Nonparametric bootstrapping for hierarchical data is relatively underdeveloped and not straightforward: certainly it does not make sense to use simple nonparametric resampling, which treats all observations as independent. We have provided some resampling strategies of hierarchical data, proved that the strategy of nonparametric bootstrapping on the highest level (randomly sampling all other levels without replacement within the highest level selected by randomly sampling the highest levels with replacement) is better than that on lower levels, analyzed real data and performed simulation studies.random effects model, hierarchical data, nonparametric bootstrapping, resampling schemes, unbalanced data,

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Abstract:We describe the novel, multiply gaited, vectored water-jet, hybrid locomotion-capable, amphibious spherical robot III (termed ASR-III) featuring a wheel-legged, water-jet composite driving system incorporating a lifting and supporting wheel mechanism (LSWM) and mechanical legs with a water-jet thruster. The LSWM allows the ASR-III to support the body and slide flexibly on smooth (flat) terrain. The composite driving system facilitates two on-land locomotion modes (sliding and walking) and underwater locomotion mode with vectored thrusters, improving adaptability to the amphibious environment. Sliding locomotion improves the stability and maneuverability of ASR-III on smooth flat terrain, whereas walking locomotion allows ASR-III to conquer rough terrain. We used both forward and reverse kinematic models to evaluate the walking and sliding gait efficiency. The robot can also realize underwater locomotion with four vectored water-jet thrusters, and is capable of forward motion, heading angle control and depth control. We evaluated LSWM efficiency and the sliding velocities associated with varying extensions of the LSWM. To explore gait stability and mobility, we performed on-land experiments on smooth flat terrain to define the optimal stride length and frequency. We also evaluated the efficacy of waypoint tracking when the sliding gait was employed, using a closed-loop proportional-integral-derivative (PID) control mechanism. Moreover, experiments of forward locomotion, heading angle control and depth control were conducted to verify the underwater performance of ASR-III. Comparison of the previous robot and ASR-III demonstrated the ASR-III had better amphibious motion performance.

Compared to the doubly fed machine, the brushless doubly fed machine (BDFM) has high reliability and low maintenance requirements. First, by taking the negative conjugation of the control motor variables in rotor reference frame, a state-space model of BDFM is derived. It is then transformed into synchronous reference frame, called synchronous reference frame state-space model (SSSM). In this way, all the variables of the SSSM are DC under the static state. Second, on the basis of the analysis of static equations, the possible output torque limits are obtained. Third, the causes of losing control are analyzed by the flux and the torque derivatives. A new control strategy called synthetic vector direct torque control (SVDTC) is proposed to solve the losing control problems of the conventional direct torque control (DTC). Finally, the correctness of the results of this paper is verified by calculation examples and simulation results, the losing control problems can be solved, and the theoretical output capacity limits can be reached using SVDTC.

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