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The ``prediction + optimal control'' scheme has shown good performance in many applications of automotive, traffic, robot, and building control. In practice, the prediction results are simply considered correct in the optimal control design process. However, in reality, these predictions may never be perfect. Under a conventional stochastic optimal control formulation, it is difficult to answer questions like ``what if the predictions are wrong''. This paper presents an analysis framework for predictive optimal control where the subjective belief about the future is no longer considered perfect. A novel concept called the hidden prediction state is proposed to establish connections among the predictors, the subjective beliefs, the control policies and the objective control performance. Based on this framework, the predictor evaluation problem is analyzed. Three commonly-used predictor evaluation measures, including the mean squared error, the regret and the log-likelihood, are considered. It is shown that neither using the mean square error nor using the likelihood can guarantee a monotonic relationship between the predictor error and the optimal control cost. To guarantee control cost improvement, it is suggested the predictor should be evaluated with the control performance, e.g., using the optimal control cost or the regret to evaluate predictors. Numerical examples and examples from automotive applications with real-world driving data are provided to illustrate the ideas and the results.

The GelSight-like visual tactile (VT) sensor has gained popularity as a high-resolution tactile sensing technology for robots, capable of measuring touch geometry using a single RGB camera. However, the development of multi-modal perception for VT sensors remains a challenge, limited by the mono camera. In this paper, we propose the GelSplitter, a new framework approach the multi-modal VT sensor with synchronized multi-modal cameras and resemble a more human-like tactile receptor. Furthermore, we focus on 3D tactile reconstruction and implement a compact sensor structure that maintains a comparable size to state-of-the-art VT sensors, even with the addition of a prism and a near infrared (NIR) camera. We also design a photometric fusion stereo neural network (PFSNN), which estimates surface normals of objects and reconstructs touch geometry from both infrared and visible images. Our results demonstrate that the accuracy of RGB and NIR fusion is higher than that of RGB images alone. Additionally, our GelSplitter framework allows for a flexible configuration of different camera sensor combinations, such as RGB and thermal imaging.

High-resolution multi-modality information acquired by vision-based tactile sensors can support more dexterous manipulations for robot fingers. Optical flow is low-level information directly obtained by vision-based tactile sensors, which can be transformed into other modalities like force, geometry and depth. Current vision-tactile sensors employ optical flow methods from OpenCV to estimate the deformation of markers in gels. However, these methods need to be more precise for accurately measuring the displacement of markers during large elastic deformation of the gel, as this can significantly impact the accuracy of downstream tasks. This study proposes a self-supervised optical flow method based on deep learning to achieve high accuracy in displacement measurement for vision-based tactile sensors. The proposed method employs a coarse-to-fine strategy to handle large deformations by constructing a multi-scale feature pyramid from the input image. To better deal with the elastic deformation caused by the gel, the Helmholtz velocity decomposition constraint combined with the elastic deformation constraint are adopted to address the distortion rate and area change rate, respectively. A local flow fusion module is designed to smooth the optical flow, taking into account the prior knowledge of the blurred effect of gel deformation. We trained the proposed self-supervised network using an open-source dataset and compared it with traditional and deep learning-based optical flow methods. The results show that the proposed method achieved the highest displacement measurement accuracy, thereby demonstrating its potential for enabling more precise measurement of downstream tasks using vision-based tactile sensors.

In recent years, multi-scale generative adversarial networks (GANs) have been proposed to build generalized image processing models based on single sample. Constraining on the sample size, multi-scale GANs have much difficulty converging to the global optimum, which ultimately leads to limitations in their capabilities. In this paper, we pioneered the introduction of PAC-Bayes generalized bound theory into the training analysis of specific models under different adversarial training methods, which can obtain a non-vacuous upper bound on the generalization error for the specified multi-scale GAN structure. Based on the drastic changes we found of the generalization error bound under different adversarial attacks and different training states, we proposed an adaptive training method which can greatly improve the image manipulation ability of multi-scale GANs. The final experimental results show that our adaptive training method in this paper has greatly contributed to the improvement of the quality of the images generated by multi-scale GANs on several image manipulation tasks. In particular, for the image super-resolution restoration task, the multi-scale GAN model trained by the proposed method achieves a 100% reduction in natural image quality evaluator (NIQE) and a 60% reduction in root mean squared error (RMSE), which is better than many models trained on large-scale datasets.