arXiv subjects

Stephen L. Smith

Publications and source records attributed to Stephen L. Smith.

At least 73 records · Page 4Linked to original sources

arXiv2019

On Re-Balancing Self-Interested Agents in Ride-Sourcing Transportation Networks

This paper focuses on the problem of controlling self-interested drivers in ride-sourcing applications. Each driver has the objective of maximizing its profit, while the ride-sourcing company focuses on customer experience by seeking to minimizing the expected wait time for pick-up. These objectives are not usually aligned, and the company has no direct control on the waiting locations of the drivers. In this paper, we provide two indirect control methods to optimize the set of waiting locations of the drivers, thereby minimizing the expected wait time of the customers: 1) sharing the location of all drivers with a subset of drivers, and 2) paying the drivers to relocate. We show that finding the optimal control for each method is NP-hard and we provide algorithms to find near-optimal control in each case. We evaluate the performance of the proposed control methods on real-world data and show that we can achieve between 20% to 80% improvement in the expected response.

cs.MA↗

arXiv2019

Robotic Coverage for Continuous Mapping Ahead of a Moving Vehicle

In this paper we investigate the problem of using a UAV to provide current map information of the environment in front of a moving ground vehicle. We propose a simple coverage plan called a conformal lawn mower plan that enables a UAV to scan the route ahead of the ground vehicle. The plan requires only limited knowledge of the ground vehicle's future path. For a class of curvature-constrained ground vehicle paths, we show that the proposed plan requires a UAV velocity that is no more than twice the velocity required to cover the optimal plan. We also establish necessary and sufficient UAV velocities, relative to the ground vehicle velocity, required to successfully cover any path in the curvature restricted set. In simulation, we validate the proposed plan, showing that the required velocity to provide coverage is strongly related to the curvature of the ground vehicle's path. Our results also illustrate the relationship between mapping requirements and the relative velocities of the UAV and ground vehicle.

cs.RO↗

arXiv2019

Learning a Lattice Planner Control Set for Autonomous Vehicles

This paper introduces a method to compute a sparse lattice planner control set that is suited to a particular task by learning from a representative dataset of vehicle paths. To do this, we use a scoring measure similar to the Fréchet distance and propose an algorithm for evaluating a given control set according to the scoring measure. Control actions are then selected from a dense control set according to an objective function that rewards improvements in matching the dataset while also encouraging sparsity. This method is evaluated across several experiments involving real and synthetic datasets, and it is shown to generate smaller control sets when compared to the previous state-of-the-art lattice control set computation technique, with these smaller control sets maintaining a high degree of manoeuvrability in the required task. This results in a planning time speedup of up to 4.31x when using the learned control set over the state-of-the-art computed control set. In addition, we show the learned control sets are better able to capture the driving style of the dataset in terms of path curvature.

cs.RO↗

arXiv2019

Computing a Minimal Set of t-Spanning Motion Primitives for Lattice Planners

In this paper we consider the problem of computing an optimal set of motion primitives for a lattice planner. The objective we consider is to compute a minimal set of motion primitives that t-span a configuration space lattice. A set of motion primitives t-span a lattice if, given a real number t greater or equal to one, any configuration in the lattice can be reached via a sequence of motion primitives whose cost is no more than t times the cost of the optimal path to that configuration. Determining the smallest set of t-spanning motion primitives allows for quick traversal of a state lattice in the context of robotic motion planning, while maintaining a t-factor adherence to the theoretically optimal path. While several heuristics exist to determine a t-spanning set of motion primitives, these are presented without guarantees on the size of the set relative to optimal. This paper provides a proof that the minimal t-spanning control set problem for a lattice defined over an arbitrary robot configuration space is NP-complete, and presents a compact mixed integer linear programming formulation to compute an optimal t-spanner. We show that solutions obtained by the mixed integer linear program have significantly fewer motion primitives than state of the art heuristic algorithms, and out perform a set of standard primitives used in robotic path planning.

cs.RO↗

arXiv2019

Multi-Robot Routing for Persistent Monitoring with Latency Constraints

In this paper we study a multi-robot path planning problem for persistent monitoring of an environment. We represent the areas to be monitored as the vertices of a weighted graph. For each vertex, there is a constraint on the maximum time spent by the robots between visits to that vertex, called the latency, and the objective is to find the minimum number of robots that can satisfy these latency constraints. The decision version of this problem is known to be PSPACE-complete. We present a $O(\log ρ)$ approximation algorithm for the problem where $ρ$ is the ratio of the maximum and the minimum latency constraints. We also present an orienteering based heuristic to solve the problem and show through simulations that in most of the cases the heuristic algorithm gives better solutions than the approximation algorithm. We evaluate our algorithms on large problem instances in a patrolling scenario and in a persistent scene reconstruction application. We also compare the algorithms with an existing solver on benchmark instances.

cs.RO↗

arXiv2019

Bayesian Active Learning for Collaborative Task Specification Using Equivalence Regions

Specifying complex task behaviours while ensuring good robot performance may be difficult for untrained users. We study a framework for users to specify rules for acceptable behaviour in a shared environment such as industrial facilities. As non-expert users might have little intuition about how their specification impacts the robot's performance, we design a learning system that interacts with the user to find an optimal solution. Using active preference learning, we iteratively show alternative paths that the robot could take on an interface. From the user feedback ranking the alternatives, we learn about the weights that users place on each part of their specification. We extend the user model from our previous work to a discrete Bayesian learning model and introduce a greedy algorithm for proposing alternative that operates on the notion of equivalence regions of user weights. We prove that with this algorithm the revision active learning process converges on the user-optimal path. In simulations on realistic industrial environments, we demonstrate the convergence and robustness of our approach.

cs.RO↗

arXiv2017

Distributed Submodular Maximization with Limited Information

We consider a class of distributed submodular maximization problems in which each agent must choose a single strategy from its strategy set. The global objective is to maximize a submodular function of the strategies chosen by each agent. When choosing a strategy, each agent has access to only a limited number of other agents' choices. For each of its strategies, an agent can evaluate its marginal contribution to the global objective given its information. The main objective is to investigate how this limitation of information about the strategies chosen by other agents affects the performance when agents make choices according to a local greedy algorithm. In particular, we provide lower bounds on the performance of greedy algorithms for submodular maximization, which depend on the clique number of a graph that captures the information structure. We also characterize graph-theoretic upper bounds in terms of the chromatic number of the graph. Finally, we demonstrate how certain graph properties limit the performance of the greedy algorithm. Simulations on several common models for random networks demonstrate our results.

cs.DS↗

arXiv2017

Clustering in Discrete Path Planning for Approximating Minimum Length Paths

In this paper we consider discrete robot path planning problems on metric graphs. We propose a clustering method, Gamma-Clustering for the planning graph that significantly reduces the number of feasible solutions, yet retains a solution within a constant factor of the optimal. By increasing the input parameter Gamma, the constant factor can be decreased, but with less reduction in the search space. We provide a simple polynomial- time algorithm for finding optimal Gamma-Clusters, and show that for a given Gamma, this optimal is unique. We demonstrate the effectiveness of the clustering method on traveling salesman instances, showing that for many instances we obtain significant reductions in computation time with little to no reduction in solution quality.

cs.RO↗

arXiv2016

On Efficient Computation of Shortest Dubins Paths Through Three Consecutive Points

In this paper, we address the problem of computing optimal paths through three consecutive points for the curvature-constrained forward moving Dubins vehicle. Given initial and final configurations of the Dubins vehicle, and a midpoint with an unconstrained heading, the objective is to compute the midpoint heading that minimizes the total Dubins path length. We provide a novel geometrical analysis of the optimal path, and establish new properties of the optimal Dubins' path through three points. We then show how our method can be used to quickly refine Dubins TSP tours produced using state-of-the-art techniques. We also provide extensive simulation results showing the improvement of the proposed approach in both runtime and solution quality over the conventional method of uniform discretization of the heading at the mid-point, followed by solving the minimum Dubins path for each discrete heading.

eess.SY↗

arXiv2014

Robot Monitoring for the Detection and Confirmation of Stochastic Events

In this paper we consider a robot patrolling problem in which events arrive randomly over time at the vertices of a graph. When an event arrives it remains active for a random amount of time. If that time active exceeds a certain threshold, then we say that the event is a true event; otherwise it is a false event. The robot(s) can traverse the graph to detect newly arrived events, and can revisit these events in order to classify them as true or false. The goal is to plan robot paths that maximize the number of events that are correctly classified, with the constraint that there are no false positives. We show that the offline version of this problem is NP-hard. We then consider a simple patrolling policy based on the traveling salesman tour, and characterize the probability of correctly classifying an event. We investigate the problem when multiple robots follow the same path, and we derive the optimal (and not necessarily uniform) spacing between robots on the path.

cs.RO↗

arXiv2013

Rebalancing the Rebalancers: Optimally Routing Vehicles and Drivers in Mobility-on-Demand Systems

In this paper we study rebalancing strategies for a mobility-on-demand urban transportation system blending customer-driven vehicles with a taxi service. In our system, a customer arrives at one of many designated stations and is transported to any other designated station, either by driving themselves, or by being driven by an employed driver. The system allows for one-way trips, so that customers do not have to return to their origin. When some origins and destinations are more popular than others, vehicles will become unbalanced, accumulating at some stations and becoming depleted at others. This problem is addressed by employing rebalancing drivers to drive vehicles from the popular destinations to the unpopular destinations. However, with this approach the rebalancing drivers themselves become unbalanced, and we need to "rebalance the rebalancers" by letting them travel back to the popular destinations with a customer. Accordingly, in this paper we study how to optimally route the rebalancing vehicles and drivers so that stability (in terms of boundedness of the number of waiting customers) is ensured while minimizing the number of rebalancing vehicles traveling in the network and the number of rebalancing drivers needed; surprisingly, these two objectives are aligned, and one can find the optimal rebalancing strategy by solving two decoupled linear programs. Leveraging our analysis, we determine the minimum number of drivers and minimum number of vehicles needed to ensure stability in the system. Interestingly, our simulations suggest that, in Euclidean network topologies, one would need between 1/3 and 1/4 as many drivers as vehicles.

math.OC↗

arXiv2013

Distributed Dominating Sets on Grids

This paper presents a distributed algorithm for finding near optimal dominating sets on grids. The basis for this algorithm is an existing centralized algorithm that constructs dominating sets on grids. The size of the dominating set provided by this centralized algorithm is upper-bounded by $\lceil\frac{(m+2)(n+2)}{5}\rceil$ for $m\times n$ grids and its difference from the optimal domination number of the grid is upper-bounded by five. Both the centralized and distributed algorithms are generalized for the $k$-distance dominating set problem, where all grid vertices are within distance $k$ of the vertices in the dominating set.

cs.DS↗

arXiv2012

Optimal Multi-Robot Path Planning with LTL Constraints: Guaranteeing Correctness Through Synchronization

In this paper, we consider the automated planning of optimal paths for a robotic team satisfying a high level mission specification. Each robot in the team is modeled as a weighted transition system where the weights have associated deviation values that capture the non-determinism in the traveling times of the robot during its deployment. The mission is given as a Linear Temporal Logic (LTL) formula over a set of propositions satisfied at the regions of the environment. Additionally, we have an optimizing proposition capturing some particular task that must be repeatedly completed by the team. The goal is to minimize the maximum time between successive satisfying instances of the optimizing proposition while guaranteeing that the mission is satisfied even under non-deterministic traveling times. Our method relies on the communication capabilities of the robots to guarantee correctness and maintain performance during deployment. After computing a set of optimal satisfying paths for the members of the team, we also compute a set of synchronization sequences for each robot to ensure that the LTL formula is never violated during deployment. We implement and experimentally evaluate our method considering a persistent monitoring task in a road network environment.

cs.RO↗

arXiv2012

Persistent Monitoring in Discrete Environments: Minimizing the Maximum Weighted Latency Between Observations

In this paper, we consider the problem of planning a path for a robot to monitor a known set of features of interest in an environment. We represent the environment as a graph with vertex weights and edge lengths. The vertices represent regions of interest, edge lengths give travel times between regions, and the vertex weights give the importance of each region. As the robot repeatedly performs a closed walk on the graph, we define the weighted latency of a vertex to be the maximum time between visits to that vertex, weighted by the importance (vertex weight) of that vertex. Our goal is to find a closed walk that minimizes the maximum weighted latency of any vertex. We show that there does not exist a polynomial time algorithm for the problem. We then provide two approximation algorithms; an $O(\log n)$-approximation algorithm and an $O(\log ρ_G)$-approximation algorithm, where $ρ_G$ is the ratio between the maximum and minimum vertex weights. We provide simulation results which demonstrate that our algorithms can be applied to problems consisting of thousands of vertices, and a case study for patrolling a city for crime.

cs.DS↗

arXiv2012

The Maximum Traveling Salesman Problem with Submodular Rewards

In this paper, we look at the problem of finding the tour of maximum reward on an undirected graph where the reward is a submodular function, that has a curvature of $κ$, of the edges in the tour. This problem is known to be NP-hard. We analyze two simple algorithms for finding an approximate solution. Both algorithms require $O(|V|^3)$ oracle calls to the submodular function. The approximation factors are shown to be $\frac{1}{2+κ}$ and $\max\set{\frac{2}{3(2+κ)},2/3(1-κ)}$, respectively; so the second method has better bounds for low values of $κ$. We also look at how these algorithms perform for a directed graph and investigate a method to consider edge costs in addition to rewards. The problem has direct applications in monitoring an environment using autonomous mobile sensors where the sensing reward depends on the path taken. We provide simulation results to empirically evaluate the performance of the algorithms.

math.OC↗

arXiv2012

Robust Multi-Robot Optimal Path Planning with Temporal Logic Constraints

In this paper we present a method for automatically planning robust optimal paths for a group of robots that satisfy a common high level mission specification. Each robot's motion in the environment 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 by the regions of the environment. In addition, an optimizing proposition must repeatedly be satisfied. The goal is to minimize the maximum time between satisfying instances of the optimizing proposition while ensuring that the LTL formula is satisfied even with uncertainty in the robots' traveling times. We characterize a class of LTL formulas that are robust to robot timing errors, for which we generate optimal paths if no timing errors are present, and we present bounds on the deviation from the optimal values in the presence of errors. We implement and experimentally evaluate our method considering a persistent monitoring task in a road network environment.

cs.RO↗

arXiv2011

Optimal Multi-Robot Path Planning with Temporal Logic Constraints

In this paper we present a method for automatically planning optimal paths for a group of robots that satisfy a common high level mission specification. Each robot's motion in the environment is modeled as a weighted transition system. The mission is given as a Linear Temporal Logic formula. In addition, an optimizing proposition must repeatedly be satisfied. The goal is to minimize the maximum time between satisfying instances of the optimizing proposition. Our method is guaranteed to compute an optimal set of robot paths. We utilize a timed automaton representation in order to capture the relative position of the robots in the environment. We then obtain a bisimulation of this timed automaton as a finite transition system that captures the joint behavior of the robots and apply our earlier algorithm for the single robot case to optimize the group motion. We present a simulation of a persistent monitoring task in a road network environment.

cs.RO↗

arXiv2011

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.

math.OC↗