In this paper, we propose a computationally efficient quadratic programming (QP) approach for generating smooth, $C^1$ continuous paths for mobile robots using piece-wise quadratic Bezier (PWB) curves. Our method explicitly incorporates safety margins within a structured optimization framework, balancing trajectory smoothness and robustness with manageable numerical complexity suitable for real-time and embedded applications. Comparative simulations demonstrate clear advantages over traditional piece-wise linear (PWL) path planning methods, showing reduced trajectory deviations, enhanced robustness, and improved overall path quality. These benefits are validated through simulations using a Pure-Pursuit controller in representative scenarios, highlighting the practical effectiveness and scalability of our approach for safe navigation.

This paper introduces a novel learning-based modeling framework for a magnetically steerable soft suction device designed for endoscopic endonasal brain tumor resection. The device is miniaturized (4 mm outer diameter, 2 mm inner diameter, 40 mm length), 3D printed using biocompatible SIL 30 material, and integrates embedded Fiber Bragg Grating (FBG) sensors for real-time shape feedback. Shape reconstruction is represented using four Bezier control points, allowing for a compact and smooth representation of the device's deformation. A data-driven model was trained on 5,097 experimental samples covering a range of magnetic field magnitudes (0-14 mT), actuation frequencies (0.2-1.0 Hz), and vertical tip distances from the surface of the electromagnet coil table (90-100 mm), using both Neural Network (NN) and Random Forest (RF) architectures. The RF model outperformed the NN across all metrics, achieving a mean root mean square error of 0.087 mm in control point prediction and a mean shape reconstruction error of 0.064 mm. Feature importance analysis further revealed that magnetic field components predominantly influence distal control points, while frequency and distance affect the base configuration. This learning-based approach effectively models the complex nonlinear behavior of hyperelastic soft robots under magnetic actuation without relying on simplified physical assumptions. By enabling sub-millimeter shape prediction accuracy and real-time inference, this work represents an advancement toward the intelligent control of magnetically actuated soft robotic tools in minimally invasive neurosurgery.

An End-to-End Framework for Optimizing Foot Trajectory and Force in Dry Adhesion Legged Wall-Climbing Robots Jichun Xiao 1 Jiawei Nie 2 Lina Hao 1 Zhi Li 2 Abstract -- Foot trajectory planning for dry adhesion legged climbing robots presents challenges, as the phases of foot detachment, swing, and adhesion significantly influence the adhesion and detachment forces essential for stable climbing. T o tackle this, an end-to-end foot trajectory and force optimization framework (FTFOF) is proposed, which optimizes foot adhesion and detachment forces through trajectory adjustments. This framework accepts general foot trajectory constraints and user-defined parameters as input, ultimately producing an optimal single foot trajectory. It integrates three-segment C 2 continuous Bezier curves, tailored to various foot structures, enabling the generation of effective climbing trajectories. A dilate-based GRU predictive model establishes the relationship between foot trajectories and the corresponding foot forces. Multi-objective optimization algorithms, combined with a redundancy hierarchical strategy, identify the most suitable foot trajectory for specific tasks, thereby ensuring optimal performance across detachment force, adhesion force and vibration amplitude. Experimental validation on the quadruped climbing robot MST - M3F showed that, compared to commonly used trajectories in existing legged climbing robots, the proposed framework achieved reductions in maximum detachment force by 28 %, vibration amplitude by 82 %, which ensures the stable climbing of dry adhesion legged climbing robots. I NTRODUCTION A legged wall-climbing robot is a mobile robot with leg-like structures, designed to navigate vertical, inclined, or even inverted surfaces. These robots are used in tasks that pose risks or challenges for humans, such as inspection [1] [2], maintenance [3], cleaning [4] [5], and search-and-rescue operations [6] [7]. The adhesion methods for legged wall-climbing robots can be classified into magnetic adhesion [8] [9], electrostatic adhesion [10] [11], vacuum adhesion [3] [12], and dry adhesion [13] [14]. Compared to other adhesion types, legged robots utilizing dry adhesion offer distinct advantages.

OpenStreetMap (OSM) has gained popularity recently in autonomous navigation due to its public accessibility, lower maintenance costs, and broader geographical coverage. However, existing methods often struggle with noisy OSM data and incomplete sensor observations, leading to inaccuracies in trajectory planning. These challenges are particularly evident in complex driving scenarios, such as at intersections or facing occlusions. To address these challenges, we propose a robust and explainable two-stage framework to learn an Orientation Field (OrField) for robot navigation by integrating LiDAR scans and OSM routes. In the first stage, we introduce the novel representation, OrField, which can provide orientations for each grid on the map, reasoning jointly from noisy LiDAR scans and OSM routes. To generate a robust OrField, we train a deep neural network by encoding a versatile initial OrField and output an optimized OrField. Based on OrField, we propose two trajectory planners for OSM-guided robot navigation, called Field-RRT* and Field-Bezier, respectively, in the second stage by improving the Rapidly Exploring Random Tree (RRT) algorithm and Bezier curve to estimate the trajectories. Thanks to the robustness of OrField which captures both global and local information, Field-RRT* and Field-Bezier can generate accurate and reliable trajectories even in challenging conditions. We validate our approach through experiments on the SemanticKITTI dataset and our own campus dataset. The results demonstrate the effectiveness of our method, achieving superior performance in complex and noisy conditions. Our code for network training and real-world deployment is available at https://github.com/IMRL/OriField.

In Rectified Flow, by obtaining the rectified flow several times, the mapping relationship between distributions can be distilled into a neural network, and the target distribution can be directly predicted by the straight lines of the flow. However, during the pairing process of the mapping relationship, a large amount of error accumulation will occur, resulting in a decrease in performance after multiple rectifications. In the field of flow models, knowledge distillation of multi - teacher diffusion models is also a problem worthy of discussion in accelerating sampling. I intend to combine multi - teacher knowledge distillation with Bezier curves to solve the problem of error accumulation. Currently, the related paper is being written by myself.

Adjusting the control actions of a wheeled robot to eliminate oscillations and ensure smoother motion is critical in applications requiring accurate and soft movements. Fuzzy controllers enable a robot to operate smoothly while accounting for uncertainties in the system. This work uses fuzzy theories and parallel distributed compensation to establish a robust controller for wheeled mobile robots. The use of fuzzy logic type I and type II controllers are covered in the study, and their performance is compared with a PID controller. Experimental results demonstrate that fuzzy logic type II outperforms type I and the classic controller. Further, we deploy parallel distributed compensation, sector of nonlinearity, and local approximation strategy in our design. These strategies help analyze the stability of each rule of the fuzzy controller separately and map the if-then rules of the fuzzy box into parallel distributed compensation using Linear Matrix Inequalities (LMI) analysis. Also, they help manage the uncertainty flow in the equations that exist in the kinematic model of a robot. Last, we propose a Bezier curve to represent the different pathways for the wheeled mobile robot.

Image research has shown substantial attention in deblurring networks in recent years. Yet, their practical usage in real-world deblurring, especially motion blur, remains limited due to the lack of pixel-aligned training triplets (background, blurred image, and blur heat map) and restricted information inherent in blurred images. This paper presents a simple yet efficient framework to synthetic and restore motion blur images using Inertial Measurement Unit (IMU) data. Notably, the framework includes a strategy for training triplet generation, and a Gyroscope-Aided Motion Deblurring (GAMD) network for blurred image restoration. The rationale is that through harnessing IMU data, we can determine the transformation of the camera pose during the image exposure phase, facilitating the deduction of the motion trajectory (aka. blur trajectory) for each point inside the three-dimensional space. Thus, the synthetic triplets using our strategy are inherently close to natural motion blur, strictly pixel-aligned, and mass-producible. Through comprehensive experiments, we demonstrate the advantages of the proposed framework: only two-pixel errors between our synthetic and real-world blur trajectories, a marked improvement (around 33.17%) of the state-of-the-art deblurring method MIMO on Peak Signal-to-Noise Ratio (PSNR).

This paper investigates the high-level decision-making problem in highway scenarios regarding lane changing and over-taking other slower vehicles. In particular, this paper aims to improve the Travel Assist feature for automatic overtaking and lane changes on highways. About 9 million samples including lane images and other dynamic objects are collected in simulation. This data; Overtaking on Simulated HighwAys (OSHA) dataset is released to tackle this challenge. To solve this problem, an architecture called SwapTransformer is designed and implemented as an imitation learning approach on the OSHA dataset. Moreover, auxiliary tasks such as future points and car distance network predictions are proposed to aid the model in better understanding the surrounding environment. The performance of the proposed solution is compared with a multi-layer perceptron (MLP) and multi-head self-attention networks as baselines in a simulation environment. We also demonstrate the performance of the model with and without auxiliary tasks. All models are evaluated based on different metrics such as time to finish each lap, number of overtakes, and speed difference with speed limit. The evaluation shows that the SwapTransformer model outperforms other models in different traffic densities in the inference phase. In the past decade, the field of autonomous driving has received lots of attention. Self-driving cars or autonomous vehicles (AV) represent a novelty of artificial intelligence (AI), robotics, computer vision, and sensor technology Grigorescu et al. (2020); Xiao et al. (2020); Zablocki et al. (2022). Many works focused on end-to-end learning approaches from camera to direct actions such as steering wheel, acceleration, and break Bojarski et al. (2016); Kim & Park (2017); Yang et al. (2018); however, there are many challenges such as lack of interpretability, data efficiency, safety and robustness, generalization, and trade-off between layers that make the end-to-end training less suitable for self-driving cars reliability. On the other hand, modular approaches break down the problem into different tasks such as perception and sensor cognition, motion prediction, high-level and low-level path planner, and motion controller Grigorescu et al. (2020); Atakishiyev et al. (2021); Teng et al. (2023).

In this paper, a feature extraction approach for the deformable linear object is presented, which uses a Bezier curve to represent the original geometric shape. The proposed extraction strategy is combined with a parameterization technique, the goal is to compute the regression features from the visual-feedback RGB image, and finally obtain the efficient shape feature in the low-dimensional latent space. Existing works of literature often fail to capture the complex characteristics in a unified framework. They also struggle in scenarios where only local shape descriptors are used to guide the robot to complete the manipulation. To address these challenges, we propose a feature extraction technique using a parameterization approach to generate the regression features, which leverages the power of the Bezier curve and linear regression. The proposed extraction method effectively captures topological features and node characteristics, making it well-suited for the deformation object manipulation task. Large mount of simulations are conducted to evaluate the presented method. Our results demonstrate that the proposed method outperforms existing methods in terms of prediction accuracy, robustness, and computational efficiency. Furthermore, our approach enables the extraction of meaningful insights from the predicted links, thereby contributing to a better understanding of the shape of the deformable linear objects. Overall, this work represents a significant step forward in the use of Bezier curve for shape representation.