Showing papers by "Swaroop Darbha published in 2013"

Optimal minimax pursuit evasion on a Manhattan grid

Abstract: The optimal control of a pursuer searching for a slower moving evader on a Manhattan grid road network is considered. The pursuer does not have on-board capability to detect the evader and relies instead on Unattended Ground Sensors (UGSs) to locate the evader. We assume that all the intersections in the road network have been instrumented with UGSs. When an evader passes by an UGS location, it triggers the UGS and this time-stamped information is stored by the UGS. When the pursuer arrives at an UGS location, the UGS informs the pursuer if and when the evader passed by. When the evader and the pursuer arrive at an UGS location simultaneously, the UGS is triggered and this information is instantly relayed to the pursuer, thereby enabling “capture”.We derive exact values for the optimal worst case time to capture the evader on the Manhattan grid and the corresponding pursuit policy.

Computation of lower bounds for a multiple depot, multiple vehicle routing problem with motion constraints

Abstract: In this paper, the problem of planning paths for a collection of vehicles passing through a set of targets is considered. Each vehicle starts at a specified location (called a depot) and it is required that each target be on the path of at least one vehicle. Every vehicle has a motion constraint and the path of each vehicle must satisfy that constraint. In this article, we developed a method to compute lower bounds to this path planning problem by relaxing some of the constraints and posing it as a standard multiple traveling salesmen problem. For those problem instances where the distance between every pair of targets is at least 4 units, another method is developed to compute a lower bound using the convexity property of the length of such paths. The proposed bounds are numerically corroborated.

Optimal Cooperative Pursuit on a Manhattan Grid

Abstract: The optimal control of two pursuers searching for a slower moving evader on a Manhattan grid road network is considered. The pursuers do not have on-board capability to detect the evader and rely instead on Unattended Ground Sensors (UGSs) to locate the evader. We assume that all the intersections in the road network have been instrumented with UGSs. When an evader passes by an UGS location, it triggers the UGS and this time-stamped information is stored by the UGS. When a pursuer arrives at an UGS location, the UGS informs the pursuer if and when the evader passed by. When the evader and a pursuer arrive at an UGS location simultaneously, the UGS is triggered and this information is instantly relayed to the pursuer, thereby enabling “capture”. We derive exact values for the minimum time guaranteed capture of the evader on the Manhattan grid and the corresponding pursuit policy.

Vehicle formations using directed information flow graphs

Abstract: In this paper, we investigate vehicle formations using a ring graph. A ring graph is a directed graph with a unique path for communication between any two vehicles in the formation. In vehicle platoons, a ring type directed information flow graph is formed when each vehicle receives information from its predecessor and the first vehicle receives information from the last vehicle, thus forming a communication ring in its basic form. In such basic form of the ring information structure, the communication distance between the first and the last vehicle increases with platoon size, which creates implementation issues. To overcome this limitation, alternative ring graphs which keep the ring structure but allow for smaller communication distances between vehicles are studied in this paper. If one were to employ a communication protocol such as the token ring protocol, the delay in updating information and communication arise from the need for the token to travel across the information flow graph. For a given formation and a constraint on the maximum allowable communication distance between any two vehicles, an algorithm to create an alternative ring graph can be obtained by formulating this problem as an instance of the traveling salesman problem (TSP); this follows because of the similarity between a ring graph and a Hamiltonian cycle. In addition to vehicle platoons, this algorithm can also be used for two- and three-dimensional formations. An experimental setup consisting of four differential drive mobile robots is used to conduct formation experiments with the basic and alternative ring graphs; a sample of these results will be shown and discussed. We also discuss scalability issues related to ring graphs and conclude with a summary of this work.

Approximate Dynamic Programming Applied to UAV Perimeter Patrol

Abstract: One encounters the curse of dimensionality in the application of dynamic programming to determine optimal policies for large scale controlled Markov chains. In this chapter, we consider a base perimeter patrol stochastic control problem. To determine the optimal control policy, one has to solve a Markov decision problem,whose large size renders exact dynamic programming methods intractable. So, we propose a state aggregation based approximate linear programming method to construct provably good sub-optimal policies instead. The state-space is partitioned and the optimal cost-to-go or value function is approximated by a constant over each partition. By minimizing a non-negative cost function defined on the partitions, one can construct an approximate value function which also happens to be an upper bound for the optimal value function of the original Markov chain. As a general result, we show that this approximate value function is independent of the non-negative cost function (or state dependent weights; as it is referred to in the literature) and moreover, this is the least upper bound that one can obtain, given the partitions. Furthermore,we show that the restricted system of linear inequalities also embeds a family of Markov chains of lower dimension, one of which can be used to construct a tight lower bound on the optimal value function. In general, the construction of the lower bound requires the solution to a combinatorial problem. But the perimeter patrol problem exhibits a special structure that enables tractable linear programming formulations for both the upper and lower bounds. We demonstrate this and also provide numerical results that corroborate the efficacy of the proposed methodology.

A methodology to assess the safety of automatically controlled vehicles

Abstract: Automated driving is getting a step closer to reality. However, systematic methods for analyzing the safety benefits of deploying automated vehicles on roads are lacking. In this paper, we provide an outline of a methodology that may be adopted to assess the safety benefits of automatic vehicle following in an emergency braking scenario. Automated vehicles travel in a single straight lane and the maximum deceleration of every vehicle in the lane is a random variable with a known probability distribution. The lead vehicle in the lane brakes at its maximum value of deceleration. The deceleration of each following vehicle is limited by its maximum deceleration and is specified by a vehicle following law. If the vehicle following law commands a deceleration greater than or equal to the maximum deceleration, the controlled vehicle can only brake at its maximum deceleration. Clearly, the deceleration of every controlled vehicle in this case is also a random variable and we provide a methodology to compute its probability distribution. The importance of the probability distribution of deceleration of a vehicle can be readily seen from its variance; for a given initial following distance, if the initial relative velocity is small, variance in their deceleration is small and the mean is the same, then the probability of a collision is correspondingly small. Since the deceleration of every vehicle is a random variable, the following distance and relative velocity of a following vehicle with respect to its immediate predecessor in the lane are also random variables. We say that a violation occurs if the following distance of a vehicle is zero and the corresponding severity is the value of its relative velocity with respect to its predecessor. The notion of violation is a surrogate for the notion of a collision and does not depend on any model of collision or on detailed vehicle dynamical models. We then provide a methodology to compute metrics of safety in terms of the probability of a violation, expected number of violations and severity of a violation.

Combinatorial Motion Planning Algorithms for a Heterogeneous Collection of Unmanned Vehicles

Abstract: : The project dealt with two classes of core decision-making algorithms related to operator-UV collaboration; the first class involves the routing of UVs through the set of targets nominated by the operator and the second class of problems involves decision-making algorithms for UVs to accommodate uncertainty. We have developed approximation, lower bounding and exact algorithms to address the two classes of problems. We have also implemented these algorithms in simulations to corroborate the performance of these algorithms. In the ensuing discussion, we will summarize our work for the project, and our main results.