B-spline Interpolation Algorithm Research Articles

Design and motion planning of a 7-DOF assembly robot with heavy load in spacecraft module

Currently, there is great demand for automated assembly of equipment inside spacecraft module, which would require an assembly robot with small size, large workspace, high load capacity, and high flexibility. To meet this demand, a redundant seven-degree-of-freedom (7-DOF) assembly robot with three prismatic joints and four rotating joints is proposed in this study. First, a kinematic model of the assembly robot is established, and the positional forward kinematics are derived. Then, the positional inverse kinematic equations are derived by using the fixed joint method and the coordinate inverse transformation method for the characteristics of the robot with redundant degrees of freedom. The inverse solution optimization model of the assembly robot is designed based on genetic algorithm, and B-spline interpolation algorithm is used for joint trajectory planning. Next, NSGA-2 algorithm is used to construct the trajectory optimization model, and the time-pulsation multi-objective Pareto optimal frontier is obtained. Finally, the joint simulation model of mechatronics and the prototype experiment are established to verify the effectiveness of the optimization results. Analysis shows that the proposed assembly robot has better load-bearing capacity and dynamic characteristics than similar existing assembly robots. Furthermore, the segmented trajectory optimization strategy for the assembly robot using inverse solution optimization, interpolation algorithm, and NSGA-2 based multi-objective optimization gets each motion joint to realize the trajectory tracking function quickly and stably, and the trajectory tracking error is small enough to meet the requirements of end positioning accuracy.

An FPGA-Based Hardware Low-Cost, Low-Consumption Target-Recognition and Sorting System

In autonomous driving systems, high-speed and real-time image processing, along with object recognition, are crucial technologies. This paper builds upon the research achievements in industrial item-sorting systems and proposes an object-recognition and sorting system for autonomous driving. In industrial sorting lines, goods-sorting robots often need to work at high speeds to efficiently sort large volumes of items. This poses a challenge to the robot’s real-time vision and sorting capabilities, making it both practical and economically viable to implement a real-time and low-cost sorting system in a real-world industrial sorting line. Existing sorting systems have limitations such as high cost, high computing resource consumption, and high power consumption. These issues mean that existing sorting systems are typically used only in large industrial plants. In this paper, we design a high-speed, low-cost, low-resource-consumption FPGA (Field-Programmable Gate Array)-based item-sorting system that achieves similar performance to current mainstream sorting systems but at a lower cost and consumption. The recognition component employs a morphological-recognition method, which segments the image using a frame difference algorithm and then extracts the color and shape features of the items. To handle sorting, a six-degrees-of-freedom robotic arm is introduced into the sorting segment. The improved cubic B-spline interpolation algorithm is employed to plan the motion trajectory and consequently control the robotic arm to execute the corresponding actions. Through a series of experiments, this system achieves an average recognition delay of 25.26 ms, ensures smooth operation of the gripping motion trajectory, minimizes resource consumption, and reduces implementation costs.

Ship hull surface reconstruction from scattered points cloud using an RBF neural network mapping technology

The ship hull surface reconstruction based on three-dimensional scattered points cloud is vital to Computer-Aided Design modeling of ship reverse engineering. There are several problems with traditional methods: the preprocessing of a large-scale scattered points cloud is complicated, and the result is susceptible to noise. Because of the “black box” characteristic, the surface reconstruction based on neural networks cannot apply to the practical engineering. To address these issues, combining the Radial Basis Function neural network and Non-Uniform Rational B-Spline interpolation algorithm, a new ship hull surface reconstruction method was proposed, which can satisfy the standard geometric model description in Computer-Aided Design system. Firstly, the Radial Basis Function neural network was used to pre-fit the three-dimensional scattered points cloud. Then the mathematical model of the surface was mapped. Finally, based on the bilinear interpolation algorithm, the mathematical model was transformed to a Non-Uniform Rational B-Spline surface to apply to the ship practical engineering. In addition, by comparing our method with the traditional method, the advantages of our method in surface reconstruction quality and surface repair ability were verified, which provided a new way for the application of Radial Basis Function neural network in ship reverse engineering.

Automatic method for individual parcellation of manganese-enhanced magnetic resonance imaging of rat brain.

AimsTo construct an automatic method for individual parcellation of manganese-enhanced magnetic resonance imaging (MEMRI) of rat brain with high accuracy, which could preserve the inherent voxel intensity and Regions of interest (ROI) morphological characteristics simultaneously.Methods and resultsThe transformation relationship from standardized space to individual space was obtained by firstly normalizing individual image to the Paxinos space and then inversely transformed. On the other hand, all the regions defined in the atlas image were separated and resaved as binary mask images. Then, transforming the mask images into individual space via the inverse transformations and reslicing using the 4th B-spline interpolation algorithm. The boundary of these transformed regions was further refined by image erosion and expansion operator, and finally combined together to generate the individual parcellations. Moreover, two groups of MEMRI images were used for evaluation. We found that the individual parcellations were satisfied, and the inherent image intensity was preserved. The statistical significance of case-control comparisons was further optimized.ConclusionsWe have constructed a new automatic method for individual parcellation of rat brain MEMRI images, which could preserve the inherent voxel intensity and further be beneficial in case-control statistical analyses. This method could also be extended to other imaging modalities, even other experiments species. It would facilitate the accuracy and significance of ROI-based imaging analyses.

Path Optimization of Agricultural Robot Based on Immune Ant Colony: B-Spline Interpolation Algorithm

This study presents a path planning algorithm based on immune ant colony B spline interpolation to eliminate path duplication and corner inflection points, increase the smoothness of the agricultural robot’s path trajectory, and enhance the path planning performance. Firstly, this study improves the convergence speed of the algorithm by introducing an adaptive factor that obeys the normal distribution to optimize the path heuristic function. Secondly, to strengthen the variety of the target path search, an immune algorithm was utilized to perform a global investigation of the appropriate routes and assign the initial pheromones of the ant colony. Then, the adaptive judgment factor is introduced based on the incentive degree function and the pheromone evaporation coefficient, and the update formula are adjusted to promote the algorithm’s flexibility while suppressing the optimal regional problem. Finally, the pathways are processed using a cubic B spline interpolation method to remove the edges and minimize the peak inflection points. To verify the specific optimization performance of the algorithm in this paper, we have selected the same type of improved algorithm as a comparison and tested it in a raster map model. The simulation results demonstrate that the values of the proposed algorithm paths and the standard deviation of the tracks are smaller than the comparison algorithm, which indicates the higher performance of the algorithm in searching the optimal routes and more flexible and accurate search. Compared with the comparison algorithm, the average time-consuming reduction rate of the algorithm in this paper is between 38% and 45% in different grid maps, and the number of turns is reduced by 33% to 58%. It meets the requirements of the actual work on the robot.

Time-optimal trajectory planning of manipulator with simultaneously searching the optimal path

Time-optimal trajectory planning can improve the efficiency of the manipulator, which has a paramount research significance. Nonetheless, almost all the current algorithms have the problem of path limitation — the algorithm constantly searches for the optimal motion time of the manipulator on a specific motion path. To solve this problem, we design a time-optimal trajectory planning method for the manipulator by searching the optimal path simultaneously. We propose using a cubic uniform B-spline interpolation algorithm to derive the motion curve expression of the manipulator joint with unknown path points. Then we use a genetic algorithm to optimize the path point and the motion time of the manipulator at the same time to get the time-optimal motion path of the manipulator. Moreover, we prove that the algorithm proposed in this paper is comparable with similar algorithms with known paths through experiments.

Remaining useful life prediction of bearing based on stacked autoencoder and recurrent neural network

Remaining Useful Life (RUL) prediction play a crucial part in bearing maintenance, which directly affects the production efficiency and safety of equipment. Moreover, the accuracy of the prediction model is constrained by the feature extraction process and full life data of bearings. In this paper, the life prediction method of faulty rolling bearing with limited data is presented including degradation state model and RUL prediction model. In order to obtain health indication (HI) without human interference in the degradation state modeling stage, the bottleneck structure of Stacked Autoencoder (SAE) is utilized to fuse the four selected features into one HI using Intelligent Maintenance Systems (IMS) bearing dataset as training sample. In RUL prediction model, the Long Short-Term Memory (LSTM) neural network is carried out to establish the model with Standard deviation (Std) input and HI training label. In order to solve the problem of large training error caused by insufficient data in the failure stage of bearing acceleration test, the third-order spline curve interpolation is utilized to enhance the data points. Through parameter analysis, the RMSE and MAE of the test set on the prediction model are 0.032582 and 0.024038, respectively. Furthermore, the effectiveness of the proposed method is further validated by dataset from Case Western Reserve University (CWRU) with different bearing fault degrees. The analysis indicates that the RUL prediction of bearing fault data is consistent with the size of artificial added faults, that is,the more severe the fault the shorter the time of remaining life. The results validate that the proposed method can effectively extract the bearing health state by incorporating feature fusion and establish accurately prediction model for bearing remaining life.

Time-Optimal Point Stabilization Control for WIP Vehicles Using Quasi-Convex Optimization and B-Spline Adaptive Interpolation Techniques

This paper addresses a time-optimal point stabilization control for inherent unstable wheeled inverted pendulum (WIP) vehicles using quasi-convex optimization and B-spline adaptive interpolation techniques. First, to handle the difficulty caused by the inherent unstable characteristic, a state feedback control law is introduced to the state-space model deduced with the kinematic coupling relationship between the longitudinal motion and tilt angle of vehicle body. Then, by system discretization, a standard quasi-convex optimization problem is formulated to plan a time-optimal trajectory with various constraints being taken into account, and the optimization problem can be solved by a bisection method combined with solving a series of convex feasibility problems. Next, to obtain the analytic expression of the discrete optimal trajectory, a B-spline interpolation algorithm with adaptive curve refinement is presented based on feature points recognition. Furthermore, as the time-optimal trajectories with analytic expressions, including displacement, velocity, and acceleration trajectories, have been obtained, a proportional-integral-derivative (PID) tracking controller is applied to control the vehicle to track the optimal trajectories and, thus, the time-optimal point stabilization control for the WIP vehicle can be realized. Finally, simulation results of a numerical example is presented to validate the feasibility and effectiveness of the proposed method.

High-Precision Trajectory Data Reconstruction for TT&C Systems Using LS B-Spline Approximation

Existing trajectory data reconstruction algorithms for tracking, telemetry, and command (TT&C) channel simulators cannot achieve continuity and noise reduction simultaneously. By combining the B-spline interpolation algorithm with the least-square (LS) approximation algorithm, we propose a novel trajectory data reconstruction algorithm using LS B-spline approximation. In addition, a polyphase structure is proposed to implement the algorithm. Compared with existing algorithms, the proposed algorithm achieves higher reconstruction precision when the known trajectory data include measurement errors; moreover, it preserves continuity. Numerical simulation results verified the validity and effectiveness of our proposed algorithm.

Vessel Trajectory Similarity Based on Cubic B-spline Interpolation + Time-constrained Hausdorff Algorithm

The spatio-temporal trajectory data sampling period is large, and the general trajectory similarity is not suitable. This paper proposes a new algorithm, cubic B-spline interpolation + time-constrained Hausdorff algorithm to calculate the trajectory distance. This paper compares the time-constrained Hausdorff algorithm, cubic B-spline interpolation algorithm and cubic B-spline interpolation + time-constrained Hausdorff algorithm. The experimental results show that the cubic B-spline interpolation + time-constrained Hausdorff algorithm is significantly higher than other algorithms in the accuracy of vessel trajectory similarity.

Acceleration smoothing algorithm for global motion in high-speed machining

When machining a series of short linear segments, the computer numerical control system interpolates the machining path with the pre-specified spline curve to obtain continuous feed motion. However, to obtain adequate smooth tool-paths to smooth the feed velocity and acceleration, the computer-aided manufacturing system needs to use a higher order spline curve, which will be limited by some technical bottlenecks. In this article, a new real-time interpolation algorithm is proposed from the perspective of kinematics to achieve uninterrupted feed motion throughout the global tool-path. At the same time, the acceleration profile achieves G2 continuous to avoid unnecessary feed frustration and inertial impact, reaching the balance between time-optimal and motion performance. First, the jounce-limited acceleration curve is blended at the corner of the machining path, and the optimal cornering transition velocity is obtained by adding the velocity, acceleration and contour error constraints to the corner transition motion. Then, according to the linear segments with different lengths between the corners, combined with the feed motion around the corner, a look-ahead interpolation algorithm is proposed to calculate the maximum feed rate with the constraint of the linear segment length and kinematic boundary conditions. At last, for the linear segments whose corner contours overlap with each other after interpolation, the smooth transition between the two corners can be realized by mixing the feed motion of the next corner. Compared with non-uniform rational B-spline interpolation algorithm, the proposed algorithm reduces the total machining time by 14% and the computer numerical control system improves the computational efficiency by 11%. It proves that the proposed algorithm has better application value in the manufacturing of complex parts.

BGIDB: A fundus ground truth building tool with automatic DDLS classification for glaucoma research

Taking advantage of the new standard HTML5, we designed an online tool called a browser/server-based glaucoma image database builder (BGIDB) for the demarcation of the optic disk and cup’s ellipse-like boundaries. The B-spline interpolation algorithm is used, and a specially designed algorithm is proposed for classifying the disease grade according to the disc damage likelihood scale criterion, which is correlated strongly with the glaucoma process by quantity. This tool exhibits the best performance with a low overlapping error of 4.34% for the optic disk demarcation and 8.31% for the optic cup demarcation. It also has preferable time-consuming as compared to other tools and is a cross-platform system. This tool has already been utilized in building the ophthalmic image database in the cooperation of Center for Ophthalmic Imaging Research and The Second Xiangya Hospital.

An improved empirical mode decomposition method based on the cubic trigonometric B-spline interpolation algorithm

Empirical mode decomposition (EMD) is a new method presented recently for analyzing nonlinear and non-stationary signals. Its basic idea is to decompose the signal into a series of complete orthogonal intrinsic mode functions (IMFs) based on the local characteristics of the signal in time domain. The key step of EMD is to use the cubic spline interpolation to connect the maximum and minimum values of the signals into upper and lower envelopes respectively, and then calculate the mean values of upper and lower envelopes. Based on the cubic trigonometric B-spline interpolation algorithm, a new improved method for EMD is proposed named CTB-EMD in this paper. In this method, the interpolation curve is more flexible because of the adjustability of shape of the cubic trigonometric B-splines curve. Thus, the overshoot and undershoot problems in the cubic spline interpolation curve can be avoided, and then the decomposition of the signal is more accurate and effect. Through numerical experiments, we compare the effect of this method with other methods on decomposing simulation signals and real signals. Experimental results show that this method can decompose signals more effectively and accurately.

Research on Trajectory Planning of 6-DOF Cutting-robot in Machining Complex Surface

It is important and difficult for the complicated surface processing in mechanical industry. In this paper, an improved algorithm for trajectory planning is proposed in impeller surface processing by using 6-DOF cutting-robot. Taking a single finished path of the impeller blade as an example, the feedrate of the cutter, bow height error, cutter-orientation and position are planned by the B-spline interpolation algorithm, the best cutting trajectory is obtained. On the basis of trajectory planning, the optimal movement scheme of 6-DOF cutting-robot joints is obtained, the 6-DOF cutting-robot feedrate and trajectory smooth transition is achieved and the joints movement adaptive adjustment is completed. Finally, the angles, the angular velocitys of the joints and their interrelated properties are analyzed. The research works indicate that the robot joint angle curves are continuous and stable, which has met the requirements of smooth movement of the robot, and the results show that the trajectory planning is effective and practical.

Near-optimal trajectory generation, using a compound B-spline interpolation and minimum distance criterion with dynamical feasibility correction

Trajectory generation for robotic vehicles tries to provide real time computing of a collision free path from one point to another, which usually involves minimizing a performance measure, to accomplish a desired task. A novel hierarchical method for generating near-optimal and collision free trajectories is proposed here to be used on-line in three-dimensional space. At the top level, the off-line optimal trajectory problem is solved in a complex environment, using B-spline interpolation and genetic algorithm, while considering the dynamic constraints of the vehicle. At the intermediate level, the path is modified for any possible on-line intersections with unexpected obstacles, using a minimum distance correction technique. The feasibility of the generated path is assessed at the lowest level by considering dynamic constraints of the vehicle. A novel method is presented at this level for correcting the path and obtaining near-optimal and dynamically feasible trajectories. Each part is assessed by a separate robotic vehicle to ensure the capability and performance. Lastly, the consistency between the levels of hierarchy is evaluated by presenting a differential-drive robot example. The final path is also verified with two commercial software codes for path planning and optimal trajectory generation.

Interpolation using non-uniform rational B-spline for the smooth milling of ruled-surface impeller blades

The integral impeller is a complex part characterized by highly curved surfaces. Modeling and interpolation methods for manufacturing integral impellers are currently the subject of intensive research. In this study, to represent the shape of the ruled-surface blades, third-order non-uniform rational B-splines are constructed from data points for the hub and shoulder on the pressure and suction sides of the blade. Various methods for determining the tool axis vector offset and the location of the tool center for a cylindrical ball cutter are developed and verified with simulations of machining operations. To obtain a smooth interpolation and high accuracy in machining, a third-order non-uniform rational B-spline interpolation algorithm for ruled-surface blades is developed. This method can create a smooth transition between the hub and the blade shoulders. The method is implemented in an open-architecture computer numerical control controller. Simulations and experimental tests of machining tasks are performed to verify the non-uniform rational B-spline interpolation method. The test results show that this interpolation technique can produce a smooth and continuous path along the axes of motion. The new technique has the advantages of requiring fewer lines of numerical control code and producing higher machining accuracy.

Very Low Resolution Face Image Super-Resolution Based on DCT

This paper introduces the Very Low Resolution (VLR) problem in the fleld of face image super-resolution reconstruction. With the extensive application of the surveillance cameras, the very low resolution problem happens in many face recognition applications, which has brought great inconvenience to users. In order to research this problem, this paper proposes the improved DCT algorithm, and our flnal experimental results have compared with the common DCT algorithm, Cubic B-Spline interpolation algorithm and Baker et al’s method. Experimental results show that the improved DCT algorithm can get better performance in the very low resolution face image super-resolution reconstruction problem.

Efficient Cubic B-spline Image Interpolation on a GPU

Application of geometric transformation to images requires an interpolation step. When applied to image rotation, the presently most efficient GPU implementation for the cubic spline image interpolation still costs about eight times as much as linear interpolation. The implementation involves two steps: a prefilter step performs a two-pass forward-backward recursive filter, then a cubic polynomial interpolation step is implemented thanks to a cascade of linear interpolations. This article proposes a simpler and faster implementation for the prefilter—which is the most time consuming—in terms of a direct convolution. The overall cost for our cubic B-spline interpolation algorithm then reduces to 4.5 times the cost of linear interpolation.

Sample Rate Conversion Using B-Spline Interpolation for OFDM Based Software Defined Radios

This paper proposes arbitrary ratio sample rate conversion (SRC) architectures and a simpler B-spline interpolation algorithm for orthogonal frequency division multiplexing (OFDM) based software defined radios (SDRs) with multiband and multi-channel capabilities. Different from conventional standalone digital front-end designs for SDRs, the proposed SRC architectures combine the B-spline interpolation with OFDM modulation and equalization for OFDM transmitter and receiver respectively. With this combined design, the passband droop introduced by the B-spline interpolation can be more efficiently compensated using frequency-domain pre-distortion, instead of conventional time-domain pre-filtering, and hence an overall system complexity reduction is achieved. A novel multi-period B-spline interpolation and re-sampling structure is then constructed, and an interpolation algorithm with lower implementation complexity than that of the conventional Farrow structure is further developed. The SRC performance is also analysed by deriving the signal-to-peak distortion ratio formulas which can be used as design tools for determining the required orders of B-splines in the OFDM transmitter and receiver respectively. Finally, SRC examples used in a high-speed multiband multi-channel microwave backhaul system are given and compared with conventional polyphase filterbank interpolation to demonstrate the practicality and performance of the proposed SRC architectures and interpolation algorithm.

A NURBS interpolation algorithm with continuous feedrate

The high-speed precision machining of a part requires minimal feedrate fluctuation and contour error, and parametric spline interpolations have proven to be superior over linear and circular interpolations. However, parametric spline interpolations may result in large feedrate fluctuation due to an inaccurate mapping between the spline parameter u and the displacement S. This paper presents a non-uniform rational B-spline interpolation algorithm with compensatory parameter to minimize feedrate fluctuation and contour error. Since the cubic or quintic polynomials expressing the u-S mapping are acquired, they can be calculated by two consecutive interpolation points with the continuity condition. Thus, the parameter u can be calculated quickly and accurately by substituting the desired displacement S into the cubic or quintic polynomials. Simulation shows that the feedrate fluctuation of the proposed algorithm is much smaller than that of Taylor interpolation algorithms and Feed correction algorithm.