In this work, we address the deployment problem for a team of mobile guards that tries to maintain a line-ofsight with an unpredictable mobile intruder. First, we present a computationally efficient strategy for generating a set of points, called kernel points, that covers the entire polygon. We then introduce a polygon partitioning technique based on the location of the kernel points. Next, we propose control laws for a free guard to track an intruder in general polygonal environments based on the analysis of a pursuit-evasion game around a single corner [1]. Finally, we present several variations of the proposed control laws that include capture and search, and illustrate the improvement in the overall visual footprint of the team of mobile guards based on extensive simulations.

In this work, we address a visbility-based target tracking problem in a polygonal environment in which a group of mobile observers try to maintain a line-of-sight with a mobile intruder. We build a bridge between data mining and visibility-based tracking using a novel tiling scheme for the polygon. First, we propose a tracking strategy for a team of guards located on the tiles to dynamically track an intruder when complete coverage of the polygon cannot be ensured. Next, we propose a novel variant of the Voronoi Diagram to construct navigation strategies for a team of co-located guards to track an intruder from any initial position in the environment. We present empirical analysis to illustrate the efficacy of the proposed tiling scheme. Simulations and testbed demonstrations are present in a video attachment.

In this paper, we consider the refuel scheduling problem for a team of ground robots deployed in "aislelike" environments wherein the robots are constrained to move along rows. In order to maintain a minimum service rate or throughput for the ground robots, we investigate the problem of scheduling a team of mobile charging stations deployed to replace the batteries on-board the ground robots without any interruption in their task. We propose two scheduling schemes for the mobile chargers to serve the ground robots for long-term service, and derive the parameters associated with the system required for persistent uninterrupted operation.

We consider the problem of generating a fixed path for a mobile observer in a polygonal environment that can maintain a line-of-sight with an unpredictable target. In contrast to purely off-line or on-line techniques, we propose a hierarchical tracking strategy in which an off-line path generation technique based on a RRT is coupled with an online feedback-control technique to generate trajectories for the mobile observer.

This work presents an efficient and implementable solution to the problem of joint task allocation and path planning in a multi-UAV platform. The sensing requirement associated with the task gives rise to an uncanny variant of the traditional vehicle routing problem with coverage/sensing constraints. As is the case in several multi-robot path-planning problems, our problem reduces to an mTSP problem. In order to tame the computational challenges associated with the problem, we propose a hierarchical solution that decouples the vehicle routing problem from the target allocation problem. As a tangible solution to the allocation problem, we use a clustering-based technique that incorporates temporal uncertainty in the cardinality and position of the robots. Finally, we implement the proposed techniques on our multi-quadcopter platforms.

In this paper, we address the visibility-based target tracking problem in which a mobile observer moving along a p-route, which we define as a fixed path for target tracking, tries to keep a mobile target in its field-of-view. By drawing a connection to the watchman's route problem, we find a set of conditions that must be satisfied by the p-route. Then we propose a metric for tracking to estimate a sufficient speed for the observer given the geometry of the environment. We show that the problem of finding the p-route on which the observer requires minimum speed is computationally intractable. We present a technique to find a p-route on which the observer needs at most twice the minimum speed to track the intruder and a reactive motion strategy for the observer.

In this paper, we address a class of visibility-based pursuit-evasion game in which a mobile observer tries to maintain a line-of-sight (LOS) with a mobile target in an environment containing obstacles. The observer knows the current position of the target as long as the target is in the observer's LOS. At first, we address this problem in an environment containing a single corner. We formulate the game as an optimal control problem of maximizing the time for which the observer can keep the reachability set of the target in its field-of-view. Using Pontryagin's principle, we show that the primitives for optimal motion of the observer are straight lines (ST ) and spiral-like curves (C). Next, we present the synthesis of the optimal trajectories from any given initial position of the observer. We show that the optimal path of the observer belongs to the class {ST, C - ST, ST - C - ST }. Given any initial position of the target, we present a partition of the workspace around a corner based on the optimal control policy of the observer.

We investigate a variation of the art gallery problem in which a team of mobile guards tries to track an unpredictable intruder in a simply-connected polygonal environment. The guards are deployed based on the strategy initially proposed in [1] which restricts them to move along a specific diagonal within the environment. However, the intruder can move freely within the environment. We define critical regions to generate event-triggered strategies for the guards. Additionally, a hybrid automaton is designed to model the problem, and sufficient conditions are presented for [n/4] guards for persistent surveillance.

In this work, we address the problem of centralized scheduling and motion planning for multiple grain carts with finite capacity that serve a group of combine harvesters engaged in a harvesting operation. First, we solve a facility location problem of finding the optimal depot position to minimize the distance traveled by the grain carts. Next, we formulate the scheduling problem as a constraint satisfaction problem. For a rectangular field, we present two schemes which allow the grain carts to unload all the combine harvesters without interrupting the harvesting activity. Finally, for both schemes, we present a relation between the physical parameters of the vehicles that need to be satisfied in order to meet the scheduling constraints.

We investigate a variation of the art gallery problem in which a team of mobile guards tries to track an unpredictable intruder in a simply-connected polygonal environment. The guards are confined to move along the diagonals of a polygon, and are deployed according to the strategy proposed in [1] that provides an upper bound of ⌊ n/4 ⌋ mobile guards to cover a simply-connected polygonal environment. We introduce the concept of critical regions to generate event-triggered strategies for the guards. Based on these strategies, we present sufficient conditions for ⌊ n/4 ⌋ guards to track an unpredictable mobile intruder forever.

In this paper, we address the problem of motion planning for an autonomous grain cart. Contrary to prevailing practices in farming wherein one grain cart is allocated to each combine harvester, we envision a scenario in which one grain cart can serve multiple combine harvesters. This gives rise to challenging problems in scheduling and motion planning for the grain cart. In this work, we initially propose a scheduling scheme for a single grain cart to unload multiple combine harvesters without any interruption in the activity of the combines. The proposed algorithm can accommodate arbitrary number of combines. Based on the scheduling scheme, a planner is used to synthesize a feasible path for the grain cart. Finally, simulation results are presented to validate the feasibility of the proposed technique.

The task of locating a source based on the measurements of the signal emitted/emanating from it is called the source-seeking problem. In the past few years, there has been a lot of interest in deploying autonomous platforms for source-seeking. Some of the challenging issues with implementing autonomous source-seeking are the lack of a priori knowledge about the distribution of the emitted signal and presence of noise in both the environment and on-board sensor measurements. This paper proposes a planner for a swarm of robots engaged in seeking an electromagnetic source. The navigation strategy for the planner is based on Particle Swarm Optimization (PSO) which is a population-based stochastic optimization technique. An equivalence is established between particles generated in the traditional PSO technique, and the mobile agents in the swarm. Since the positions of the robots are updated using the PSO algorithm, modifications are required to implement the PSO algorithm on real robots to incorporate collision avoidance strategies. The modifications necessary to implement PSO on mobile robots, and strategies to adapt to real environments are presented in this paper. Our results are also validated on an experimental testbed. Note to Practitioners-This paper is inspired by the source seeking problem in which the signal emitted from the source is assumed to be very noisy, and the spatial distribution is assumed to be non-smooth. We focus our work specifically on electromagnetic sources. However, the strategies proposed in this paper are also applicable to other kinds of sources, for example, nuclear, radiological, chemical or biological. We develop a planner for a swarm of mobile agents that try to locate an unknown electromagnetic source. The mobile agents know their own positions and can measure the signal strength at their current location. They can share information among themselves, and plan for the next step. We propose a complete solution to ensure the effectiveness of PSO in complex environments where collisions may occur. We incorporate static and dynamic obstacle avoidance strategies in PSO to make it fully applicable to real-world scenario. We validate the proposed technique on an experimental testbed. As a part of our future work, we will extend the technique to locate multiple sources of different kinds.

We provide two novel adaptive-rate compressive sensing (CS) strategies for sparse, time-varying signals using side information. The first method uses extra cross-validation measurements, and the second one exploits extra low-resolution measurements. Unlike the majority of current CS techniques, we do not assume that we know an upper bound on the number of significant coefficients that comprises the images in the video sequence. Instead, we use the side information to predict the number of significant coefficients in the signal at the next time instant. We develop our techniques in the specific context of background subtraction using a spatially multiplexing CS camera such as the single-pixel camera. For each image in the video sequence, the proposed techniques specify a fixed number of CS measurements to acquire and adjust this quantity from image to image. We experimentally validate the proposed methods on real surveillance video sequences.

This work addresses a vision-based target tracking problem between a mobile observer and a target in the presence of a circular obstacle. The task of keeping the target in the observer's field-of-view is modeled as a pursuit-evasion game by assuming that the target is adversarial in nature. Due to the presence of obstacles, this is formulated as a game with state constraints. The objective of the observer is to maintain a line-of-sight with the target at all times. The objective of the target is to break the line-of-sight in finite amount of time. First, we establish that the value of the game exists in this setting. Then we reduce the dimension of the problem by formulating the game in relative coordinates, and present a discretization in time and space for the reduced game. Based on this discretization, we use a fully discrete semi-Lagrangian scheme to compute the Kružkov transform of the value function numerically, and show that the scheme converges for our problem. Finally, we compute the optimal control action of the players from the Kružkov transform of the value function, and demonstrate the performance of the numerical scheme by numerous simulations.

In this work, we study the problem of power allocation and adaptive modulation in teams of decision makers. We consider the special case of two teams with each team consisting of two mobile agents. Agents belonging to the same team communicate over wireless ad hoc networks, and they try to split their available power between the tasks of communication and jamming the nodes of the other team. The agents have constraints on their total energy and instantaneous power usage. The cost function adopted is the difference between the rates of erroneously transmitted bits of each team. We model the adaptive modulation problem as a zero-sum matrix game which in turn gives rise to a a continuous kernel game to handle power control. Based on the communications model, we present sufficient conditions on the physical parameters of the agents for the existence of a pure strategy saddle-point equilibrium (PSSPE).

In this paper, we present a visual servo controller that effects optimal paths for a nonholonomic differential drive robot with field-of-view constraints imposed by the vision system. The control scheme relies on the computation of homographies between current and goal images, but unlike previous homography-based methods, it does not use the homography to compute estimates of pose parameters. Instead, the control laws are directly expressed in terms of individual entries in the homography matrix. In particular, we develop individual control laws for the three path classes that define the language of optimal paths: rotations, straight-line segments, and logarithmic spirals. These control laws, as well as the switching conditions that define how to sequence path segments, are defined in terms of the entries of homography matrices. The selection of the corresponding control law requires the homography decomposition before starting the navigation. We provide a controllability and stability analysis for our system and give experimental results.

This paper presents a switched homography-based visual control for differential drive vehicles. The goal is defined by an image taken at the desired position, which is the only previous information needed from the scene. The control takes into account the field-of-view constraints of the vision system through the specific design of the paths with optimality criteria. The optimal paths consist of straight lines and curves that saturate the sensor viewing angle. We present the controls that move the robot along these paths based on the convergence of the elements of the homography matrix. Our contribution is the design of the switched homography-based control, following optimal paths guaranteeing the visibility of the target.

In this paper, we consider the problem of planning optimal paths for a differential-drive robot with limited sensing, that must maintain visibility of a fixed landmark as it navigates in its environment. In particular, we assume that the robot's vision sensor has a limited field of view (FOV), and that the fixed landmark must remain within the FOV throughout the robot's motion. We first investigate the nature of extremal paths that satisfy the FOV constraint. These extremal paths saturate the camera pan angle. We then show that optimal paths are composed of straight-line segments and sections of these these extremal paths. We provide the complete characterization of the shortest paths for the system by partitioning the plane into a set of disjoint regions, such that the structure of the optimal path is invariant over the individual regions

This work presents the proof of controllability for a differential drive robot that maintains visibility of a landmark. The robot has limited sensing capabilities (angle of view). We also present properties of optimal paths for this system

In this paper we describe a new representation for a configuration space for formations of robots that translate in the plane. What makes this representation unique is that it is permutation-invariant, so the relabeling of robots does not affect the configuration. Earlier methods generally either pre-assign roles for each individual robot, or rely on local planning and behaviors to build emergent behaviors. Our method first plans the formation as a set, and only afterwards determines which robot takes which role. To build our representation of this formation space, we make use of a property of complex polynomials: they are unchanged by permutations of their roots. Thus we build a characteristic polynomial whose roots are the robot locations, and use its coefficients as a representation. Mappings between work spaces and formation spaces amount to building and solving polynomials. In this paper we also perform basic path planning on this new representation, and show some practical and theoretical properties. We show that the paths generated are invariant-relative to their endpoints - with respect to linear coordinate transforms, and in most cases produce reasonable, if not linear, paths from start to finish.

This work addresses the problem of computing the motions of a robot observer in order to maintain visibility of a moving target at a fixed surveillance distance. In this paper, we deal specifically with the situation in which the observer has bounded velocity. We give necessary conditions for the existence of a surveillance strategy and give an algorithm that generates surveillance strategies.

This work presents the minimal length paths, for a robot that maintains visibility of a landmark. The robot is a differential drive system and has limited sensing capabilities (range and angle of view). The optimal paths are composed of straight lines and curves that saturate the camera pan angle.