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Search Results (222)

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Keywords = real-time trajectory smoothing

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24 pages, 7253 KB  
Article
On the Design of Smooth Curvature Tunable Paths for Safe Motion of Autonomous Vehicles
by Gianfranco Parlangeli
Designs 2026, 10(2), 42; https://doi.org/10.3390/designs10020042 - 7 Apr 2026
Abstract
Navigation is an essential ability for autonomous systems, and efficient motion planning for mobile robots is a central topic for autonomous vehicle design and service robotics. Most path-planning algorithms produce reference paths with sharp or discontinuous turns, inducing several drawbacks during mission execution, [...] Read more.
Navigation is an essential ability for autonomous systems, and efficient motion planning for mobile robots is a central topic for autonomous vehicle design and service robotics. Most path-planning algorithms produce reference paths with sharp or discontinuous turns, inducing several drawbacks during mission execution, such as unexpected inertial stress and strain on the mechanical structure, passenger discomfort, and unsafe and unpredictable deviation of the real trajectory with respect to the reference planned one. Oppositely, smooth and feasible trajectories are often desired in real-time navigation for nonholonomic mobile robots where the surrounding environment can have a dynamic and complex shape with obstacles. In this paper, we propose a novel technique for the generation of smooth, collision-free, and near time-optimal paths for nonholonomic mobile robots. The proposed method exploits the features of a set of tunable bump functions, with the goal of pursuing smooth reference curves with tunable features (such as curvature, or jerk) yet seeking a reasonable length minimality, thus combining the advantages of the two most adopted techniques, namely Bezier interpolation and Dubins curves. After a thorough description of the analytical methods, the paper is primarily concerned with the design and tuning methods of the path-planning algorithm. Both a graphical method and numerical investigations and examples are performed to fully exploit the algorithm potentialities and to show the efficiency of the proposed strategy. Full article
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14 pages, 1247 KB  
Article
A Scalable Post-Processing Pipeline for Large-Scale Free-Space Multi-Agent Path Planning with PIBT
by Arjo Chakravarty, Michael X. Grey, M. A. Viraj J. Muthugala and Rajesh Mohan Elara
Mathematics 2026, 14(7), 1195; https://doi.org/10.3390/math14071195 - 3 Apr 2026
Viewed by 168
Abstract
Free-space multi-agent path planning remains challenging at large scales. Most existing methods either offer optimality guarantees but do not scale beyond a few dozen agents or rely on grid-world assumptions that do not generalize well to continuous space. In this paper, we propose [...] Read more.
Free-space multi-agent path planning remains challenging at large scales. Most existing methods either offer optimality guarantees but do not scale beyond a few dozen agents or rely on grid-world assumptions that do not generalize well to continuous space. In this paper, we propose a hybrid, rule-based planning framework that combines Priority Inheritance with Backtracking (PIBT) with a novel safety-aware path smoothing method. Our approach extends PiBT to eight-connected grids and selectively applies string-pulling-based smoothing while preserving collision safety through local interaction awareness and a fallback collision resolution step based on Safe Interval Path Planning (SIPP). This design allows us to reduce overall path lengths while maintaining real-time performance. We demonstrate that our method can scale to over 500 agents in large free-space environments, outperforming existing any-angle and optimal methods in terms of runtime, while producing near-optimal trajectories in sparse domains. Our results suggest this framework is a promising building block for scalable, real-time multi-agent navigation in robotics systems operating beyond grid constraints. Full article
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16 pages, 3040 KB  
Article
Rank-Aware Conditional Synthesis: Feasible Quantum Generative Modeling on Matrix Product State Manifolds
by Dongkyu Lee, Won-Gyeong Lee, Hyunjun Hong and Ohbyung Kwon
Symmetry 2026, 18(4), 605; https://doi.org/10.3390/sym18040605 - 2 Apr 2026
Viewed by 214
Abstract
Matrix Product States (MPSs) have become an indispensable symmetry-based representation for simulating quantum systems on near-term hardware by constraining entanglement entropy through a fixed bond dimension χ. This study identifies a critical “rank explosion” phenomenon that destabilizes this low-rank manifold during conditional [...] Read more.
Matrix Product States (MPSs) have become an indispensable symmetry-based representation for simulating quantum systems on near-term hardware by constraining entanglement entropy through a fixed bond dimension χ. This study identifies a critical “rank explosion” phenomenon that destabilizes this low-rank manifold during conditional quantum diffusion processes. We empirically demonstrate that the introduction of conditional guidance—essential for semantic control—injects global correlations that drive the effective Schmidt rank to increase by 4× (from χ=4 to 16), saturating the simulation limits and necessitating quantum circuits with approximately 1.8×103 Controlled-NOT (CNOT) gates. Such circuit depths fundamentally exceed the operational coherence budgets of Noisy Intermediate-Scale Quantum (NISQ) devices. To mitigate this structural instability, we propose Rank-Aware Conditional Synthesis (RACS), a sampling framework that maintains the latent trajectory within a prescribed MPS manifold through step-wise manifold projection and time-shift error correction. Experimental results on real-world semantic data reveal that RACS reduces reconstruction error, or Mean Squared Error (MSE) by 30.8% and enhances latent trajectory smoothness by 36.8% compared to conventional post hoc truncation. At a fixed hardware-efficient rank of χ=4, RACS achieves a +4.8% fidelity gain and exhibits superior robustness against depolarizing noise. By resolving the tension between conditional expressivity and entanglement constraints, RACS provides a principled, hardware-aware methodology for high-fidelity quantum generative modeling. Full article
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28 pages, 5422 KB  
Article
Vision-Guided Dual-Loop Control of a Truck-Mounted Electric Water Cannon for Autonomous Fire Suppression
by Zhiyuan Chen and Chaofeng Liu
Appl. Sci. 2026, 16(7), 3469; https://doi.org/10.3390/app16073469 - 2 Apr 2026
Viewed by 154
Abstract
Fire trucks equipped with truck-mounted electric water cannons are key mobile firefighting assets for urban and industrial fire response. However, due to the inherent mechanical inertia of the cannon body, its low-frequency motion response cannot match high-frequency control commands, making the system prone [...] Read more.
Fire trucks equipped with truck-mounted electric water cannons are key mobile firefighting assets for urban and industrial fire response. However, due to the inherent mechanical inertia of the cannon body, its low-frequency motion response cannot match high-frequency control commands, making the system prone to oscillations and control instability. To address this command–execution frequency mismatch, this paper proposes a decoupled dual closed-loop control architecture for truck-mounted electric water cannons on mobile fire trucks: the fast loop is used for fire-source tracking and rapid localization, while the slow loop is used for water-jet aiming alignment. In the fast loop, a 2-D quadrant positioning rule drives the pan–tilt unit to achieve rapid fire tracking and accurate centering. In the slow loop, Kalman-filter-based state estimation and delay-aligned prediction generate feedforward aiming commands; these commands are fused with error feedback and further processed through command limiting and trajectory optimization, ultimately producing smooth and executable angle references. The visual perception module ran at 58 FPS, satisfying the real-time requirement of the proposed system. In five repeated extinguishment tests under controlled open-site conditions, the proposed method successfully completed all trials and reduced the mean extinguishment time to 13.55 s, compared with 15.83 s for the incremental-PID baseline and 23.76 s for the coupled proportional baseline, while also showing smoother correction and less redundant oscillation. Full article
(This article belongs to the Section Mechanical Engineering)
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25 pages, 2828 KB  
Article
Adaptive Nonsingular Fast Terminal Sliding Mode Control for Space Robot Based on Wavelet Neural Network Under Lumped Uncertainties
by Junwei Mei, Yawei Zheng, Haiping Ai, Feilong Xiong, An Zhu and Xiaodong Fu
Aerospace 2026, 13(4), 334; https://doi.org/10.3390/aerospace13040334 - 2 Apr 2026
Viewed by 106
Abstract
This paper proposes an adaptive wavelet neural network nonsingular fast terminal sliding mode control strategy based on a finite-time framework for a space robot system under external disturbances and model uncertainties. Firstly, the dynamic model of space robot is established based on the [...] Read more.
This paper proposes an adaptive wavelet neural network nonsingular fast terminal sliding mode control strategy based on a finite-time framework for a space robot system under external disturbances and model uncertainties. Firstly, the dynamic model of space robot is established based on the second Lagrange equation. Unlike sliding mode control, which converges asymptotically, terminal sliding mode control (TSMC) has been proposed to ensure finite-time convergence for a space robot system. Based on the aforementioned TSMC framework, the fast terminal sliding mode control (FTSMC) is proposed to enhance system convergence rate. However, TSMC exhibits a singularity issue attributed to the presence of negative fractional order. To avoid this issue, a nonsingular fast terminal sliding mode controller (NFTSMC) has been proposed. The controller is designed to integrate linear and nonlinear terms into a novel nonsingular fast terminal sliding mode surface. The method achieves fast finite-time convergence concurrently with improved robustness, while effectively avoiding singularities. To compensate for external disturbances and model uncertainties in the space robot system, this paper proposes the combination of wavelet neural network (WNN) for the real-time estimation of lumped uncertainties. Network parameters are dynamically adjusted via an adaptive law to mitigate chattering effectively and enhance trajectory tracking precision. Utilizing Lyapunov stability theory and numerical simulations, the space robot system’s stability is rigorously proven and the controller effectiveness is validated. Compared with the traditional NFTSMC, the proposed control strategy reduces the convergence time by 20.74%. In the case of trajectory tracking comparison, the root mean square error (RMSE) improves by 35.85%, the mean tracking error improves by 63.29%, the integral of absolute error (IAE) improves by 29.37%, and the integral of time-weighted absolute error (ITAE) improves by 93.06%. Additionally, a comparative simulation with RBFNN is included in this paper. Compared with RBFNN, the proposed control strategy reduces input torque energy consumption by 77.36% and improves control smoothness by 87.03%, quantitatively demonstrating the effectiveness of the proposed control strategy. Full article
(This article belongs to the Special Issue Space Navigation and Control Technologies (2nd Edition))
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23 pages, 2866 KB  
Article
A Cloud–Robot–Wearable System for Bilateral Reaching Rehabilitation: Affected-Side Identification and Quality Quantification
by Chia-Hau Chen, Li-Hsien Tang, Chang-Hsin Yeh, Eric Hsiao-Kuang Wu and Shih-Ching Yeh
Electronics 2026, 15(7), 1459; https://doi.org/10.3390/electronics15071459 - 1 Apr 2026
Viewed by 256
Abstract
Therapist shortages make home-based rehabilitation an essential component of post-stroke care, yet patients often exhibit reduced adherence when functional gains are difficult to quantify and interpret. This study presents a cloud-enabled assessment framework centered on a dynamic reaching task for upper-limb rehabilitation in [...] Read more.
Therapist shortages make home-based rehabilitation an essential component of post-stroke care, yet patients often exhibit reduced adherence when functional gains are difficult to quantify and interpret. This study presents a cloud-enabled assessment framework centered on a dynamic reaching task for upper-limb rehabilitation in individuals with mild stroke. The proposed system combines wearable sensing and Internet of Things (IoT) connectivity to stream kinematic data to the cloud for near real-time analysis, and integrates a force-feedback rehabilitation robot to deliver motion guidance during training. The pipeline proceeds in three stages. First, smoothness-related kinematic descriptors are extracted and fed into a deep multi-class classifier to discriminate the affected side (left, right, or healthy). Second, movement quality is modeled using a Gaussian Mixture Model (GMM) trained on IoT-acquired trajectories to quantify performance via probabilistic similarity. Third, a calibrated scoring function transforms GMM log-likelihood into a normalized 0–1 quality index, producing visual reports that support interpretable feedback for patients and therapists. The framework is validated using motion data collected from stroke patients at Taipei Veterans General Hospital. Experimental results demonstrate that the neural network multi-classifier achieved an F1-score of 0.95. Incorporating robot-derived interaction signals further improved classification performance by approximately 5%. For movement quality assessment, the derived scores showed a significant positive correlation (Pearson correlation = 0.632, p = 0.02) with therapist-defined gold reference standards for right-affected patients. Additionally, integrating robot force-feedback signals and AIoT-enabled dynamic streams improved score accuracy by 8% and score responsiveness by 10%. These quantitative outcomes substantiate the efficacy of combining IoT-driven sensing and robot-assisted training for objective, interpretable, and remotely deployable motor assessment. Full article
(This article belongs to the Section Computer Science & Engineering)
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16 pages, 34530 KB  
Article
A Hybrid θ*-APF-Q Framework for Energy-Aware Path Planning of Unmanned Surface Vehicles Under Wind and Current
by Xiaojie Sun, Zhanhong Dong, Xinbo Chen, Lifan Sun and Yanheng An
Sensors 2026, 26(7), 2116; https://doi.org/10.3390/s26072116 - 29 Mar 2026
Viewed by 278
Abstract
Safe and energy-aware navigation is still difficult for unmanned surface vehicles (USVs), especially in cluttered waters where obstacles, smooth motion, and wind or current effects must be considered at the same time. If these issues are handled separately, the path may become longer [...] Read more.
Safe and energy-aware navigation is still difficult for unmanned surface vehicles (USVs), especially in cluttered waters where obstacles, smooth motion, and wind or current effects must be considered at the same time. If these issues are handled separately, the path may become longer and the vehicle may turn more often, which raises propulsion effort and hurts stability. To reduce these problems, a hybrid path planning method called θ-APF-Q is proposed, and it combines global planning, learning-based decisions, and local adjustment in a three-layer structure. First, an any-angle θ global planner is employed to generate a near-optimal backbone trajectory by line-of-sight pruning, thereby reducing redundant waypoints and limiting detours. Second, an enhanced tabular Q-learning model is executed in an expanded eight-direction action space, and policy learning is guided by a multi-objective reward that jointly encourages distance reduction, alignment with ocean current and wind-induced forces for energy saving, smooth heading variation to suppress excessive steering, and maintenance of a safety margin near obstacles. Third, an adaptive artificial potential field (APF) module is used for real-time local correction, providing repulsion in high-risk regions and assisting trajectory smoothing to reduce unnecessary turning operations. A decision bias strategy further couples instantaneous APF forces with long-term state–action values, while the influence weight is adaptively adjusted according to environmental complexity. The algorithm is validated on the randomly generated marine grid maps and on the real-world satellite map scenario, with comparisons against a conventional four-direction Q-learning baseline. Across randomized tests, average path length, turning frequency, and the composite energy indicator are reduced by 22.3%, 55.6%, and 26.4%, respectively, and the success rate increases by 16%. The results indicate that integrating global guidance, adaptive learning, and local reactive decision making supports practical, energy-aware USV navigation. Full article
(This article belongs to the Special Issue Intelligent Sensing and Control Technology for Unmanned Vehicles)
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21 pages, 2822 KB  
Article
Policy-Guided Model Predictive Path Integral for Safe Manipulator Trajectory Planning
by Liang Liang, Chengdong Wu and Xiaofeng Wang
Sensors 2026, 26(7), 2074; https://doi.org/10.3390/s26072074 - 26 Mar 2026
Viewed by 429
Abstract
Aiming at the problems of difficult hard-constraint enforcement and weak environmental generalization ability in the safe trajectory planning of manipulators in complex environments, a Policy-Guided Model Predictive Path Integral (PG-MPPI) planning framework is proposed. This framework integrates the advantages of reinforcement learning and [...] Read more.
Aiming at the problems of difficult hard-constraint enforcement and weak environmental generalization ability in the safe trajectory planning of manipulators in complex environments, a Policy-Guided Model Predictive Path Integral (PG-MPPI) planning framework is proposed. This framework integrates the advantages of reinforcement learning and model predictive control to construct a global prior guidance, local real-time optimization and hard-constraint safety assurance: a Constraint-Discounted Soft Actor–Critic (CD-SAC) offline learning policy is designed, which incorporates the configuration-space distance field as a safety guidance term to realize the learning of obstacle avoidance behavior; the offline policy is used to guide the online sampling and optimization of MPPI, improving sampling efficiency and planning quality; and a Control Barrier Function (CBF) safety filter is introduced to revise control commands in real time, ensuring the strict satisfaction of constraints. Taking the SIASUN T12B manipulator as the research object, simulation comparison experiments are carried out in multi-obstacle scenarios. The results show that the PG-MPPI algorithm outperforms the comparison algorithms in the success rate of collision-free target reaching, ensures the smoothness and feasibility of the trajectory, and has a good adaptive capacity to complex environments with unknown obstacle configurations, thus providing an efficient solution for the autonomous and safe operation of manipulators. Full article
(This article belongs to the Section Navigation and Positioning)
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19 pages, 34223 KB  
Article
A Real Time Multi Modal Computer Vision Framework for Automated Autism Spectrum Disorder Screening
by Lehel Dénes-Fazakas, Ioan Catalin Mateas, Alexandru George Berciu, László Szilágyi, Levente Kovács and Eva-H. Dulf
Electronics 2026, 15(6), 1287; https://doi.org/10.3390/electronics15061287 - 19 Mar 2026
Viewed by 348
Abstract
Background: The early detection of autism spectrum disorder (ASD) is imperative for enhancing long-term developmental outcomes. Nevertheless, conventional screening methods depend on time-consuming, expert-driven behavioral assessments and are characterized by limited scalability. Automated video-based analysis provides a noninvasive and objective approach for the [...] Read more.
Background: The early detection of autism spectrum disorder (ASD) is imperative for enhancing long-term developmental outcomes. Nevertheless, conventional screening methods depend on time-consuming, expert-driven behavioral assessments and are characterized by limited scalability. Automated video-based analysis provides a noninvasive and objective approach for the extraction of behavioral biomarkers from naturalistic recordings. Methods: A modular multimodal framework was developed that integrates motion-based video analysis and facial feature extraction for the purpose of ASD versus typically developing (TD) classification. The system is capable of processing RGB videos, skeleton/stickman representations, and motion trajectory streams. A comprehensive set of kinematic features was extracted, encompassing joint trajectories, velocity and acceleration profiles, posture variability, movement smoothness, and bilateral asymmetry. The repetitive stereotypical behaviors exhibited by the subjects were characterized using frequency-domain analysis via FFT within the 0.3–7.0 Hz band. Facial expression features derived from normalized face crops and landmark-based morphological descriptors were integrated as complementary modalities. The feature-level fusion process was executed subsequent to z-score normalization, and the classification procedure was conducted using a Random Forest model with stratified 5-fold cross validation. The implementation of GPU acceleration was instrumental in facilitating near real-time inference. Results: The motion-based ComplexVideos pipeline demonstrated a cross-validated accuracy of 94.2 ± 2.1% with an area under the ROC curve (AUC) of 0.93. Skeleton-based KinectStickman inputs demonstrated moderate performance, with an accuracy range of 60–80%. In contrast, facial-only models exhibited an accuracy of approximately 60%. The integration of multiple modalities through feature fusion has been demonstrated to enhance the robustness of classification algorithms and mitigate the occurrence of false negative outcomes, thereby surpassing the performance of single-modality models. The mean inference time remained below one second per video frame under standard operating conditions. Conclusions: The experimental results demonstrate that the integration of multimodal cues, including motion and facial features, facilitates the development of effective and efficient video-based screening methods for autism spectrum disorder (ASD). The proposed framework is designed to offer a scalable, extensible, and computationally efficient solution that can support early screening in clinical and remote assessment settings. Full article
(This article belongs to the Special Issue Computer Vision and Machine Learning for Biometric Systems)
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25 pages, 1126 KB  
Article
Energy-Efficient Path Planning for AMR Using Modified A* Algorithm with Machine Learning Integration
by Mishell Cadena-Yanez, Danel Rico-Melgosa, Ekaitz Zulueta, Angela Bernardini and Jorge Rodriguez-Guerra
Robotics 2026, 15(3), 62; https://doi.org/10.3390/robotics15030062 - 18 Mar 2026
Viewed by 312
Abstract
Energy consumption optimisation has emerged as a critical need in Autonomous Mobile Robots (AMRs). Conventional A* implementations typically minimise path distance, neglecting energy-relevant factors such as directional changes and trajectory smoothness that significantly impact battery life and operational costs. This work proposes two [...] Read more.
Energy consumption optimisation has emerged as a critical need in Autonomous Mobile Robots (AMRs). Conventional A* implementations typically minimise path distance, neglecting energy-relevant factors such as directional changes and trajectory smoothness that significantly impact battery life and operational costs. This work proposes two energy-aware A* variants trained on empirical data from the KUKA KMP 1500 platform, where energy consumption is measured as battery SoC depletion: A*-RF, which integrates a Random Forest (RF) model directly into the cost function, and A*-MOD, which approximates the energy model through RF feature importance weights, achieving linear computational complexity O(nf). The RF model predicted energy consumption with an RMSE below 1.5% relative error, identifying travel distance and rotation angle as the dominant energy factors. Experimental validation across 42 path planning scenarios on a real industrial factory floor demonstrates that A*-MOD reduces energy consumption by up to 58.91% and improves operational autonomy by 2.21 times, with statistically significant improvements (p < 0.01) across all evaluated metrics. Full article
(This article belongs to the Section Sensors and Control in Robotics)
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24 pages, 10468 KB  
Article
BGSE-RRT*: A Goal-Guided and Multi-Sector Sampling-Expansion Path Planning Algorithm for Complex Environments
by Wenhao Yue, Xiang Li, Ziyue Liu, Xiaojiang Jiang and Lanlan Pan
Sensors 2026, 26(6), 1837; https://doi.org/10.3390/s26061837 - 14 Mar 2026
Viewed by 268
Abstract
In complex ground environments, conventional RRT* often suffers from low planning efficiency and poor path quality for robot path planning. This paper proposes BGSE-RRT* (Bi-tree Cooperative, Goal-guided, low-discrepancy Sampling, multi-sector Expansion). First, BGSE-RRT* constructs a nonlinear switching probability via bi-tree cooperative adaptive switching, [...] Read more.
In complex ground environments, conventional RRT* often suffers from low planning efficiency and poor path quality for robot path planning. This paper proposes BGSE-RRT* (Bi-tree Cooperative, Goal-guided, low-discrepancy Sampling, multi-sector Expansion). First, BGSE-RRT* constructs a nonlinear switching probability via bi-tree cooperative adaptive switching, together with KD-Tree nearest-neighbor acceleration and multi-condition triggering, to adaptively balance global exploration and local convergence. Meanwhile, a goal-guided expansion with dynamic target binding and adaptive step size, under a multi-constraint feasibility check, accelerates the convergence of the two trees. When the goal-guided expansion becomes blocked, BGSE-RRT* generates candidate points in local multi-sector regions using a 2D Halton low-discrepancy sequence and selects the best candidate for expansion; if the multi-sector expansion still fails, a sampling-point-guided expansion is activated to continue advancing and search for a feasible path. Second, B-spline smoothing is applied to improve trajectory continuity. Finally, in five simulation environments and ROS/real-robot joint validation, compared with GB-RRT*, BI-RRT*, BI-APF-RRT*, and BAI-RRT*, BGSE-RRT* reduces planning time by up to 84.71%, shortens path length by 2.94–6.88%, and improves safety distance by 20.68–48.33%. In ROS/real-robot validation, the trajectory-tracking success rate reaches 100%. Full article
(This article belongs to the Section Sensors and Robotics)
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31 pages, 4728 KB  
Article
Hierarchical Dynamic Obstacle-Avoidance Strategy Combining Hybrid A* and DWA with Adaptive Path Re-Entry for Unmanned Surface Vessels
by Qin Wang, Leilei Cheng, Kexin Wang and Gang Zhang
Appl. Sci. 2026, 16(6), 2692; https://doi.org/10.3390/app16062692 - 11 Mar 2026
Viewed by 307
Abstract
Obstacle-avoidance risk threshold control and global discrete keypoint re-entry are critical factors influencing the smooth dynamic obstacle avoidance of unmanned vessels. For underactuated USVs, which operate in planar motion with three degrees of freedom (surge, sway, and yaw) but only two independent control [...] Read more.
Obstacle-avoidance risk threshold control and global discrete keypoint re-entry are critical factors influencing the smooth dynamic obstacle avoidance of unmanned vessels. For underactuated USVs, which operate in planar motion with three degrees of freedom (surge, sway, and yaw) but only two independent control inputs (surge velocity and yaw rate), this paper designs a layered obstacle-avoidance strategy featuring adaptive global path re-entry points, combined with short- and long-term obstacle trajectory prediction and risk perception. This method employs an Interactive Multiple Model (IMM) integrating Constant Velocity (CV), Constant Acceleration (CA), and Constant Turn Rate and Acceleration (CTRA) models to perform long-term spatiotemporal trajectory prediction for dynamic obstacles, constructing a spatiotemporal risk cost map. Long-term dynamic obstacle-avoidance trajectory planning is achieved through optimized adaptive global trajectory re-entry points and an improved A* algorithm. This long-term avoidance trajectory replaces the global path from the avoidance start to the re-entry point, providing a smooth, continuous long-term avoidance prediction. To ensure real-time collision avoidance effectiveness, an improved Dynamic Window Approach (DWA) algorithm uses the long-term avoidance trajectory as a foundation. It integrates the IMM’s short-term spatiotemporal obstacle trajectory prediction, sampling in the velocity and steering angle space to generate short-term avoidance control commands. Finally, the long-term and short-term obstacle-avoidance planning are executed in a receding-horizon manner, where the local DWA planner updates control inputs over a short rolling window without solving a full constrained optimization problem. This establishes a hierarchical avoidance strategy: long-term prediction enables smooth avoidance, while short-term prediction enables real-time avoidance, ensuring the continuity and timeliness of dynamic obstacle avoidance. Simulation results demonstrate that compared with traditional A* planning, the proposed risk-aware A* reduces cumulative collision risk by 62% and increases the minimum obstacle clearance distance by over 32.1%, while maintaining acceptable path length growth. This approach effectively reduces collision risks during navigation, enhances path smoothness, and improves navigation safety. Full article
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36 pages, 805 KB  
Article
Real-Time Embedded NMPC for Autonomous Vehicle Path Tracking with Curvature-Aware Speed Adaptation and Sensitivity Analysis
by Taoufik Belkebir, Hicham Belkebir and Anass Mansouri
Automation 2026, 7(2), 44; https://doi.org/10.3390/automation7020044 - 6 Mar 2026
Viewed by 507
Abstract
Local path tracking is a critical challenge for autonomous vehicles, requiring precise trajectory following under nonlinear dynamics, strict constraints, and real-time execution. While Nonlinear Model Predictive Control (NMPC) has emerged as a leading approach, many existing methods decouple velocity planning from tracking, lack [...] Read more.
Local path tracking is a critical challenge for autonomous vehicles, requiring precise trajectory following under nonlinear dynamics, strict constraints, and real-time execution. While Nonlinear Model Predictive Control (NMPC) has emerged as a leading approach, many existing methods decouple velocity planning from tracking, lack formal stability guarantees, or do not demonstrate feasibility on embedded platforms. We present a unified NMPC framework that integrates curvature-aware velocity adaptation directly into the cost function. The controller makes use of cubic spline paths, recursive feasibility constraints, and Lyapunov-based terminal costs to ensure stability. The nonlinear optimization problem is implemented in CasADi and solved using IPOPT, with warm-starting and efficient discretization techniques enabling real-time performance. Our approach has been validated in the CARLA simulator across a variety of urban scenarios, including straight roads, intersections, and roundabouts. The controller achieves a mean cross-track error of 0.10 m on straight roads, 0.44 m on roundabouts, and 1.36 m on tight intersections, while maintaining smooth control inputs and bounded actuator effort. A curvature-aware cost term yields a 14.4% reduction in lateral tracking error compared to the curvature-unaware baseline. Benchmarking results indicate that the Raspberry Pi 5 outperforms the NVIDIA Xavier AGX by 1.5–1.6×, achieving mean execution times of 38–45 ms across all scenarios. This demonstrates that advanced NMPC can run in real time on low-cost consumer hardware ($80 vs. $700). Systematic ablation studies reveal the critical role of state weighting (Q) and input regularization (R): removing Q degrades tracking by 10% and destabilizes control effort (+54% acceleration, +477% steering), while omitting R induces oscillatory behavior with +907% acceleration effort. Euler integration provides no computational benefit (+8% solver time) while degrading accuracy by 25%, confirming RK4 as strictly superior. Sensitivity analysis via Latin Hypercube Sampling identifies the prediction horizon (N) and discretization timestep (Δt) as dominant parameters. Per-scenario Pareto analysis yields a balanced operating point (N=15, Δt=0.055 s) used for all primary evaluations, while a global sweep identifies a robust alternative (N=12, Δt=0.086 s) suitable for general deployment tuning. This framework bridges the gap between spline-based local planning and stability-guaranteed NMPC, offering a simulation-validated, real-time solution for embedded autonomous driving research. Future work will focus on hardware-in-the-loop and full-vehicle deployment, integration with high-level decision-making, and learning-enhanced MPC. Full article
(This article belongs to the Section Robotics and Autonomous Systems)
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26 pages, 2942 KB  
Article
Real-Time Adaptive Linear Quadratic Regulator Control for the QUBE–2 Rotary Inverted Pendulum
by Cynthia Lopez-Jordan and Mohammad Jafari
Math. Comput. Appl. 2026, 31(2), 33; https://doi.org/10.3390/mca31020033 - 27 Feb 2026
Viewed by 469
Abstract
This paper presents a real-time adaptive Linear Quadratic Regulator (LQR) control strategy for the rotary inverted pendulum. The state weighting matrix of the LQR cost function is continuously adapted online based on real-time tracking error, state dynamics, and sliding-mode-inspired robustness measures. Unlike conventional [...] Read more.
This paper presents a real-time adaptive Linear Quadratic Regulator (LQR) control strategy for the rotary inverted pendulum. The state weighting matrix of the LQR cost function is continuously adapted online based on real-time tracking error, state dynamics, and sliding-mode-inspired robustness measures. Unlike conventional LQR controllers with fixed weighting matrices or hybrid schemes that apply sliding mode control directly to the control input, the proposed approach modulates the LQR cost function itself, enabling dynamic reshaping of controller behavior while preserving smooth control action. The real-time adaptive controller is implemented using a continuous-time Riccati differential equation solved online, making the method suitable for real-time deployment. Experimental validation is conducted on two Quanser QUBE-Servo 2 rotary inverted pendulum platforms under square, sinusoidal, and sawtooth reference trajectories. Performance is compared against a fixed-gain LQR controller using multiple quantitative metrics, including tracking error and control effort. Experimental results demonstrate substantial improvements in tracking accuracy, with reductions exceeding 70–90% in error metrics, while simultaneously achieving over 94% reduction in control effort. These findings verify that adaptive cost shaping provides an effective and practical mechanism for enhancing LQR performance in underactuated experimental systems. Full article
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30 pages, 3881 KB  
Article
A Bio-Inspired Fluid Dynamics Approach for Unified and Efficient Path Planning and Control
by Mohammed Baziyad, Raouf Fareh, Tamer Rabie, Ibrahim Kamel and Brahim Brahmi
Actuators 2026, 15(3), 133; https://doi.org/10.3390/act15030133 - 27 Feb 2026
Viewed by 332
Abstract
This paper presents a novel bio-inspired fluid dynamics framework that unifies path planning and control within a single continuous navigation process. Unlike conventional approaches that separate trajectory generation and execution, the proposed method models the robot as a particle immersed in an artificial [...] Read more.
This paper presents a novel bio-inspired fluid dynamics framework that unifies path planning and control within a single continuous navigation process. Unlike conventional approaches that separate trajectory generation and execution, the proposed method models the robot as a particle immersed in an artificial fluid field, where the goal acts as a sink and obstacles modify the flow to produce collision-free motion. To ensure global optimality and eliminate local minima traps, the framework incorporates a sampling-based enhancement that evaluates multiple trajectories within high-flow regions and selects the optimal path using graph-based optimization. A fluid-based control law directly converts the velocity field into robot motion commands, enabling seamless integration between planning and execution. Theoretical stability is established using Lyapunov analysis, guaranteeing convergence to the goal. Extensive experiments on a Pioneer P3-DX robot demonstrate that the proposed approach achieves execution speeds 1.5 to 9.7 times faster than A*, PRM, and RRT*, while producing paths 3.6% to 29.5% shorter. Furthermore, the unified framework provides smooth and accurate motion with tracking errors within ±0.1 m. These results confirm that the proposed method improves path quality, computational efficiency, and real-time navigation performance. Full article
(This article belongs to the Section Actuators for Robotics)
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Figure 1

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