Stephen L. Smith

Dynamic Vehicle Routing for Robotic Systems

Recent years have witnessed great advancements in the science and technology of autonomy, robotics, and networking. This paper surveys recent concepts and algorithms for dynamic vehicle routing (DVR), that is, for the automatic planning of optimal multivehicle routes to perform tasks that are generated over time by an exogenous process. We consider a rich variety of scenarios relevant for robotic applications. We begin by reviewing the basic DVR problem: demands for service arrive at random locations at random times and a vehicle travels to provide on-site service while minimizing the expected wait time of the demands. Next, we treat different multivehicle scenarios based on different models for demands (e.g., demands with different priority levels and impatient demands), vehicles (e.g., motion constraints, communication, and sensing capabilities), and tasks. The performance criterion used in these scenarios is either the expected wait time of the demands or the fraction of demands serviced successfully. In each specific DVR scenario, we adopt a rigorous technical approach that relies upon methods from queueing theory, combinatorial optimization, and stochastic geometry. First, we establish fundamental limits on the achievable performance, including limits on stability and quality of service. Second, we design algorithms, and provide provable guarantees on their performance with respect to the fundamental limits.

Persistent Robotic Tasks: Monitoring and Sweeping in Changing Environments

In this paper, we present controllers that enable mobile robots to persistently monitor or sweep a changing environment. The environment is modeled as a field that is defined over a finite set of locations. The field grows linearly at locations that are not within the range of a robot and decreases linearly at locations that are within range of a robot. We assume that the robots travel on given closed paths. The speed of each robot along its path is controlled to prevent the field from growing unbounded at any location. We consider the space of speed controllers that are parametrized by a finite set of basis functions. For a single robot, we develop a linear program that computes a speed controller in this space to keep the field bounded, if such a controller exists. Another linear program is derived to compute the speed controller that minimizes the maximum field value over the environment. We extend our linear program formulation to develop a multirobot controller that keeps the field bounded. We characterize, both theoretically and in simulation, the robustness of the controllers to modeling errors and to stochasticity in the environment.

Brief A hierarchical cyclic pursuit scheme for vehicle networks

The agreement problem is studied whereby a group of mobile agents achieves convergence to a common point. A hierarchical cyclic pursuit scheme is introduced, and it is shown that this scheme yields a very significant increase in the rate of convergence to a common point when compared to traditional cyclic pursuit. A second scheme is introduced in which there are more communication links between vehicles. It is shown that this scheme produces a rate of convergence greater than the traditional scheme but significantly less than the hierarchical scheme.

Optimal path planning for surveillance with temporal-logic constraints*

In this paper we present a method for automatically generating optimal robot paths satisfying high-level mission specifications. The motion of the robot in the environment is modeled as a weighted transition system. The mission is specified by an arbitrary linear temporal-logic (LTL) formula over propositions satisfied at the regions of a partitioned environment. The mission specification contains an optimizing proposition, which must be repeatedly satisfied. The cost function that we seek to minimize is the maximum time between satisfying instances of the optimizing proposition. For every environment model, and for every formula, our method computes a robot path that minimizes the cost function. The problem is motivated by applications in robotic monitoring and data-gathering. In this setting, the optimizing proposition is satisfied at all locations where data can be uploaded, and the LTL formula specifies a complex data-collection mission. Our method utilizes Büchi automata to produce an automaton (which can be thought of as a graph) whose runs satisfy the temporal-logic specification. We then present a graph algorithm that computes a run corresponding to the optimal robot path. We present an implementation for a robot performing data collection in a road-network platform.

Robotic load balancing for mobility-on-demand systems

In this paper we develop methods for maximizing the throughput of a mobility-on-demand urban transportation system. We consider a finite group of shared vehicles, located at a set of stations. Users arrive at the stations, pickup vehicles, and drive (or are driven) to their destination station where they drop-off the vehicle. When some origins and destinations are more popular than others, the system will inevitably become out of balance: vehicles will build up at some stations, and become depleted at others. We propose a robotic solution to this rebalancing problem that involves empty robotic vehicles autonomously driving between stations. Specifically, we utilize a fluid model for the customers and vehicles in the system. Then, we develop a rebalancing policy that lets every station reach an equilibrium in which there are excess vehicles and no waiting customers and that minimizes the number of robotic vehicles performing rebalancing trips. We show that the optimal rebalancing policy can be found as the solution to a linear program. We use this solution to develop a real-time rebalancing policy which can operate in highly variable environments. Finally, we verify policy performance in a simulated mobility-on-demand environment and in hardware experiments.

Optimality and Robustness in Multi-Robot Path Planning with Temporal Logic Constraints

In this paper we present a method for automatic planning of optimal paths for a group of robots that satisfy a common high-level mission specification. The motion of each robot is modeled as a weighted transition system, and the mission is given as a linear temporal logic (LTL) formula over a set of propositions satisfied at the regions of the environment. In addition, an optimizing proposition must repeatedly be satisfied. The goal is to minimize a cost function that captures the maximum time between successive satisfactions of the optimizing proposition while guaranteeing that the formula is satisfied. When the robots can follow a given trajectory exactly, our method computes a set of optimal satisfying paths that minimize the cost function and satisfy the LTL formula. However, if the traveling times of the robots are uncertain, then the robots may not be able to follow a given trajectory exactly, possibly violating the LTL formula during deployment. We handle such cases by leveraging the communication capabilities of the robots to guarantee correctness during deployment and provide bounds on the deviation from the optimal values. We implement and experimentally evaluate our method for various persistent surveillance tasks in a road network environment.

Curve Shortening and the Rendezvous Problem for Mobile Autonomous Robots

If a smooth, closed, and embedded curve is deformed along its normal vector field at a rate proportional to its curvature, it shrinks to a circular point. This curve evolution is called Euclidean curve shortening and the result is known as the Gage-Hamilton-Grayson theorem. Motivated by the rendezvous problem for mobile autonomous robots, we address the problem of creating a polygon shortening flow. A linear scheme is proposed that exhibits several analogues to Euclidean curve shortening: The polygon shrinks to an elliptical point, convex polygons remain convex, and the perimeter of the polygon is monotonically decreasing.

Monotonic Target Assignment for Robotic Networks

Consider an equal number of mobile robotic agents and distinct target locations dispersed in an environment. Each agent has a limited communication range and either: 1) knowledge of every target position or 2) a finite-range sensor capable of acquiring target positions and no a priori knowledge of target positions. In this paper we study the following target assignment problem: design a distributed algorithm with which the agents divide the targets among themselves and, simultaneously, move to their unique target. We evaluate an algorithms performance by characterizing its worst-case asymptotic time to complete the target assignment; that is the task completion time as the number of agents (and targets) increases, and the size of the environment scales to accommodate them. We introduce the intuitive class of monotonic algorithms, and give a lower bound on its worst-case completion time. We design and analyze two algorithms within this class: the ETSP Assgmt algorithm which works under assumption 1), and the Grid Assgmt algorithm which works under either assumption 1) or 2). In ldquosparse environments,rdquo where communication is infrequent, the ETSP Assgmt algorithm is within a constant factor of the optimal monotonic algorithm for worst-case initial conditions. In ldquodense environments,rdquo where communication is more prevalent, the Grid Assgmt algorithm is within a constant factor of the optimal monotonic algorithm for worst-case initial conditions. In addition we characterize the performance of the Grid Assgmt algorithm for uniformly distributed targets and agents, and for the case when there are more agents than targets.

LTL Control in Uncertain Environments with Probabilistic Satisfaction Guarantees

We present a method to generate a robot control strategy that maximizes the probability to accomplish a task. The task is given as a Linear Temporal Logic (LTL) formula over a set of properties that can be satisfied at the regions of a partitioned environment. We assume that the probabilities with which the properties are satisfied at the regions are known, and the robot can determine the truth value of a proposition only at the current region. Motivated by several results on partitioned-based abstractions, we assume that the motion is performed on a graph. To account for noisy sensors and actuators, we assume that a control action enables several transitions with known probabilities. We show that this problem can be reduced to the problem of generating a control policy for a Markov Decision Process (MDP) such that the probability of satisfying an LTL formula over its states is maximized. We provide a complete solution for the latter problem that builds on existing results from probabilistic model checking. We include an illustrative case study.

Multi-robot monitoring in dynamic environments with guaranteed currency of observations

In this paper we consider the problem of monitoring a known set of stationary features (or locations of interest) in an environment. To observe a feature, a robot must visit its location. Each feature changes over time, and we assume that the currency, or accuracy of an observation decays linearly with time. Thus, robots must repeatedly visit the features to update their observations. Each feature has a known rate of change, and so the frequency of visits to a feature should be proportional to its rate. The goal is to route the robots so as to minimize the maximum change of a feature between observations. We focus on the asymptotic regime of a large number of features distributed according to a probability density function. In this regime we determine a lower bound on the maximum change of a feature between visits, and develop a robot control policy that, with probability one, performs within a factor of two of the optimal. We also provide a single robot lower bound which holds outside of the asymptotic regime, and present a heuristic algorithm motivated by our asymptotic analysis.