Entropy-based methods have received considerable attention in the quantification of structural complexity of real-world systems. Among numerous empirical entropy algorithms, conditional entropy-based methods such as sample entropy, which are associated with amplitude distance calculation, are quite intuitive to interpret but require excessive data lengths for meaningful evaluation at large scales. To address this issue, we propose the variational embedding multiscale sample entropy (veMSE) method and conclusively demonstrate its ability to operate robustly, even with several times shorter data than the existing conditional entropy-based methods. The analysis reveals that veMSE also exhibits other desirable properties, such as the robustness to the variation in embedding dimension and noise resilience. For rigor, unlike the existing multivariate methods, the proposed veMSE assigns a different embedding dimension to every data channel, which makes its operation independent of channel permutation. The veMSE is tested on both stimulated and real world signals, and its performance is evaluated against the existing multivariate multiscale sample entropy methods. The proposed veMSE is also shown to exhibit computational advantages over the existing amplitude distance-based entropy methods.

Indoor mobile robots are widely used in modern industry. Traditional motion control methods for robots suffer from discontinuous path curvature, low planning efficiency, and insufficient verification of theoretical algorithms. Therefore, a motion control system for an intelligent indoor robot was designed. By optimizing the radar map detecting and positioning, path planning, and chassis motion control, the performance of the system has been improved. First, a map of the warehouse environment is established, and the number of resampling particles interval is set for the Gmapping building process to improve the efficiency of map construction. Second, an improved A* algorithm is proposed, which converts the path solution with obstacles between two points into the path solution without obstacles between multiple points based on the Rapidly expanding Random Trees and Jump Point Search algorithms and further improves the pathfinding speed and efficiency of the A* algorithm by screening the necessary expansion nodes. The Dynamic Window Approach (DWA) algorithm based on the dynamic window is used to smooth the path, and the target velocity is reasonably assigned according to the kinematic model of the robot to ensure the smooth motion of the chassis. By establishing raster map models of different sizes, the traditional and improved A* pathfinding algorithms are compared and validated. The results illustrate that the improved pathfinding algorithm reduces the computing time by 67% and increases the pathfinding speed by 47% compared with the A* algorithm. Compared with the traditional method, the speed and effect are greatly improved, and the motion control system can meet the requirements of autonomous operation of mobile robots in indoor storage.

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The extension of sample entropy methodologies to multivariate signals has received considerable attention, with traditional univariate entropy methods, such as sample entropy (SampEn) and fuzzy entropy (FuzzyEn), introduced to measure the complexity of chaotic systems in terms of irregularity and randomness. The corresponding multivariate methods, multivariate multiscale sample entropy (MMSE) and multivariate multiscale fuzzy entropy (MMFE), were developed to explore the structural richness within signals at high scales. However, the requirement of high scale limits the selection of embedding dimension and thus, the performance is unavoidably restricted by the trade-off between the data size and the required high scale. More importantly, the scale of interest in different situations is varying, yet little is known about the optimal setting of the scale range in MMSE and MMFE. To this end, we extend the univariate cosine similarity entropy (CSE) method to the multivariate case, and show that the resulting multivariate multiscale cosine similarity entropy (MMCSE) is capable of quantifying structural complexity through the degree of self-correlation within signals. The proposed approach relaxes the prohibitive constraints between the embedding dimension and data length, and aims to quantify the structural complexity based on the degree of self-correlation at low scales. The proposed MMCSE is applied to the examination of the complex and quaternion circularity properties of signals with varying correlation behaviors, and simulations show the MMCSE outperforming the standard methods, MMSE and MMFE.