A spherical robot is a nonlinear, nonholonomic, and unstable system which increases the difficulty of the direction and trajectory tracking problem. In this study, we propose a new direction controller Hierarchical Terminal Sliding Mode Controller (HTSMC), an instruction planning controller called Model Prediction Control-based Planner (MPCBP), and a trajectory tracking framework named MPCBP-HTSMC-HSMC (MHH). The HTSMC is designed by integrating a fast terminal algorithm, a hierarchical method, the motion features of a spherical robot, and its dynamics. In addition, the new direction controller has an excellent control effect with a quick response speed and strong stability. MPCBP can obtain optimal commands that are then transmitted to the velocity and direction controller. Since the two torque controllers in MHH are all Lyapunov-based sliding mode controllers, the MHH framework may achieve optimal control performance while assuring stability. Finally, the two controllers eliminate the requirement for MPCBP's stability and dynamic constraints. Finally, hardware experiments demonstrate the efficacy of the HTSMC, MPCBP, and MHH.

One controller cannot work on multiple and unknown terrains in the velocity control of the spherical robot, because the dynamic models of the robot vary on different terrains, and unmodeled dynamics and uncertainties exist in estimated dynamic models. Based on the above problem, a new velocity controller for spherical robot is designed. This controller combines a hierarchical sliding mode controller (HSMC), an adaptive RBF neural network (RBFNN) and a variable step-size algorithm. The RBFNN is used to online estimate the uncertainties, and the Lyapunov function is utilized to design the adaptive law for the RBFNN. In order to learn the uncertainties faster, while minimizing overshoot and preventing velocity oscillations, a variable step-size algorithm is proposed. The practical experiments demonstrate that, this controller of the spherical robot achieves velocity tracking on multiple and complex terrains, while eliminating steady-state error, having a good control effect, and maintaining high stability.

As alternative herbal medicine gains soar in popularity around the world, it is necessary to apply a fast and convenient means for classifying and evaluating herbal medicines. In this work, an electronic nose system with seven classification algorithms is used to discriminate between 12 categories of herbal medicines. The results show that these herbal medicines can be successfully classified, with support vector machine (SVM) and linear discriminant analysis (LDA) outperforming other algorithms in terms of accuracy. When principal component analysis (PCA) is used to lower the number of dimensions, the time cost for classification can be reduced while the data is visualized. Afterwards, conformal predictions based on 1NN (1-Nearest Neighbor) and 3NN (3-Nearest Neighbor) (CP-1NN and CP-3NN) are introduced. CP-1NN and CP-3NN provide additional, yet significant and reliable, information by giving the confidence and credibility associated with each prediction without sacrificing of accuracy. This research provides insight into the construction of a herbal medicine flavor library and gives methods and reference for future works.

In this letter, a general robust reference path selection method (RPSM) that can be integrated into current existing motion planning algorithms is proposed to improve the mobile performance of autonomous patrol robots. The proposed RPSM maintains a dynamic array of path candidates that contains newly found paths, optimal historical paths, and hybrid paths that incorporate local trajectories. All these candidates will be evaluated in a unified criterion, and the best path with the minimal cost will be presented for trajectory tracking, ensuring the consistency and smoothness of the actual motion. Experiments with two different kinds of robots in various scenarios confirm that RPSM enriches the diversity and robustness of reference paths, and improves the execution efficiency by significantly reducing the average actual trajectory distance, orientation change, and total execution time, with an acceptable extra computational cost in comparison to the corresponding original hybrid A* algorithm.

In machine learning applications, the reliability of predictions is significant for assisted decision and risk control. As an effective framework to quantify the prediction reliability, conformal prediction (CP) was commonly developed with $k$ -nearest neighbor, known as CPKNN. However, the conventional CPKNN suffers from high variance and bias, and long computational time as the feature dimensionality increases. To address these limitations, a new CP framework-CP with shrunken centroids (CPSC) is proposed. It regularizes the class centroids to attenuate the irrelevant features and shrink the sample space for predictions and reliability quantification. We have also compared the CPSC with CP based on SVM, LightGBM, RF on the herbal medicine dataset, with the electronic nose as a case and assessed them in two tasks: 1) off-line prediction: the training set was fixed, and the accuracy on the testing set was evaluated and 2) online prediction with data augmentation: CPKNN and CPSC filtered unlabeled data to augment the training data based on the prediction reliability, and the final accuracy of the testing set was compared. The result shows that CPSC significantly outperformed CPKNN in both two tasks: 1) CPSC reached a significantly higher accuracy with lower computation cost, and with the same credibility output, CPSC generally achieved higher accuracy and 2) the data augmentation process with CPSC robustly manifested a statistically significant improvement in prediction accuracy with different reliability thresholds, and the augmented data were more balanced in classes. This novel CPSC provides higher prediction accuracy and better reliability quantification, which can assist in reliable decision support.

This letter proposes a novel linear online identification framework for the spherical robot to address the modeling difficulties posed by nonlinearity and time-varying characteristics. Firstly, the Koopman theory is applied to the spherical robot to build a linear model to approximate the nonlinearity. After selecting a set of observables based on spherical robots' dynamics, the model is identified from data. Then, a new online system identification algorithm based on the Kalman filter and noise estimation was presented, which updates the model in real time to track the time-varying system characteristics. Experiments demonstrate that the Koopman-based linear model meets the precision criteria for long-term forecasting of the nonlinear spherical robot. Through the Kalman filter online identification algorithm, the model parameters can achieve stable convergence, accurately tracking the system changes caused by elements like terrain, load, and actuators. The performance, robustness, and application potential of our algorithm significantly exceed those of traditional methods. After providing a foundation for the spherical robot's adaptive control, this study is also a useful reference for other robots' and nonlinear systems' online identification.