Brian J. Julian

Distributed robotic sensor networks: An information-theoretic approach

In this paper we present an information-theoretic approach to distributively control multiple robots equipped with sensors to infer the state of an environment. The robots iteratively estimate the environment state using a sequential Bayesian filter, while continuously moving along the gradient of mutual information to maximize the informativeness of the observations provided by their sensors. The gradient-based controller is proven to be convergent between observations and, in its most general form, locally optimal. However, the computational complexity of the general form is shown to be intractable, and thus non-parametric methods are incorporated to allow the controller to scale with respect to the number of robots. For decentralized operation, both the sequential Bayesian filter and the gradient-based controller use a novel consensus-based algorithm to approximate the robots’ joint measurement probabilities, even when the network diameter, the maximum in/out degree, and the number of robots are unknown. The approach is validated in two separate hardware experiments each using five quadrotor flying robots, and scalability is emphasized in simulations using 100 robots.

Characterization of the indoor magnetic field for applications in Localization and Mapping

To improve our understanding of the indoor properties of the perturbed Earths magnetic field, we have developed a methodology to obtain dense and spatially referenced samples of the magnetic vector field on the grounds 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 grounds 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.

Optimal coverage for multiple hovering robots with downward facing cameras

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 LaSalles 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.

Magnetic maps of indoor environments for precise localization of legged and non-legged locomotion

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 environments 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.

Simultaneous Localization and Mapping for pedestrians using distortions of the local magnetic field intensity in large indoor environments

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.

On mutual information-based control of range sensing robots for mapping applications

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 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 monotonic properties of mutual information. Since it is dependent on 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. We also provide an algorithmic implementation for computing mutual information and show that its worst-case time and space complexities are quadratic and linear, respectively, with respect to the map’s spatial resolution. Lastly, we present the results of experiments employing an omnidirectional ground robot equipped with a laser range finder. Our experimental results support our theoretical and computational findings.

A lightweight modular 12-DOF print-and-fold hexapod

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.

A Location-Based Algorithm for Multi-Hopping State Estimates within a Distributed Robot Team

Mutual knowledge of state information among robots is a crucial requirement for solving distributed control problems, such as coverage control of mobile sensing networks. This paper presents a strategy for exchanging state estimates within a robot team. We introduce a deterministic algorithm that broadcasts estimates of nearby robots more frequently than distant ones. We argue that this frequency should be exponentially proportional to an importance function that monotonically decreases with distance between robots. The resulting location-based algorithm increases propagation rates of state estimates in local neighborhoods when compared to simple flooding schemes.

Distributed Approximation of Joint Measurement Distributions Using Mixtures of Gaussians

This paper presents an approach to distributively approximate the continuous probability distribution that describes the fusion of sensor measurements from many networked robots. Each robot forms a weighted mixture of Gaussians to represent the measurement distribution of its local observation. From this mixture set, the robot then draws samples of Gaussian elements to enable the use of a consensus-based algorithm that evolves the corresponding canonical parameters. We show that the these evolved parameters describe a distribution that converges weakly to the joint of all the robots’ unweighted mixture distributions, which itself converges weakly to the joint measurement distribution as more system resources are allocated. The major innovation of this approach is to combine sample-based sensor fusion with the notion of pre-convergence termination that results in scalable multi-robot system. We also derive bounds and convergence rates for the approximated joint measurement distribution, specifically the elements of its information vectors and the eigenvalues of its information matrices. Most importantly, these performance guarantees do not come at a cost of complexity, since computational and communication complexity scales quadratically with respect to the Gaussian dimension, linearly with respect to the number of samples, and constant with respect to the number of robots. Results from numerical simulations for object localization are discussed using both Gaussians and mixtures of Gaussians.

Modifications to the sliding-window kernel RLS algorithm for time-varying nonlinear systems: Online resizing of the kernel matrix

A kernel-based recursive least-squares algorithm that implements a fixed size “sliding-window” 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 algorithms computation time.