Trajectory Error Research Articles

Sensing equivalent kinematics enables robot-assisted mirror rehabilitation training via a broaden learning system

IntroductionRobot-assisted mirror therapy has been widely developed to help remodeling of premotor cortex for patients suffering from motor disability of limbs. Nevertheless, it is difficult to achieve real-time adaptive control in robot-assisted mirror rehabilitation training, particularly for patients with varying levels of limb impairment.MethodsThis paper proposes an equivalent kinematics control framework based on the Broaden Learning System model for active robotic mirror rehabilitation, where people’s bilateral upper limbs actively perform mirror movements to enhance the impaired limb’s participation. The framework accommodates a broaden learning model from sensing multi-kinematic features to adjust the robotic damping coefficient in assisting human participants to complete mirror-symmetry training. Besides, in order to adapt to inter-patients’ variability with different disability levels, a challenge-level modification interface is also fused for safer training. This model is verified by additional symmetry indicator such as position trajectory error and force.ResultsExperimental results show that the weaker subjects can also maintain mirror movement with the stronger subjects under the help of this model and verify the performance of framework in mirror-symmetry effects and movement smoothness. This leads us to believe that the framework can safely and efficiently assist human participants in completing mirror-symmetry movement.DiscussionThe framework has the potential to improve outcomes in smoother and safer mirror-symmetry training by sensing multi-kinematic features. Future studies are necessary to involve clinical trials with actual patients.

Design and Optimization of Non-Coplanar Orbits for Orbital Photovoltaic Panel Cleaning Robots

Aiming at the problem that it is difficult for an orbital photovoltaic panel cleaning robot to span a large distance between photovoltaic panels, a method of designing and optimizing a non-coplanar orbit based on Bezier curves is proposed. Firstly, the robot’s motion law is analyzed to obtain trajectory data for a single work cycle. Then, Bezier curves are utilized for trajectory design to ensure a smooth transition during the spanning motion phase. Thirdly, with the average value of the minimum distance between the Bezier curve and the point set data of the spanning motion phase as the optimization objective function, the nonlinear planning based on the SQP algorithm was adopted for the optimization of the upper and lower trajectories. Finally, the results of the case calculations indicate that the standard deviation of the optimized upper and lower trajectories was reduced by 35.63% and 40.57%, respectively. Additionally, the ADAMS simulation validation demonstrates that the trajectory errors of the four wheels decreased by a maximum of 8.79 mm, 23.78 mm, 10.11 mm, and 14.97 mm, respectively, thereby confirming the effectiveness of the trajectory optimization.

Intelligent multi-robot collaborative transport system

The research on multi-robot systems has been divided into various fields, such as communication, navigation, task allocation, and collaborative transport. While significant progress has been made in each area, there has been limited research integrating these fields to build a fully autonomous multi-robot collaborative transport system. Therefore, we identify the key issues and propose a multi-robot collaborative transport system founded on ROS1 and conduct validation in a simulated environment, laying a solid foundation for the system to run on real robots. The primary contributions of this study include three key areas: (1) modeling and validating robot collaborative transport, (2) developing a visual task allocation system leveraging FastDDS service, and (3) resolving path collision issues in multi-robot navigation through both traditional methods and reinforcement learning techniques. Extensive experimental evaluations demonstrate that the proposed intelligent multi-robot collaborative transport system can autonomously navigate to target points for collaborative transport task. Performance assessments, based on the error between the target point and the object’s arrival point as well as the transport trajectory error, reveal that the system effectively completes the assigned tasks.

Bionic ankle-assisted rehabilitation training system based on biomechanical evaluation

In modern society, people’s life rhythm is getting faster and faster. Ankle injury would significantly reduce the frequency of people’s activities, which has a great impact on people’s normal work and life. As a new medical method, the bionic ankle rehabilitation training system is used to assist rehabilitation doctors to help patients complete joint flexibility and recovery training. In the research method of ankle biomechanical characteristics, the detection of ankle joint patient’s motion is particularly important. The purpose of this paper is to study how to design a bionic ankle assisted rehabilitation training system based on image processing. Therefore, this paper proposes an image-based moving target detection method, which has the advantages of high reliability and simple operation, and can improve the recognition rate of the ankle joint movement. The experimental results of this paper showed that the system can realize the predetermined trajectory movement and run the system stably. In terms of patient following error, it was kept within 0.03cm. The following error of the ankle joint trajectory was up to 0.03cm and the lowest was 0.01cm, which was almost negligible. In terms of accuracy, the accuracy of the system was also very high, and it can respond and determine the patient’s actions quickly, thereby helping patients to better perform rehabilitation training.

Enhancing the MCL-SLAM algorithm to overcome the issue of illumination variation, non-static environment and kidnapping to present the NIK-SLAM

AbstractSimultaneous Localization and Mapping (SLAM) is a major challenge that has been comprehensively investigated by scholars. SLAM’s ability to support autonomous navigation helps the robot to move from one place to another without being controlled by humans. This achievement has attracted the attention of scholars towards focusing on this area. Over the decades, countless procedures have been developed with extraordinary accomplishments. However, some problems can degrade the efficiency of SLAM (Simultaneous Localization and Mapping) technique, and examples of such problems include environmental noises (light intensity and shadow), non-static environment, and kidnap robots. These problems create inconsistency in measurement that can lead to erroneous navigation for an unmanned vehicle. In minimizing the effect of these problems, a novel SLAM technique based on several re-modifications of MCL is presented in this paper. This innovative technique is known as NIK-SLAM. The NIK-SLAM is equipped with filters alongside some modifications of the original Monte-Carlo algorithm (MCL) to maximize its performance. The filters were employed to overcome the effect of shadow and light intensity while the re-modification of MCL is used to overcome the limitation of kidnapping and non-static objects. A publicly available dataset (TUM-RGBD) and a private dataset were used for evaluation. Matlab was used for simulation while assessments were based on quantitative and qualitative validation. The results demonstrated a better performance of the NIK-SLAM, attaining a lower trajectory error for most experiments when compared to the original MCL and other SLAM algorithms found in the literature, but at the expense of delayed processing time. Furthermore, this accomplishment supports pathway planning, and exploration into unstable environments while it decreases accident rates/human fatalities, and in the future study, the issue of delayed processing time will be addressed.

Adaptive control scheme for cooperative transport systems navigation under uncertainty

An adaptive robust control scheme for a cooperative transport system is proposed to tackle the challenges arising from parameter uncertainty, external interference, measurement errors, and other factors. The cooperative transport system consists of a leader automated ground vehicle, a baggage carrier, and a follower automated ground vehicle. Firstly, a mechanics-based independent dynamic model without constraints is established for each component within the system, and the coupling relationship between components is analyzed to design the constraint function. Secondly, to address inaccuracies in initial conditions, the trajectory errors in both their zero- and first-order forms are introduced. A closed-form dynamic model that is subject to constraints is then developed for the entire cooperative system, incorporating both structural and performance constraints. Thirdly, an innovative adaptive robust control scheme is introduced for mechanical systems facing uncertainty. An adaptive law is devised to estimate the bounds of uncertainty. The control is deterministic and can be mathematically expressed in a closed-form. Fourthly, a constrained optimization problem is formulated using the fuzzy information of uncertainty to choose an appropriate optimal gain kopt of the adaptive law. This is achieved by minimizing the combination of average fuzzy system performance and control effort. Finally, numerical simulations are conducted to verify the effectiveness and adaptability of the proposed control method. The performance of controlled cooperative transport system is both deterministically guaranteed and fuzzily optimized.

Trajectory error compensation method for grinding robots based on kinematic calibration and joint variable prediction

Trajectory accuracy, a crucial metric in assessing the dynamic performance of grinding robots, is influenced by the uncertain movement of the tool center point, directly impacting the surface quality of processed workpieces. This article introduces an innovative method for compensating trajectory errors. Initially, a strategy for error compensation is derived using differential kinematics theory. Subsequently, a robot kinematic calibration method utilizing ring particle swarm optimization (RPSO) is proposed to address static errors in the grinding robot. Simultaneously, a method for predicting robot joint variables based on a dual-channel feedforward neural network (DCFNN) is designed to mitigate dynamic errors. Finally, a simulation platform is developed to validate the proposed method. Simulation analysis using extensive data demonstrates an 89.3% improvement in absolute position accuracy and a 74.2% reduction in error fluctuation range, outperforming sparrow search algorithm (SSA), improved mayfly algorithm (IMA), multi-representation integrated predictive neural network (MRIPNN), etc. Algorithmic comparison reveals that kinematic calibration significantly reduces the average trajectory error, while joint variable prediction notably minimizes error fluctuation. Validation through trajectory straightness testing and a 3D printing propeller grinding experiment achieves a trajectory straightness of 0.2425 mm. Implementing this method enables achieving 86.1% surface machining allowance within tolerance, making it an optimal solution for grinding robots.

Adaptive control of magnetic levitation system based on fuzzy inversion

A novel adaptive tracking controller for magnetic levitation systems (MLS) is developed. The controller is based on a special adaptive control scheme incorporating fuzzy model of electromagnetic acceleration enabling fast and accurate fuzzy inversion. The controller ensures accurate tracking of any smooth desired position signal, despite unknown MLS parameters. The closed-loop system stability, in the sense of uniform ultimate boundedness (UUB) of error trajectories, is proved using Lyapunov approach. The closed-loop system performance is investigated during numerical experiments. Finally the proposed controller is verified by successful implementation on a DSP board controlling a typical magnetic levitation ball system. Performed tests and experiments demonstrate that the proposed control technique is robust against discretization and unknown MLS model parameters, provides high tracking accuracy, is easily implementable, and simple to tune.

Design and Mechanical Validation of Commercially Viable, Personalized Passive Prosthetic Feet

Abstract Current high-performance prosthetic feet work well for many users, but the low resolution of size and stiffness categories may limit walking performance for certain users. A line of prosthetic feet with a high resolution of sizes and stiffnesses, designed through amputee-specific personalization, could provide clinical and economic value. The lower leg trajectory error (LLTE) design framework facilitates the design of high-performance, amputee-specific prosthetic feet; however, previous foot prototypes were not designed to satisfy the economic, mechanical, and aesthetic requirements for commercial adoption. The aims of this work were to understand how a personalized, affordable prosthetic foot can align with the clinical-commercial ecosystem, innovate a viable future product, and inform other prosthesis designers of considerations required to connect innovation to real-world implementation. We evaluated needs by identifying how products, capital, and services flow between stakeholders, and we elucidated design requirements for a personalized prosthetic foot that can be manufactured, distributed, and clinically provided. Based on material properties and manufacturing process capabilities, computer numerically controlled (CNC) machining of Nylon 6/6 satisfies these requirements. We present a novel parametric foot architecture that can be CNC machined, fits within a commercial foot shell, and can be designed for individual users’ body characteristics and activity levels. Prototypes made using the new foot design behaved as anticipated (1–12% error in modeled displacement), satisfied industry-standard strength (ISO 10328) and mechanical performance (AOPA dynamic heel/keel) requirements, and elicited positive feedback from both amputees and prosthetists.

Brain-body-task co-adaptation can improve autonomous learning and speed of bipedal walking.

Inspired by animals that co-adapt their brain and body to interact with the environment, we present a tendon-driven and over-actuated (i.e., n joint, n+1 actuators) bipedal robot that (i) exploits its backdrivable mechanical properties to manage body-environment interactions without explicit control, and (ii) uses a simple 3-layer neural network to learn to walk after only 2 minutes of 'natural' motor babbling (i.e., an exploration strategy that is compatible with leg and task dynamics; akin to childsplay). This brain-body collaboration first learns to produce feet cyclical movements 'in air' and, without further tuning, can produce locomotion when the biped is lowered to be in slight contact with the ground. In contrast, training with 2 minutes of 'naive' motor babbling (i.e., an exploration strategy that ignores leg task dynamics), does not produce consistent cyclical movements 'in air', and produces erratic movements and no locomotion when in slight contact with the ground. When further lowering the biped and making the desired leg trajectories reach 1cm below ground (causing the desired-vs-obtained trajectories error to be unavoidable), cyclical movements based on either natural or naive babbling presented almost equally persistent trends, and locomotion emerged with naive babbling. Therefore, we show how continual learning of walking in unforeseen circumstances can be driven by continual physical adaptation rooted in the backdrivable properties of the plant and enhanced by exploration strategies that exploit plant dynamics. Our studies also demonstrate that the bio-inspired co-design and co-adaptations of limbs and control strategies can produce locomotion without explicit control of trajectory errors.

Jerk limited continuous tool path generation for flexible systems in non-cartesian coordinate systems

Inspired by computer numerical control (CNC) technology and drastic changes in the world of electronics and microcontrollers, the idea of using non-cartesian coordinate system for CNC machines became a topic of interest. Non-cartesian coordinate systems provide freedom of movement in systems with large working spaces where high dimensional accuracy is not a prime concern. Applications of such systems can be found in murals, where a painting is applied to a large wall of any arbitrary build material. In the present paper, a new design was introduced to automate the process of drawing murals on large surfaces. The proposed mechanism utilized chain and sprocket to overcome the size limitations of traditionally available x-y tables. In addition to that, the developed mechanism does not utilize the common robust structures used in the conventional CNC systems and the tool motion is created using flexible arms that are not heavily constrained. The effect of systems unwanted vibration has been eliminated using continuous trajectory and kinematic profiles. Parametric curve interpolation algorithms for trajectory planning were implemented to increase the flexibility of drawing complex curves. Parametric curves such as B-spline and non-uniform rational B-spline (NURBS) were employed to generate a jerk limited trajectory for motion control and extraction of kinematic profiles. Such trajectory constrains the jerk of the system and guarantees a smooth motion free of feed-rate fluctuations. Compared to other methods available for extracting the kinematic profiles, jerk limited method decreases the travel time and trajectory error. Ultimately, motion commands were produced by using kinematic profiles and the second order Taylor interpolator. STM32746ZG card was used as the main processor and two stepper motors controlled by a Bit Pattern interpolation algorithm were utilized to drive the proposed mechanism. The input pulses of stepper motors were stored as binary bits and transmitted to drivers in real-time. The feedback was also evaluated by two rotary encoders, placed at the end of the motors’ shafts. Encoder data were acquired and transmitted using a TCP/IP protocol to guarantee zero data loss during the transmission.

Upper Limb Rehabilitation Robots Training Analysis based on Multi-sensor Trajectory Data and Human-computer Interaction

Upper limb rehabilitation robots have important practical significance in helping patients recover their motor function, but traditional training methods often lack real-time and accurate evaluation of patient movement status and intention and have low interactive participation. Therefore, the study proposes a training system for upper limb rehabilitation robots based on multi-sensor trajectory data and human-computer interaction. The system is designed from three aspects: inertial sensor trajectory tracking, Kinect sensor image restoration, and interaction system design. A polynomial joint zero value constraint algorithm is introduced to correct errors, and variable parameter pixel filtering combined with a weighted average moving algorithm is used to improve image quality. The training results showed that the robot trajectory tracking accuracy significantly improved, and the improvement in motion trajectory error was greater than 20%. Compared with traditional training methods, interactive training had a recognition accuracy of over 85% in rehabilitation actions, and the system had better stability. This rehabilitation robot can effectively meet the feasibility and effectiveness of improving the interaction system, providing new technological means for intelligent medical services.

DZ-SLAM: A SAM-based SLAM algorithm oriented to dynamic environments

Precise localization is a fundamental prerequisite for the effective operation of Simultaneous Localization and Mapping (SLAM) systems. Traditional visual SLAM is based on static environments and therefore performs poorly in dynamic environments. While numerous visual SLAM methods have been proposed to address dynamic environments, these approaches are typically based on certain prior knowledge. This paper introduces DZ-SLAM, a dynamic SLAM algorithm that does not require any prior knowledge, based on ORB-SLAM3, to handle unknown dynamic elements in the scene. This work first introduces the FastSAM to enable comprehensive image segmentation. It then proposes an adaptive threshold-based dense optical flow approach to identify dynamic elements within the environment. Finally, combining FastSAM with optical flow method and embedding it into the SLAM framework to eliminate dynamic objects and improve positioning accuracy in dynamic environments. The experiment shows that compared with the original ORB-SLAM3 algorithm, the algorithm proposed in this paper reduces the absolute trajectory error by up to 96%; Compared to the most advanced algorithms currently available, the absolute trajectory error of our algorithm can be reduced by up to 46%. In summary, the proposed dynamic object segmentation method without prior knowledge can significantly reduce the positioning error of SLAM algorithm in various dynamic environments.

Enhancing BDS-3 PPP-B2b real-time positioning performance by tightly integrating MEMS IMU and LiDAR in GNSS-Degraded environment

Currently, BDS-3 can provide satellite-based real-time precise point positioning (PPP) service via its PPP-B2b signal. However, in a complex Global Navigation Satellite System (GNSS)-degraded environment, the BDS-3 PPP-B2b positioning performance is severely influenced. A tightly coupled PPP/microelectromechanical system inertial measurement unit (MEMS IMU)/Light Detection and Ranging (LiDAR) combination is proposed, in which the original pseudorange and carrier observations, IMU measurements, and LiDAR planar features are fused via an extended Multi-State Constraint Kalman Filter (MSCKF). Moreover, the Galileo satellites are further utilized using the broadcast ephemerides to increase the number of available satellites. And to improve the real-time computing efficiency, a planar feature tracking model based on ground segmentation is adopted. The model consists of point cloud segmentation, planar feature extraction and fusion, and data correlation. To evaluate the effectiveness of the proposed method, the experiment is conducted at both a campus and a park. The result shows that approximately sub-meter-level positioning accuracy can be achieved using tightly coupled BDS-3 PPP-B2b, IMU, and LiDAR, while the positioning errors of BDS-3 PPP-B2b and BDS-3 PPP-B2b/IMU are both larger than 5 m. Furthermore, the MEMS IMU and LiDAR measurements show the capability of bridging the gaps in the GNSS data, which enables continuous and stable positioning. Moreover, compared to the state-of-the-art A-LOAM, LEGO-LOAM, and LIO-SAM frameworks, absolute trajectory errors of less than 1.0 and 2.5 m are achieved in the campus and park, respectively, using the proposed algorithm, with improvements of more than 3.40 and 1.58 times.

Precise motion control for a space mining robot based on improved African vultures optimization

Space mining robots can develop and utilize abundant mineral resources in the outer space to solve the problem of the depletion of earth mineral resources. However, the motion errors of space mining robots in complex environments on the outer space surface of asteroids greatly hinder its applications. To bridge this research gap, a precise motion controller of the space mining robot is proposed in this study. Firstly, the kinematics model of robot’s wheels and the whole vehicle dynamics model in soft soil are established. Then, the optimal PID motion controller is developed based on the improved African vultures optimization algorithm (IAVOA). The Henon chaotic mapping, nonlinear adaptive incremental inertial weight factor and reverse learning competition strategy are introduced to optimize the initial population position, position update method and optimal solution output, respectively. Meanwhile, the excellent optimization performance of IAVOA is also validated by test results of nine benchmark functions. Lastly, the performance of controller is verified by simulations and experiments. The simulation results show that the proposed IAVOA-PID controller is superior to the original PID and AVOA-PID controller with faster response time and smaller overshoot. The experiment results show the space mining robot with the assistance of proposed motion controller can move with a trajectory error of less than 0.2 m and a motion error of less than 0.01 m.

VSLAM based on deep learning in low-textured scenes

Abstract Traditional Visual Simultaneous Localization and Mapping (VSLAM) algorithms often suffer from the low positioning accuracy and robustness of the traditional feature extraction methods. These methods typically require environments with clear features, perform poorly or even fail in low-textured scenes. To solve this problem, we propose an RGB-D VSLAM algorithm that integrates a deep learning feature extraction network. First, to solve the problem in which sufficient feature points cannot be extracted, the proposed algorithm uses the R2D2 feature extraction network to extract keypoints and generate descriptors. We also perform lightweight optimization on the R2D2 network, ensuring accuracy while doubling the inference speed. Subsequently, we employ the L2 distance to measure the distance between descriptors, thereby enhancing the accuracy of keypoint matching. Ultimately, we add a dense mapping thread to obtain a dense 3D point map generated by the RGB-D information and poses of the keyframes. The experimental results on the TUM dataset show that the average absolute trajectory error is reduced by 59% and the relative trajectory error is reduced by 56%. The results demonstrate that our algorithm significantly improves localization accuracy and system robustness in low-textured environments.

Trajectory tracking control of a four-bar linkage prosthetic knee with magnetorheological damper

In order to improve biomimicry, a four-bar linkage prosthetic knee with magnetorheological (MR) damper was developed in this paper. The principle and structure of four-bar linkage MR prosthetic knee was introduced and its kinetic model was established. A MR damper matching the proposed prosthetic knee was designed, fabricated and tested, and the forward and inverse mechanical model were conducted. In addition, to solve the problems of complex model, poor bionics and low trajectory tracking accuracy in the MR prosthetic knee, a PD-type iterative learning control (ILC) controller was developed. The simulated and experimental test results show that the positive maximum error of the knee joint swing trajectory based on PD-type ILC controller are 2.2°(speed of 0.5 m/s), 4.1°(speed of 1.0 m/s), and 1.9°(speed of 1.5 m/s), respectively, and the negative maximum error of that are −1.4°(speed of 0.5 m/s), −6.7°(speed of 1.0 m/s), and −5.5°(speed of 1.5 m/s), respectively, which effectively tracks the reference swing trajectory.

Research on SLAM Localization Algorithm for Orchard Dynamic Vision Based on YOLOD-SLAM2

With the development of agriculture, the complexity and dynamism of orchard environments pose challenges to the perception and positioning of inter-row environments for agricultural vehicles. This paper proposes a method for extracting navigation lines and measuring pedestrian obstacles. The improved YOLOv5 algorithm is used to detect tree trunks between left and right rows in orchards. The experimental results show that the average angle deviation of the extracted navigation lines was less than 5 degrees, verifying its accuracy. Due to the variable posture of pedestrians and ineffective camera depth, a distance measurement algorithm based on a four-zone depth comparison is proposed for pedestrian obstacle distance measurement. Experimental results showed that within a range of 6 m, the average relative error of distance measurement did not exceed 1%, and within a range of 9 m, the maximum relative error was 2.03%. The average distance measurement time was 30 ms, which could accurately and quickly achieve pedestrian distance measurement in orchard environments. On the publicly available TUM RGB-D dynamic dataset, YOLOD-SLAM2 significantly reduced the RMSE index of absolute trajectory error compared to the ORB-SLAM2 algorithm, which was less than 0.05 m/s. In actual orchard environments, YOLOD-SLAM2 had a higher degree of agreement between the estimated trajectory and the true trajectory when the vehicle was traveling in straight and circular directions. The RMSE index of the absolute trajectory error was less than 0.03 m/s, and the average tracking time was 47 ms, indicating that the YOLOD-SLAM2 algorithm proposed in this paper could meet the accuracy and real-time requirements of agricultural vehicle positioning in orchard environments.

Multi-level surfel map construction for accurate localization in intelligent vehicles

Abstract The role of mapping in achieving accurate localization in intelligent vehicles is crucial. Accurate maps enable intelligent vehicles to attain accuracy in localization and path planning, ultimately enhancing the safety and overall driving experience. However, the interference of dynamic objects poses a challenge to map updates and subsequent localization. To address this issue, this study proposes a novel algorithm for constructing multi-level semantic surfel maps, along with a corresponding hierarchical localization method. The proposed method divides the map into three levels: semantic level, surfel level, and trajectory level. During the map construction phase, we utilize semantic segmentation technology to accurately distinguish between static and dynamic environments, filter out dynamic point clouds, and focus solely on modeling static scenes. This effectively eliminates the interference of dynamic objects on map updates, ensuring the construction of a precise and reliable static environment model. In the subsequent hierarchical localization phase, a node-level localization method is introduced, which achieves coarse localization by matching perception information with the map.The results of experiments conducted in various scenarios indicate an average absolute trajectory error of 4cm between the transformation matrices of each node in the map. Our algorithm achieves a 92% success rate in node-level localization and an average pose-level localization error of 8.2cm, demonstrating the feasibility and robustness of the proposed algorithm.

Integrated error modeling for abrasive waterjet cutting at various nozzle tilt angle

The research investigates the specific impact of high-pressure abrasive waterjet (AWJ) on the cutting accuracy of circular trajectories. The coupling relationship between the kerf taper and the jet lag of the cutting front profiles is analyzed. Thus, an integrated error model for abrasive waterjet cutting of circular trajectories is innovatively established, which can predict the deformation of the circular arc trajectory not only at right angles but also at tilt angles. Cutting experiments at vertical angles were conducted, with a maximum prediction accuracy of 2.41%. Besides, arc trajectories with different diameters were conducted with a prediction accuracy of 2.26%. In order to reduce the deformation error of arc trajectories, compensation experiments for nozzle tilt ranging from 76° to 94° were carried out. The experimental results showed that when the nozzle was tilted in the direction opposite to the traverse speed up to half of the maximum deviation angle at the jet outlet point, the maximum deformation of arc trajectories was 1.218 mm, which was reduced by 0.532 mm compared to the case of vertical incidence, and the cylindricity increased by 31.74%. This adjustment can meet the precision requirements for cutting thick materials with abrasive waterjet.