We present an approach to position k servers (e.g. mobile robots) to provide a service to n independently moving clients; for example, in mobile ad-hoc networking applications where inter-agent distances need to be minimized, connectivity constraints exist between servers, and no a priori knowledge of the clients' motion can be assumed. Our primary contribution is an algorithm to compute and maintain a small representative set, called a kinematic coreset, of the n moving clients.We prove that, in any given moment, the maximum distance between the clients and any set of k servers is approximated by the coreset up to a factor of (1 ± ε), where ε > 0 is an arbitrarily small constant. We prove that both the size of our coreset and its update time is polynomial in k log(n)/ε. Although our optimization problem is NP-hard (i.e., takes time exponential in the number of servers to solve), solving it on the small coreset instead of the original clients results in a tractable controller. The approach is validated in a small scale hardware experiment using robot servers and human clients, and in a large scale numerical simulation using thousands of clients.

We present a Simultaneous Localization and Mapping (SLAM) algorithm based on measurements of the ambient magnetic field strength (MagSLAM) that allows quasi-real-time mapping and localization in buildings, where pedestrians with foot-mounted sensors are the subjects to be localized. We assume two components to be present: firstly a source of odometry (human step measurements), and secondly a sensor of the local magnetic field intensity. Our implementation follows the FastSLAM factorization using a particle filter. We augment the hexagonal transition map used in the pre-existing FootSLAM algorithm with local maps of the magnetic field strength, binned in a hierarchical hexagonal structure. We performed extensive experiments in a number of different buildings and present the results for five data sets for which we have ground truth location information. We consider the results obtained using MagSLAM to be strong evidence that scalable and accurate localization is possible without an a priori map.

The magnetic field in indoor environments is rich in features and exceptionally easy to sense. In conjunction with a suitable form of odometry, such as signals produced from inertial sensors or wheel encoders, a map of this field can be used to precisely localize a human or robot in an indoor environment. We show how the use of this field yields significant improvements in terms of localization accuracy for both legged and non-legged locomotion. We suggest various likelihood functions for sequential Monte Carlo localization and evaluate their performance based on magnetic maps of different resolutions. Specifically, we investigate the influence that measurement representation (e.g., intensity-based, vector-based) and map resolution have on localization accuracy, robustness, and complexity. Compared to other localization approaches (e.g., camera-based, LIDAR-based), there exist far fever privacy concerns when sensing the indoor environment's magnetic field. Furthermore, the required sensors are less costly, compact, and have a lower raw data rate and power consumption. The combination of technical and privacy-related advantages makes the use of the magnetic field a very viable solution to indoor navigation for both humans and robots.

In this paper we examine the correlation between the information content and the spatial realization of range measurements taken by a mapping robot. To do so, we consider the task of constructing an occupancy grid map with a binary Bayesian filter. Using a narrow beam-based sensor model (versus an additive white Gaussian noise model), we prove that any controller tasked to maximize a mutual information reward function is eventually attracted to unexplored space. This intuitive behavior is derived solely from the geometric dependencies of the occupancy grid mapping algorithm and the monotonie properties of mutual information. Since it is a function of both the robot's position and the uncertainty of the surrounding cells, mutual information encodes geometric relationships that are fundamental to robot control, thus yielding geometrically relevant reward surfaces on which the robot can navigate. Lastly, we present the results of two experiments employing an omnidirectional ground robot equipped with a laser rangefinder.

We present Pose and Paste (P&P) - an intuitive interface designed to facilitate interaction between a single user and a number of robots equipped with cameras. With this interface, a user wearing a head-mounted display is able to cycle through the real-time video streams originating from the robots' cameras. The user is also able to select a robot and remotely position it by simply walking or turning his/her head, i.e., control the robot's motion in a master/slave-type fashion. We report the results of an initial hardware experiment where a user located in the USA is tasked to position two quadrotor robots within a motion capture laboratory located in Germany. These results suggest that P&P is a feasible approach to remotely inspect disaster affected sites. Lastly, we conduct a user study to compare P&P with a baseline interface composed of a traditional computer monitor and a video game controller. The quantitative results and qualitative discussions resulting from this user study highlight how such multi-robot interfaces can be further improved.

This paper presents the design, fabrication and operation of a hexapod fabricated using a combination of printing and folding flat sheets of polyester. The polyester sheets are cut and engraved with crease patterns, which are then manually folded to create 3D functional modules, inspired by the Japanese art of Origami. These modules, when connected, form a hexapod with two degrees of freedom per leg. All custom mechanical parts are manufactured in a planar fashion using a laser cutter. We created this print-and-fold hexapod as a miniature version of a commercially available platform, to which we compare several metrics, such as weight, walking speed, and cost of transportation. Our print-and-fold hexapod has a mass of 195 g, can walk at speeds of up to 38.1 cm/sec (two body lengths per second), and can be manufactured and assembled from scratch by a single person in approximately seven hours. Experimental results of gait control and trajectory tracking are provided.

To improve our understanding of the indoor properties of the perturbed Earth's magnetic field, we have developed a methodology to obtain dense and spatially referenced samples of the magnetic vector field on the ground's surface and in the free space above. This methodology draws on the use of various tracking techniques (photometric, odometric, and motion capture) to accurately determine the pose of the magnetic sensor, which can be positioned manually by humans or autonomously by robots to acquire densely gridded sample datasets. We show that the indoor magnetic field exhibits a fine-grained and persistent micro-structure of perturbations in terms of its direction and intensity. Instead of being a hindrance to indoor navigation, we believe that the variations of the three vector components are sufficiently expressive to form re-recognizable features based on which accurate localization is possible. We provide experimental results using our methodology to map the magnetic field on the ground's surface in our indoor research facilities. With the use of a magnetometer and very little computation, these resulting maps can serve to compensate the perturbations and subsequently determine pose of a human or robot in dead reckoning applications.

This paper presents a scalable information theoretic approach to infer the state of an environment by distributively controlling robots equipped with sensors. The robots iteratively estimate the environment state using a recursive Bayesian filter, while continuously moving to improve the quality of the estimate by following the gradient of mutual information. Both the filter and the controller use a novel algorithm for approximating the robots' joint measurement probabilities, which combines consensus (for decentralization) and sampling (for scalability). The approximations are shown to approach the true joint measurement probabilities as the size of the consensus rounds grows or as the network becomes complete. The resulting gradient controller runs in constant time with respect to the number of robots, and linear time with respect to the number of sensor measurements and environment discretization cells, while traditional mutual information methods are exponential in all of these quantities. Furthermore, the controller is proven to be convergent between consensus rounds and, under certain conditions, is locally optimal. The complete distributed inference and coordination algorithm is demonstrated in experiments with five quad-rotor flying robots and simulations with 100 robots.

This paper presents a decentralized control strategy for positioning and orienting multiple robotic cameras to collectively monitor an environment. The cameras may have various degrees of mobility from six degrees of freedom, to one degree of freedom. The control strategy is proven to locally minimize a novel metric representing information loss over the environment. It can accommodate groups of cameras with heterogeneous degrees of mobility (e.g., some that only translate and some that only rotate), and is adaptive to robotic cameras being added or deleted from the group, and to changing environmental conditions. The robotic cameras share information for their controllers over a wireless network using a specially designed multihop networking algorithm. The control strategy is demonstrated in repeated experiments with three flying quadrotor robots indoors, and with five flying quadrotor robots outdoors. Simulation results for more complex scenarios are also presented.

We develop a distributed controller to position a team of aerial vehicles in a configuration that optimizes communication-link quality, to support a team of ground vehicles performing a collaborative task. We propose a gradient-based control approach where agents' positions locally minimize a physically motivated cost function. The contributions of this paper are threefold. We formulate of a cost function that incorporates a continuous, physical model of signal quality, SIR. We develop a non-smooth gradient-based controller that positions aerial vehicles to acheive optimized signal quality amongst all vehicles in the system. This controller is provably convergent while allowing for non-differentiability due to agents moving in or out of communication with one another. Lastly, we guarantee that given certain initial conditions or certain values of the control parameters, aerial vehicles will never disconnect the connectivity graph. We demonstrate our controller on hardware experiments using AscTec Hummingbird quadrotors and provide aggregate results over 10 trials. We also provide hardware-in-the-loop and MATALB simulation results, which demonstrate positioning of the aerial vehicles to minimize the cost function H and improve signal-quality amongst all communication links in the ground/air robot team.

A kernel-based recursive least-squares algorithm that implements a fixed size ldquosliding-windowrdquo technique has been recently proposed for fast adaptive nonlinear filtering applications. We propose a methodology of resizing the kernel matrix to assist in system identification of time-varying nonlinear systems. To be applicable in practice, the modified algorithm must preserve its ability to operate online. Given a bound on the maximum kernel matrix size, we define the set of all obtainable sizes as the resizing range. We then propose a simple online technique that resizes the kernel matrix within the resizing range. The modified algorithm is applied to the nonlinear system identification problem that was used to evaluate the original algorithm. Results show that an increase in performance is achieved without increasing the original algorithm's computation time.

This paper presents a distributed control strategy for deploying hovering robots with multiple downward facing cameras to collectively monitor an environment. Information per pixel is proposed as an optimization criterion for multi-camera placement problems. This metric is used to derive a specific cost function for multiple downward facing cameras mounted on hovering robot platforms. The cost function leads to a gradient-based distributed controller for positioning the robots. A convergence proof using LaSalle's invariance principle is given to show that the robots converge to locally optimal positions. The controller is demonstrated in experiments with three flying quad-rotor robots.