When the wheeled mobile robot (WMR) is required to perform specific tasks in complex environment, i.e., on the forestry, wet, icy ground or on the sharp corner, wheel skidding and slipping inevitably occur during trajectory tracking. To improve the trajectory tracking performance of WMR under unknown skidding and slipping condition, an adaptive sliding mode controller (ASMC) design approach based on the extended state observer (ESO) is presented. The skidding and slipping is regarded as external disturbance. In this paper, the ESO is introduced to estimate the lumped disturbance containing the unknown skidding and slipping, parameter variation, parameter uncertainties, etc. By designing a sliding surface based on the disturbance estimation, an adaptive sliding mode tracking control strategy is developed to attenuate the lumped disturbance. Simulation results show that higher precision tracking and better disturbance rejection of ESO-ASMC is realized for linear and circular trajectory than the ASMC scheme. Besides, experimental results indicate the ESO-ASMC scheme is feasible and effective. Therefore, ESO-ASMC scheme can enhance the energy efficiency for the differentially driven WMR under unknown skidding and slipping condition.
Variational Autoencoders (VAEs) are one of the most commonly used generative models, particularly for image data. A prominent difficulty in training VAEs is data that is supported on a lower dimensional manifold. Recent work by Dai and Wipf (2019) suggests that on low-dimensional data, the generator will converge to a solution with 0 variance which is correctly supported on the ground truth manifold.In this paper, via a combination of theoretical and empirical results, we show that the story is more subtle. Precisely, we show that for linear encoders/decoders, the story is mostly true and VAE training does recover a generator with support equal to the ground truth manifold, but this is due to the implicit bias of gradient descent rather than merely the VAE loss itself.In the nonlinear case, we show that the VAE training frequently learns a higher-dimensional manifold which is a superset of the ground truth manifold.
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