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This paper introduces a cosmic expansion model with constant speed of cosmic spatial expansion via derivation and simulations, where the speed of cosmic spatial expansion equals the speed of light c. Simulation results show that the earliest observable universe time is t = 5.084 Gyrs where the current universe time T = 13.82 Gyrs, and the furthest observable distance at the earliest observable universe time t is S = 0.632R, where R is the cosmic radius at current universe time T. The above constant cosmic expansion model does not consider the inflation period in the early universe according to the Big Bang model, nor does it considered the cosmic acceleration in recent universe time. However, this simplified cosmic expansion model could be a benchmark that will be helpful to understand the cosmic expansion and the observable universe. Based on the derivation and simulation of the constant cosmic expansion model, the threshold of observable universe for the accelerated cosmic expansion model can also be calculated similarly, as far as the speed of cosmic spatial expansion at any universe time t can be provided.

Humans have a remarkable ability to learn continuously from th e environment and inner experience. One of the grand goals of robots is to build an artificial "lifelong learning" agent that can shape a cultivated understanding of the world from the current scene and previous knowledge via an autonomous lifelong development. It is challenging for the robot learning process to retain earlier knowledge when robots encounter new tasks or information. Recent advances in computer vision and deep -learning methods have been impressive due to large-scale data sets, such as ImageNet and COCO. However, robotic vision poses unique new challenges for applying visual algorithms developed from these computer vision data sets because they implicitly assume a fixed set of categories and time -invariant task distributions.

Hand gesture recognition plays an essential role in the human-robot interaction (HRI) field. Most previous research only studies hand gesture recognition in a short distance, which cannot be applied for interaction with mobile robots like unmanned aerial vehicles (UAVs) at a longer and safer distance. Therefore, we investigate the challenging long-range hand gesture recognition problem for the interaction between humans and UAVs. To this end, we propose a novel attention-based single shot multibox detector (SSD) model that incorporates both spatial and channel attention for hand gesture recognition. We notably extend the recognition distance from 1 meter to 7 meters through the proposed model without sacrificing speed. Besides, we present a long-range hand gesture (LRHG) dataset collected by the USB camera mounted on mobile robots. The hand gestures are collected at discrete distance levels from 1 meter to 7 meters, where most of the hand gestures are small and at low resolution. Experiments with the self-built LRHG dataset show our methods reach the surprising performance-boosting over the state-of-the-art method like the SSD network on both short-range (1 meter) and long-range (up to 7 meters) hand gesture recognition tasks.