a) Previously described result (b) Previously described result, gained (c) Our result Fig. 1. We present a system that uses a novel combination of motion-adaptive burst capture, robust temporal denoising, learning-based white balance, and tone mapping to create high quality photographs in low light on a handheld mobile device. Here we show a comparison of a photograph generated by the burst photography system described in (Hasino et al. 2016) and the system described in this paper, running on the same mobile camera. In this low-light se ing (about 0.4 lux), the previous system generates an underexposed result (a). Brightening the image (b) reveals significant noise, especially chroma noise, which results in loss of detail and an unpleasantly blotchy appearance. Additionally, the colors of the face appear too orange. Our pipeline (c) produces detailed images by selecting a longer exposure time due to the low scene motion (in this se ing, extended from 0.14 s to 0.33 s), robustly aligning and merging a larger number of frames (13 frames instead of 6), and reproducing colors reliably by training a model for predicting the white balance gains specifically in low light. Additionally, we apply local tone mapping that brightens the shadows without over-clipping highlights or sacrificing global contrast.Taking photographs in low light using a mobile phone is challenging and rarely produces pleasing results. Aside from the physical limits imposed by read noise and photon shot noise, these cameras are typically handheld, have small apertures and sensors, use mass-produced analog electronics that cannot easily be cooled, and are commonly used to photograph subjects that move, like children and pets. In this paper we describe a system for capturing clean, sharp, colorful photographs in light as low as 0.3 lux, where human vision becomes monochromatic and indistinct. To permit handheld photography without ash illumination, we capture, align, and combine multiple frames. Our system employs "motion metering", which uses an estimate of motion magnitudes (whether due to handshake or moving objects) to identify the number of frames and the per-frame exposure times that together minimize both noise and motion blur in a captured burst. We combine these frames using robust alignment and merging techniques that are specialized for high-noise imagery. To ensure accurate colors in such low light, we employ a learning-based auto white balancing algorithm. To prevent the photographs from looking like they were shot in daylight, we use tone mapping techniques inspired by illusionistic painting: increasing contrast, crushing shadows to black, and surrounding the scene with darkness. All of these processes are performed using the limited computational resources of a mobile device. Our system can be used by novice photographers to produce shareable pictures in a few seconds based on a single shu er press, even in environments so dim that humans cannot see clearly.

When a battery-powered robot needs to operate for a long period of time, optimizing its energy consumption becomes critical. Driving motors are a major source of power consumption for mobile robots. In this paper, we study the problem of finding optimal paths and velocity profiles for car-like robots so as to minimize the energy consumed during motion. We start with an established model for energy consumption of DC motors. We first study the problem of finding the energy optimal velocity profiles, given a path for the robot. We present closed form solutions for the unconstrained case and for the case where there is a bound on maximum velocity. We then study a general problem of finding an energy optimal path along with a velocity profile, given a starting and goal position and orientation for the robot. Along the path, the instantaneous velocity of the robot may be bounded as a function of its turning radius, which in turn affects the energy consumption. Unlike minimum length paths, minimum energy paths may contain circular segments of varying radii. We show how to efficiently construct a graph which generalizes Dubins' paths by including segments with arbitrary radii. Our algorithm uses the closed-form solution for the optimal velocity profiles as a subroutine to find the minimum energy trajectories, up to a fine discretization. We investigate the structure of energy-optimal paths and highlight instances where these paths deviate from the minimum length Dubins' curves. In addition, we present a calibration method to find energy model parameters. Finally, we present A preliminary version of this paper without the path planning section appeared in [19].

We investigate the role of the information available to the players on the outcome of the cops and robbers game. This game takes place on a graph and players move along the edges in turns. The cops win the game if they can move onto the robber's vertex. In the standard formulation, it is assumed that the players can "see" each other at all times. A graph G is called cop-win if a single cop can capture the robber on G. We study the effect of reducing the cop's visibility. On the positive side, with a simple argument, we show that a cop with small or no visibility can capture the robber on any cop-win graph (even if the robber still has global visibility). On the negative side, we show that the reduction in cop's visibility can result in an exponential increase in the capture time. Finally, we start the investigation of the variant where the visibility powers of the two players are symmetrical. We show that the cop can establish eye contact with the robber on any graph and present a sufficient condition for capture. In establishing this condition, we present a characterization of graphs on which a natural greedy pursuit strategy suffices for capturing the robber.

Abstract-For battery-powered mobile robots to operate for long periods of time, it is critical to optimize their motion so as to minimize energy consumption. The driving motors are a major source of power consumption. In this paper, we study the problem of finding velocity profiles for car-like robots so as to minimize the energy consumed while traveling along a given path.We start with an established model for energy consumption of DC motors. We present closed form solutions for the unconstrained case and for the case where there is a bound on maximum velocity. We also study a general problem where the robot's path is composed of segments (e.g. circular arcs and line segments). We are given a velocity bound for each segment. For this problem, we present a dynamic programming solution which uses the solution for the single-constraint case as a subroutine. In addition, we present a calibration method to find model parameters. Finally, we present results from experiments conducted on a custom-built robot.

Abstract-In the lion and man game, a lion tries to capture a man who is as fast as the lion. We study a new version of this game which takes place in a Euclidean environment with a circular obstacle. We present a complete characterization of the game: for each player, we derive necessary and sufficient conditions for winning the game. Their (continuous time) strategies are constructed using techniques from differential games and arguments from geometry. Our main result is a decision algorithm which takes arbitrary initial positions as input, declares one of the players as the winner of the game and outputs a winning strategy for that player. We extend our approach to explicitly construct, in closed form, the decision boundary that partitions the arena into win and lose regions. I. OVERVIEW AND RELATED WORKIn a game of pursuit and evasion, one player (the pursuer) tries to get close to, and possibly capture the other (the evader). The evader, in turn, tries to avoid being captured. Pursuit-evasion games are of fundamental importance to researchers in the field of robotics. Consider the task of surveillance, where a guard (pursuer) has to chase and capture an intruder (evader). Another scenario is search-andrescue, where a rescue worker has to locate a lost hiker. Since the actions of the hiker are not known a priori, worstcase pursuit and evasion strategies guarantee that the hiker is found no matter what he does. Problems arising from diverse applications such as collision-avoidance [9], search-andrescue [6], [14], air-traffic control [3], and surveillance [9] have been modeled as pursuit-evasion games.A classical pursuit-evasion game is the Lion and Man game. It was originally posed in 1925 by Rado as follows A lion and a man in a closed arena have equal maximum speeds. What tactics should the lion employ to be sure of his meal? The first solution was generally accepted by 1950: the lion moves to the center of the arena and then remains on the radius that passes through the man's position. Since they have the same speed, the lion can remain on the radius and simultaneously move toward the man. Although this strategy works in discrete-time, it was later shown by Besicovitch that exact capture in continuous time takes infinitely long in a bounded arena [13]. However, if the capture distance is set to some c > 0, Alonso et al. [2] The lion and man game in the presence of obstacles remains a challenge. In this paper, we take an important step for solving the lion and man game in an environment with obstacles. We present full characterization of the game in the presence of a single circular obstacle. That is, we present a decision algorithm which determines the winner of the game. We also construct the winner's strategy.As in the original version of the game, we assume that the players know exact locations of each other at all times and have equal maximum speeds.An important line of research is to study the effect of sensing limitations. Recent progress in this direction includes the study of range-based limitation...