•Smooth point-to-point trajectory planning method for industrial robots is proposed.•Acceleration is planned with fourth-order polynomial determined by one coefficient.•Velocity, acceleration and ...jerk of each joint and end-effector are continuous.•Velocity, acceleration and jerk at the initial point and final point are zero.•Velocity, acceleration and jerk of each joint meet the kinematical constraints.
In this paper, a smooth point-to-point trajectory planning method for industrial robots is proposed. The trajectory is planned in the joint space. The joint motion is divided into three parts, namely accelerated part, constant velocity part and decelerated part. In the accelerated part and decelerated part, the acceleration is planned with fourth-order polynomial formed with the property of the root multiplicity. Then near time-optimal trajectory can be obtained by maximizing the constant velocity part under kinematical constraints. The results show that the fourth-order polynomial formed with the property of the root multiplicity is determined by only one coefficient. Compared to the classical description, the arduous stage of solving the numerous polynomial coefficients can be eliminated. With the proposed trajectory planning method, the displacement, velocity, acceleration and jerk of each joint and end-effector are all continuous. At the initial moment and end moment, the velocity, acceleration and jerk of each joint and end-effector are zero. The velocity, acceleration and jerk of each joint meet the kinematical constraints. The end-effector moves smoothly and the proposed trajectory planning method is very effective.
Time series clustering serves as a potent data mining method, facilitating the analysis of an extensive array of time series data without the prerequisite of any prior knowledge. It finds ...wide-ranging use across various sectors, including but not limited to, financial and medical data analysis, and sensor data processing. Given the high dimensionality, non-linearity, and redundancy characteristics associated with time series, conventional clustering algorithms frequently fall short in yielding satisfactory results when directly applied to this kind of data. As such, there is a critical need to judiciously select suitable feature extraction methods and dimension reduction techniques. This paper introduces a time series clustering algorithm, drawing primarily from polynomial fitting derivative features as a wellspring for feature extraction to achieve effective clustering results. Initially, Hodrick Prescott (HP) filtering comes into play for the processing of raw time series data, thereby eliminating noise and redundancy. Subsequently, polynomial curve fitting (PCF) is applied to the data to derive a globally continuous function fitting this time series. Next, by securing multi-order derivative values via this function, the time series is transformed into a multi-order derivative feature sequence. Lastly, we designed a polynomial function derivative features-based dynamic time warping (PFD_DTW) algorithm for determining the distance between two equal or unequal granular length time series, and subsequently a hierarchical clustering method anchored on the PFD_DTW distances for time series clustering after computing interspecies distances. The effectiveness of this method is corroborated by experimental results obtained from several practical datasets.
•Extend integration approach from polynomial to rational PH curves.•Linear conditions for rational integrability via partial fraction decomposition.•Optimal interpolation with shape control (no ...cusps) by solving a quadratic program.•Optimize curve energy or impose length constraints.
Using a residuum approach, we provide a complete description of the space of the rational spatial curves of given tangent directions. The rational Pythagorean hodograph curves are obtained as a special case when the norm of the direction field is a perfect square. The basis for the curve space is given explicitly. Consequently a number of interpolation problems (G1, C1, C2, C1/G2) in this space become linear, cusp avoidance can be encoded by linear inequalities, and optimization problems like minimal energy or optimal length are quadratic and can be solved efficiently via quadratic programming. We outline the interpolation/optimization strategy and demonstrate it on several examples.
In this paper, an optimized method on the basis of polynomial fitting and Lambert
W function is presented to extract parameters from the current–voltage (
I–V) characteristics of commercial silicon ...solar cells. Since the experimental outcomes have significant impact on the precision of extracted parameters, polynomial fitting serves to overcome the obstacles of measurement noise in this method. The Lambert
W function is employed to translate the transcendental equation into explicit analytical solution. Comparing with the as-reported parameters of a silicon cell and a plastic cell in the previous literature, the interesting outcomes demonstrate that the proposed approach is helpful for obtaining precise extracted data. This is further showed by the good agreements between the fitted
I–V curve and the experimental results of a commercial monocrystalline silicon solar cell. Moreover, full extracted parameters of a badly shunted multicrystalline silicon solar cells before and after laser isolation process are conducted and investigated, the good fitting results finally show the validity of this attempt again.
This paper studies the polynomial basis that generates the smallest n-simplex enclosing a given nth-degree polynomial curve in Rn. Although the Bernstein and B-Spline polynomial bases provide ...feasible solutions to this problem, the simplexes obtained by these bases are not the smallest possible, which leads to overly conservative results in many CAD (computer-aided design) applications. We first prove that the polynomial basis that solves this problem (MINVO basis) also solves for the nth-degree polynomial curve with largest convex hull enclosed in a given n-simplex. Then, we present a formulation that is independent of the n-simplex or nth-degree polynomial curve given. By using Sum-Of-Squares (SOS) programming, branch and bound, and moment relaxations, we obtain high-quality feasible solutions for any n∈N, and prove (numerical) global optimality for n=1,2,3 and (numerical) local optimality for n=4. The results obtained for n=3 show that, for any given 3rd-degree polynomial curve in R3, the MINVO basis is able to obtain an enclosing simplex whose volume is 2.36 and 254.9 times smaller than the ones obtained by the Bernstein and B-Spline bases, respectively. When n=7, these ratios increase to 902.7 and 2.997⋅1021, respectively.
•The MINVO basis finds the smallest n-simplex enclosing a polynomial curve.•The MINVO basis finds the polynomial curve with largest convex hull in an n-simplex.•Improvements up to several orders of magnitude with respect to Bernstein/B-Spline.•Numerical global optimality is proven for n = 1,2,3.•High-quality feasible solutions are obtained for any degree n.
For interior permanent magnet synchronous machines (IPMSMs), maximum torque per ampere (MTPA) control aims to find the MTPA angle to maximize the control objective (the ratio of output torque to ...stator current). This article proposes a novel online polynomial curve fitting technique for fast and accurate MTPA angle detection, which is motivated by the fact that the objective increases before MTPA angle and decreases after MTPA angle. This article proposes a polynomial-based objective model and identifies the polynomial parameters from a few test data for direct MTPA angle calculation. The proposed approach can avoid the time-consuming search process resulting in fast detection speed in comparison to existing search-based methods. In implementation, the current angle is set to a few test values to obtain the data for online curve fitting and MTPA angle calculation, in which there is no need of machine inductances and PM flux linkage. Moreover, the proposed polynomial model is analyzed to obtain the number of test data required for fast and accurate MTPA angle detection. The proposed approach is validated with extensive experiments and comparisons with existing methods on a laboratory IPMSM.
All rational parametric curves with prescribed polynomial tangent direction form a vector space. Via tangent directions with rational norm, this includes the important case of rational Pythagorean ...hodograph curves. We study vector subspaces defined by fixing the denominator polynomial and describe the construction of canonical bases for them. We also show (as an analogy to the fraction decomposition of rational functions) that any element of the vector space can be obtained as a finite sum of curves with single roots at the denominator. Our results give insight into the structure of these spaces, clarify the role of their polynomial and truly rational (non-polynomial) curves, and suggest applications to interpolation problems.
Abstract
This paper integrates multiple standard regression models for prediction of COVID-19 infected data. We have taken Linear Regression, Polynomial Regression and Logistic Regression for our ...modelling and prediction purposes. These models are created, trialled and tested in MATLAB software with available data for Covid 19 infected cases. These models evolves as we get more and more data to show better predictions. Explanations of these models are valuable. The models’ forecasts are credible to epidemiologists and provide confidence in end-users such as policy makers and healthcare institutions as an output of this study. These models can be applied at different geographic resolutions, and in this paper, it is demonstrated for states in India. The model supplies more exact forecasts, in metrics averaged across the entire India. Lastly, we analyse the performance of our models for various datapoints and regression parameters to recommend optimized regression model.
