We introduce PitVQA-Anticipation, the first VQA dataset designed for forward looking surgical reasoning. It comprises 33.5 hours of operative video and 734,769 question answer pairs built from temporally grouped clips and expert annotations across four tasks: predicting the future phase, next step, upcoming instrument, and remaining duration. We further propose SurgAnt-ViVQA, a video language model that adapts a large language model using a GRU Gated Temporal Cross-Attention module. A bidirectional GRU encodes frame to frame dynamics, while an adaptive gate injects visual context into the language stream at the token level. Parameter efficient fine tuning customizes the language backbone to the surgical domain. SurgAnt-ViVQA tested upon on PitVQA-Anticipation and EndoVis datasets, surpassing strong image and video based baselines. Ablations show that temporal recurrence and gated fusion drive most of the gains. A frame budget study indicates a trade-off: 8 frames maximize fluency, whereas 32 frames slightly reduce BLEU but improve numeric time estimation. By pairing a temporally aware encoder with fine grained gated cross-attention, SurgAnt-ViVQA advances surgical VQA from retrospective description to proactive anticipation. PitVQA-Anticipation offers a comprehensive benchmark for this setting and highlights the importance of targeted temporal modeling for reliable, future aware surgical assistance.

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arXiv2025

Zero-shot Monocular Metric Depth for Endoscopic Images

Monocular relative and metric depth estimation has seen a tremendous boost in the last few years due to the sharp advancements in foundation models and in particular transformer based networks. As we start to see applications to the domain of endoscopic images, there is still a lack of robust benchmarks and high-quality datasets in that area. This paper addresses these limitations by presenting a comprehensive benchmark of state-of-the-art (metric and relative) depth estimation models evaluated on real, unseen endoscopic images, providing critical insights into their generalisation and performance in clinical scenarios. Additionally, we introduce and publish a novel synthetic dataset (EndoSynth) of endoscopic surgical instruments paired with ground truth metric depth and segmentation masks, designed to bridge the gap between synthetic and real-world data. We demonstrate that fine-tuning depth foundation models using our synthetic dataset boosts accuracy on most unseen real data by a significant margin. By providing both a benchmark and a synthetic dataset, this work advances the field of depth estimation for endoscopic images and serves as an important resource for future research. Project page, EndoSynth dataset and trained weights are available at https://github.com/TouchSurgery/EndoSynth.

cs.CV↗

arXiv2025

Automated Cervical Os Segmentation for Camera-Guided, Speculum-Free Screening

Cervical cancer is highly preventable, yet persistent barriers to screening limit progress toward elimination goals. Speculum-free devices that integrate imaging and sampling could improve access, particularly in low-resource settings, but require reliable visual guidance. This study evaluates deep learning methods for real-time segmentation of the cervical os in transvaginal endoscopic images. Five encoder-decoder architectures were compared using 913 frames from 200 cases in the IARC Cervical Image Dataset, annotated by gynaecologists. Performance was assessed using IoU, DICE, detection rate, and distance metrics with ten-fold cross-validation. EndoViT/DPT, a vision transformer pre-trained on surgical video, achieved the highest DICE (0.50 \pm 0.31) and detection rate (0.87 \pm 0.33), outperforming CNN-based approaches. External validation with phantom data demonstrated robust segmentation under variable conditions at 21.5 FPS, supporting real-time feasibility. These results establish a foundation for integrating automated os recognition into speculum-free cervical screening devices to support non-expert use in both high- and low-resource contexts.

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arXiv2025

Exploring Pre-training Across Domains for Few-Shot Surgical Skill Assessment

Automated surgical skill assessment (SSA) is a central task in surgical computer vision. Developing robust SSA models is challenging due to the scarcity of skill annotations, which are time-consuming to produce and require expert consensus. Few-shot learning (FSL) offers a scalable alternative enabling model development with minimal supervision, though its success critically depends on effective pre-training. While widely studied for several surgical downstream tasks, pre-training has remained largely unexplored in SSA. In this work, we formulate SSA as a few-shot task and investigate how self-supervised pre-training strategies affect downstream few-shot SSA performance. We annotate a publicly available robotic surgery dataset with Objective Structured Assessment of Technical Skill (OSATS) scores, and evaluate various pre-training sources across three few-shot settings. We quantify domain similarity and analyze how domain gap and the inclusion of procedure-specific data into pre-training influence transferability. Our results show that small but domain-relevant datasets can outperform large scale, less aligned ones, achieving accuracies of 60.16%, 66.03%, and 73.65% in the 1-, 2-, and 5-shot settings, respectively. Moreover, incorporating procedure-specific data into pre-training with a domain-relevant external dataset significantly boosts downstream performance, with an average gain of +1.22% in accuracy and +2.28% in F1-score; however, applying the same strategy with less similar but large-scale sources can instead lead to performance degradation. Code and models are available at https://github.com/anastadimi/ssa-fsl.

cs.CV↗

arXiv2025

Endo-FASt3r: Endoscopic Foundation model Adaptation for Structure from motion

Accurate depth and camera pose estimation is essential for achieving high-quality 3D visualisations in robotic-assisted surgery. Despite recent advancements in foundation model adaptation to monocular depth estimation of endoscopic scenes via self-supervised learning (SSL), no prior work has explored their use for pose estimation. These methods rely on low rank-based adaptation approaches, which constrain model updates to a low-rank space. We propose Endo-FASt3r, the first monocular SSL depth and pose estimation framework that uses foundation models for both tasks. We extend the Reloc3r relative pose estimation foundation model by designing Reloc3rX, introducing modifications necessary for convergence in SSL. We also present DoMoRA, a novel adaptation technique that enables higher-rank updates and faster convergence. Experiments on the SCARED dataset show that Endo-FASt3r achieves a substantial $10\%$ improvement in pose estimation and a $2\%$ improvement in depth estimation over prior work. Similar performance gains on the Hamlyn and StereoMIS datasets reinforce the generalisability of Endo-FASt3r across different datasets.

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arXiv2025

CARES: Collaborative Agentic Reasoning for Error Detection in Surgery

Robotic-assisted surgery (RAS) introduces complex challenges that current surgical error detection methods struggle to address effectively due to limited training data and methodological constraints. Therefore, we construct MERP (Multi-class Error in Robotic Prostatectomy), a comprehensive dataset for error detection in robotic prostatectomy with frame-level annotations featuring six clinically aligned error categories. In addition, we propose CARES (Collaborative Agentic Reasoning for Error Detection in Surgery), a novel zero-shot clinically-informed and risk-stratified agentic reasoning architecture for multi-class surgical error detection. CARES implements adaptive generation of medically informed, error-specific Chain-of-Thought (CoT) prompts across multiple expertise levels. The framework employs risk-aware routing to assign error task to expertise-matched reasoning pathways based on complexity and clinical impact. Subsequently, each pathway decomposes surgical error analysis into three specialized agents with temporal, spatial, and procedural analysis. Each agent analyzes using dynamically selected prompts tailored to the assigned expertise level and error type, generating detailed and transparent reasoning traces. By incorporating clinically informed reasoning from established surgical assessment guidelines, CARES enables zero-shot surgical error detection without prior training. Evaluation demonstrates superior performance with 54.3 mF1 on RARP and 52.0 mF1 on MERP datasets, outperforming existing zero-shot approaches by up to 14% while remaining competitive with trained models. Ablation studies demonstrate the effectiveness of our method. The dataset and code will be publicly available.

cs.MA↗

arXiv2025

Temporal Cluster Assignment for Efficient Real-Time Video Segmentation

Vision Transformers have substantially advanced the capabilities of segmentation models across both image and video domains. Among them, the Swin Transformer stands out for its ability to capture hierarchical, multi-scale representations, making it a popular backbone for segmentation in videos. However, despite its window-attention scheme, it still incurs a high computational cost, especially in larger variants commonly used for dense prediction in videos. This remains a major bottleneck for real-time, resource-constrained applications. Whilst token reduction methods have been proposed to alleviate this, the window-based attention mechanism of Swin requires a fixed number of tokens per window, limiting the applicability of conventional pruning techniques. Meanwhile, training-free token clustering approaches have shown promise in image segmentation while maintaining window consistency. Nevertheless, they fail to exploit temporal redundancy, missing a key opportunity to further optimize video segmentation performance. We introduce Temporal Cluster Assignment (TCA), a lightweight and effective, fine-tuning-free strategy that enhances token clustering by leveraging temporal coherence across frames. Instead of indiscriminately dropping redundant tokens, TCA refines token clusters using temporal correlations, thereby retaining fine-grained details while significantly reducing computation. Extensive evaluations on YouTube-VIS 2019, YouTube-VIS 2021, OVIS, and a private surgical video dataset show that TCA consistently boosts the accuracy-speed trade-off of existing clustering-based methods. Our results demonstrate that TCA generalizes competently across both natural and domain-specific videos.

cs.CV↗

arXiv2025

Dynamic Obstacle Avoidance of Unmanned Surface Vehicles in Maritime Environments Using Gaussian Processes Based Motion Planning

During recent years, unmanned surface vehicles are extensively utilised in a variety of maritime applications such as the exploration of unknown areas, autonomous transportation, offshore patrol and others. In such maritime applications, unmanned surface vehicles executing relevant missions that might collide with potential static obstacles such as islands and reefs and dynamic obstacles such as other moving unmanned surface vehicles. To successfully accomplish these missions, motion planning algorithms that can generate smooth and collision-free trajectories to avoid both these static and dynamic obstacles in an efficient manner are essential. In this article, we propose a novel motion planning algorithm named the Dynamic Gaussian process motion planner 2, which successfully extends the application scope of the Gaussian process motion planner 2 into complex and dynamic environments with both static and dynamic obstacles. First, we introduce an approach to generate safe areas for dynamic obstacles using modified multivariate Gaussian distributions. Second, we introduce an approach to integrate real-time status information of dynamic obstacles into the modified multivariate Gaussian distributions. The multivariate Gaussian distributions with real-time statuses of dynamic obstacles can be innovatively added into the optimisation process of factor graph to generate an optimised trajectory. We also develop a variant of the proposed algorithm that integrates the international regulations for preventing collisions at sea, enhancing its operational effectiveness in maritime environments. The proposed algorithms have been validated in a series of benchmark simulations and a dynamic obstacle avoidance mission in a high-fidelity maritime environment in the Robotic operating system to demonstrate the functionality and practicability.

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