arXiv subjects

Stephen L. Smith

Publications and source records attributed to Stephen L. Smith.

80 records · Page 5Linked to original sources

arXiv2011

MDP Optimal Control under Temporal Logic Constraints

In this paper, we develop a method to automatically generate a control policy for a dynamical system modeled as a Markov Decision Process (MDP). The control specification is given as a Linear Temporal Logic (LTL) formula over a set of propositions defined on the states of the MDP. We synthesize a control policy such that the MDP satisfies the given specification almost surely, if such a policy exists. In addition, we designate an "optimizing proposition" to be repeatedly satisfied, and we formulate a novel optimization criterion in terms of minimizing the expected cost in between satisfactions of this proposition. We propose a sufficient condition for a policy to be optimal, and develop a dynamic programming algorithm that synthesizes a policy that is optimal under some conditions, and sub-optimal otherwise. This problem is motivated by robotic applications requiring persistent tasks, such as environmental monitoring or data gathering, to be performed.

cs.RO↗

arXiv2011

On Vehicle Placement to Intercept Moving Targets

We address optimal placement of vehicles with simple motion to intercept a mobile target that arrives stochastically on a line segment. The optimality of vehicle placement is measured through a cost function associated with intercepting the target. With a single vehicle, we assume that the target moves (i) with fixed speed and in a fixed direction perpendicular to the line segment, or (ii) to maximize the distance from the line segment, or (iii) to maximize intercept time. In each case, we show that the cost function is strictly convex, its gradient is smooth, and the optimal vehicle placement is obtained by a standard gradient-based optimization technique. With multiple vehicles, we assume that the target moves with fixed speed and in a fixed direction perpendicular to the line segment. We present a discrete time partitioning and gradient-based algorithm, and characterize conditions under which the algorithm asymptotically leads the vehicles to a set of critical configurations of the cost function.

math.DS↗

arXiv2011

Persistent Robotic Tasks: Monitoring and Sweeping in Changing Environments

We present controllers that enable mobile robots to persistently monitor or sweep a changing environment. The changing environment is modeled as a field which grows in locations that are not within range of a robot, and decreases in 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 can be parametrized by a finite set of basis functions. For a single robot, we develop a linear program that is guaranteed to compute a speed controller in this space to keep the field bounded, if such a controller exists. Another linear program is then derived whose solution is the speed controller that minimizes the maximum field value over the environment. We extend our linear program formulation to develop a multi-robot controller that keeps the field bounded. The multi-robot controller has the unique feature that it does not require communication among the robots. Simulation studies demonstrate the robustness of the controllers to modeling errors, and to stochasticity in the environment.

cs.RO↗

arXiv2010

Optimal Path Planning under Temporal Logic Constraints

In this paper we present a method for automatically generating optimal robot trajectories satisfying high level mission specifications. The motion of the robot in the environment is modeled as a general transition system, enhanced with weighted transitions. The mission is specified by a general linear temporal logic formula. In addition, we require that an optimizing proposition 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 trajectory which 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 entire formula specifies a complex (and infinite horizon) 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 which computes a path corresponding to the optimal robot trajectory. We also present an implementation for a robot performing a data gathering mission in a road network.

cs.RO↗

arXiv2009

A Dynamic Boundary Guarding Problem with Translating Targets

We introduce a problem in which a service vehicle seeks to guard a deadline (boundary) from dynamically arriving mobile targets. The environment is a rectangle and the deadline is one of its edges. Targets arrive continuously over time on the edge opposite the deadline, and move towards the deadline at a fixed speed. The goal for the vehicle is to maximize the fraction of targets that are captured before reaching the deadline. We consider two cases; when the service vehicle is faster than the targets, and; when the service vehicle is slower than the targets. In the first case we develop a novel vehicle policy based on computing longest paths in a directed acyclic graph. We give a lower bound on the capture fraction of the policy and show that the policy is optimal when the distance between the target arrival edge and deadline becomes very large. We present numerical results which suggest near optimal performance away from this limiting regime. In the second case, when the targets are slower than the vehicle, we propose a policy based on servicing fractions of the translational minimum Hamiltonian path. In the limit of low target speed and high arrival rate, the capture fraction of this policy is within a small constant factor of the optimal.

cs.RO↗

arXiv2009

Dynamic Multi-Vehicle Routing with Multiple Classes of Demands

In this paper we study a dynamic vehicle routing problem in which there are multiple vehicles and multiple classes of demands. Demands of each class arrive in the environment randomly over time and require a random amount of on-site service that is characteristic of the class. To service a demand, one of the vehicles must travel to the demand location and remain there for the required on-site service time. The quality of service provided to each class is given by the expected delay between the arrival of a demand in the class, and that demand's service completion. The goal is to design a routing policy for the service vehicles which minimizes a convex combination of the delays for each class. First, we provide a lower bound on the achievable values of the convex combination of delays. Then, we propose a novel routing policy and analyze its performance under heavy load conditions (i.e., when the fraction of time the service vehicles spend performing on-site service approaches one). The policy performs within a constant factor of the lower bound (and thus the optimal), where the constant depends only on the number of classes, and is independent of the number of vehicles, the arrival rates of demands, the on-site service times, and the convex combination coefficients.

cs.RO↗

arXiv2007

Target assignment for robotic networks: asymptotic performance under limited communication

We are given an equal number of mobile robotic agents, and distinct target locations. Each agent has simple integrator dynamics, a limited communication range, and knowledge of the position of every target. We address the problem of designing a distributed algorithm that allows the group of agents to divide the targets among themselves and, simultaneously, leads each agent to reach its unique target. We do not require connectivity of the communication graph at any time. We introduce a novel assignment-based algorithm with the following features: initial assignments and robot motions follow a greedy rule, and distributed refinements of the assignment exploit an implicit circular ordering of the targets. We prove correctness of the algorithm, and give worst-case asymptotic bounds on the time to complete the assignment as the environment grows with the number of agents. We show that among a certain class of distributed algorithms, our algorithm is asymptotically optimal. The analysis utilizes results on the Euclidean traveling salesperson problem.

cs.RO↗

arXiv2006

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.

cs.RO↗