K-BMPC: Derivative-based Koopman Bilinear Model Predictive Control For Tractor-trailer Trajectory Tracking With Unknown Parameters

Nonlinear dynamics bring difficulties to controller design for control-affine systems such as tractor-trailer vehicles, especially when the parameters in dynamics are unknown. To address this constraint, we propose a derivative-based lifting function construction method, show that the corresponding infinite dimensional Koopman bilinear model over the lifting function is equivalent to the original control-affine system. Further, we analyze the propagation and bounds of state prediction errors caused by the the truncation in derivative order. The identified finite dimensional Koopman bilinear model would serve as predictive model in next step. Koopman Bilinear Model Predictive control (K-BMPC) is proposed to solve the trajectory tracking problem. We linearize the bilinear model around the estimation of the lifted state and control input. Then the bilinear Model Predictive Control problem is approximated by a quadratic programming problem. Further, the estimation is updated at each iteration until the convergence is reached. Moreover, we implement our algorithm on a tractor-trailer dynamic system, taking into account the longitudinal and side slip effects. The open-loop simulation shows the proposed Koopman bilinear model captures the dynamics with unknown parameters and has good prediction performance. Closed loop tracking results show the proposed K-BMPC exhibits elevated tracking precision along with commendable computational efficiency. The experimental results demonstrate the feasibility of the proposed method

PlaneDepth: Plane-Based Self-Supervised Monocular Depth Estimation

Self-supervised monocular depth estimation refers to training a monocular depth estimation (MDE) network using only RGB images to overcome the difficulty of collecting dense ground truth depth. Many previous works addressed this problem using depth classification or depth regression. However, depth classification tends to fall into local minima due to the bilinear interpolation search on the target view. Depth classification overcomes this problem using pre-divided depth bins, but those depth candidates lead to discontinuities in the final depth result, and using the same probability for weighted summation of color and depth is ambiguous. To overcome these limitations, we use some predefined planes that are parallel to the ground, allowing us to automatically segment the ground and predict continuous depth for it. We further model depth as a mixture Laplace distribution, which provides a more certain objective for optimization. Previous works have shown that MDE networks only use the vertical image position of objects to estimate the depth and ignore relative sizes. We address this problem for the first time in both stereo and monocular training using resize cropping data augmentation. Based on our analysis of resize cropping, we combine it with our plane definition and improve our training strategy so that the network could learn the relationship between depth and both the vertical image position and relative size of objects. We further combine the self-distillation stage with post-processing to provide more accurate supervision and save extra time in post-processing. We conduct extensive experiments to demonstrate the effectiveness of our analysis and improvements.Comment: 12 pages, 7 figure

Diffusion Mechanism in Residual Neural Network: Theory and Applications

Diffusion, a fundamental internal mechanism emerging in many physical processes, describes the interaction among different objects. In many learning tasks with limited training samples, the diffusion connects the labeled and unlabeled data points and is a critical component for achieving high classification accuracy. Many existing deep learning approaches directly impose the fusion loss when training neural networks. In this work, inspired by the convection-diffusion ordinary differential equations (ODEs), we propose a novel diffusion residual network (Diff-ResNet), internally introduces diffusion into the architectures of neural networks. Under the structured data assumption, it is proved that the proposed diffusion block can increase the distance-diameter ratio that improves the separability of inter-class points and reduces the distance among local intra-class points. Moreover, this property can be easily adopted by the residual networks for constructing the separable hyperplanes. Extensive experiments of synthetic binary classification, semi-supervised graph node classification and few-shot image classification in various datasets validate the effectiveness of the proposed method