Sivakumar Rathinam

Kaarthik Sundar, Sivakumar Rathinam

The Multiple Depot Ring-Star Problem (MDRSP) is an important combinatorial optimization problem that arises in the context of optical fiber network design, and in applications pertaining to collecting data using stationary sensing devices and autonomous vehicles. Given the locations of a set of customers and a set of depots, the goal is to (i) find a set of simple cycles such that each cycle (ring) passes through a subset of customers and exactly one depot, (ii) assign each non-visited customer to a visited customer or a depot, and (iii) minimize the sum of the routing costs, i.e., the cost of the cycles and the assignment costs. We present a mixed integer linear programming formulation for the MDRSP and propose valid inequalities to strengthen the linear programming relaxation. Furthermore, we present a polyhedral analysis and derive facet-inducing results for the MDRSP. All these results are then used to develop a branch-and-cut algorithm to obtain optimal solutions to the MDRSP. The performance of the branch-and-cut algorithm is evaluated through extensive computational experiments on several classes of test instances.

Shizhe Zhao, Anushtup Nandy, Howie Choset et al.

This paper considers a generalization of the Path Finding (PF) problem with refuelling constraints referred to as the Gas Station Problem (GSP). Similar to PF, given a graph where vertices are gas stations with known fuel prices, and edge costs are the gas consumption between the two vertices, GSP seeks a minimum-cost path from the start to the goal vertex for a robot with a limited gas tank and a limited number of refuelling stops. While GSP is polynomial-time solvable, it remains a challenge to quickly compute an optimal solution in practice since it requires simultaneously determine the path, where to make the stops, and the amount to refuel at each stop. This paper develops a heuristic search algorithm called Refuel A$^*$ (RF-A$^*$) that iteratively constructs partial solution paths from the start to the goal guided by a heuristic while leveraging dominance rules for pruning during planning. RF-A$^*$ is guaranteed to find an optimal solution and often runs 2 to 8 times faster than the existing approaches in large city maps with several hundreds of gas stations.

Anoop Bhat, Geordan Gutow, Zhongqiang Ren et al.

The Moving Target Vehicle Routing Problem (MT-VRP) seeks trajectories for several agents that intercept a set of moving targets, subject to speed, time window, and capacity constraints. We introduce an exact algorithm, Branch-and-Price with Relaxed Continuity (BPRC), for the MT-VRP. The main challenge in a branch-and-price approach for the MT-VRP is the pricing subproblem, which is complicated by moving targets and time-dependent travel costs between targets. Our key contribution is a new labeling algorithm that solves this subproblem by means of a novel dominance criterion tailored for problems with moving targets. Numerical results on instances with up to 25 targets show that our algorithm finds optimal solutions more than an order of magnitude faster than a baseline based on previous work, showing particular strength in scenarios with limited agent capacities.

Anoop Bhat, Geordan Gutow, Surya Singh et al.

The Moving Target Vehicle Routing Problem with Obstacles (MT-VRP-O) seeks trajectories for several agents that collectively intercept a set of moving targets. Each target has one or more time windows where it must be visited, and the agents must avoid static obstacles and satisfy speed and capacity constraints. We introduce Lazy Branch-and-Price with Relaxed Continuity (Lazy BPRC), which finds optimal solutions for the MT-VRP-O. Lazy BPRC applies the branch-and-price framework for VRPs, which alternates between a restricted master problem (RMP) and a pricing problem. The RMP aims to select a sequence of target-time window pairings (called a tour) for each agent to follow, from a limited subset of tours. The pricing problem adds tours to the limited subset. Conventionally, solving the RMP requires computing the cost for an agent to follow each tour in the limited subset. Computing these costs in the MT-VRP-O is computationally intensive, since it requires collision-free motion planning between moving targets. Lazy BPRC defers cost computations by solving the RMP using lower bounds on the costs of each tour, computed via motion planning with relaxed continuity constraints. We lazily evaluate the true costs of tours as-needed. We compute a tour's cost by searching for a shortest path on a Graph of Convex Sets (GCS), and we accelerate this search using our continuity relaxation method. We demonstrate that Lazy BPRC runs up to an order of magnitude faster than two ablations.

Anoop Bhat, Geordan Gutow, Bhaskar Vundurthy et al.

The Moving Target Traveling Salesman Problem (MT-TSP) seeks a trajectory that intercepts several moving targets, within a particular time window for each target. When generic nonlinear target trajectories or kinematic constraints on the agent are present, no prior algorithm guarantees convergence to an optimal MT-TSP solution. Therefore, we introduce the Iterated Random Generalized (IRG) TSP framework. The idea behind IRG is to alternate between randomly sampling a set of agent configuration-time points, corresponding to interceptions of targets, and finding a sequence of interception points by solving a generalized TSP (GTSP). This alternation asymptotically converges to the optimum. We introduce two parallel algorithms within the IRG framework. The first algorithm, IRG-PGLNS, solves GTSPs using PGLNS, our parallelized extension of state-of-the-art solver GLNS. The second algorithm, Parallel Communicating GTSPs (PCG), solves GTSPs for several sets of points simultaneously. We present numerical results for three MT-TSP variants: one where intercepting a target only requires coming within a particular distance, another where the agent is a variable-speed Dubins car, and a third where the agent is a robot arm. We show that IRG-PGLNS and PCG converge faster than a baseline based on prior work. We further validate our framework with physical robot experiments.

Valmiki Kothare, Zhongqiang Ren, Sivakumar Rathinam et al.

The Multi-Objective Shortest Path Problem (MO-SPP), typically posed on a graph, determines a set of paths from a start vertex to a destination vertex while optimizing multiple objectives. In general, there does not exist a single solution path that can simultaneously optimize all the objectives and the problem thus seeks to find a set of so-called Pareto-optimal solutions. To address this problem, several Multi-Objective A* (MOA*) algorithms were recently developed to quickly compute solutions with quality guarantees. However, these MOA* algorithms often suffer from high memory usage, especially when the branching factor (i.e. the number of neighbors of any vertex) of the graph is large. This work thus aims at reducing the high memory consumption of MOA* with little increase in the runtime. By generalizing and unifying several single- and multi-objective search algorithms, we develop the Runtime and Memory Efficient MOA* (RME-MOA*) approach, which can balance between runtime and memory efficiency by tuning two user-defined hyper-parameters.

Kaarthik Sundar, Sivakumar Rathinam

We present a novel algorithm that fuses the existing convex-programming based approach with heuristic information to find optimality guarantees and near-optimal paths for the Shortest Path Problem in the Graph of Convex Sets (SPP-GCS). Our method, inspired by $A^*$, initiates a best-first-like procedure from a designated subset of vertices and iteratively expands it until further growth is neither possible nor beneficial. Traditionally, obtaining solutions with bounds for an optimization problem involves solving a relaxation, modifying the relaxed solution to a feasible one, and then comparing the two solutions to establish bounds. However, for SPP-GCS, we demonstrate that reversing this process can be more advantageous, especially with Euclidean travel costs. In other words, we initially employ $A^*$ to find a feasible solution for SPP-GCS, then solve a convex relaxation restricted to the vertices explored by $A^*$ to obtain a relaxed solution, and finally, compare the solutions to derive bounds. We present numerical results to highlight the advantages of our algorithm over the existing approach in terms of the sizes of the convex programs solved and computation time.

Nikhil Chandak, Kenny Chour, Sivakumar Rathinam et al.

We interleave sampling based motion planning methods with pruning ideas from minimum spanning tree algorithms to develop a new approach for solving a Multi-Goal Path Finding (MGPF) problem in high dimensional spaces. The approach alternates between sampling points from selected regions in the search space and de-emphasizing regions that may not lead to good solutions for MGPF. Our approach provides an asymptotic, 2-approximation guarantee for MGPF. We also present extensive numerical results to illustrate the advantages of our proposed approach over uniform sampling in terms of the quality of the solutions found and computation speed.

Lakshay Virmani, Zhongqiang Ren, Sivakumar Rathinam et al.

Multi-Agent Path Finding (MAPF) finds conflict-free paths for multiple agents from their respective start to goal locations. MAPF is challenging as the joint configuration space grows exponentially with respect to the number of agents. Among MAPF planners, search-based methods, such as CBS and M*, effectively bypass the curse of dimensionality by employing a dynamically-coupled strategy: agents are planned in a fully decoupled manner at first, where potential conflicts between agents are ignored; and then agents either follow their individual plans or are coupled together for planning to resolve the conflicts between them. In general, the number of conflicts to be resolved decides the run time of these planners and most of the existing work focuses on how to efficiently resolve these conflicts. In this work, we take a different view and aim to reduce the number of conflicts (and thus improve the overall search efficiency) by improving each agent's individual plan. By leveraging a Visual Transformer, we develop a learning-based single-agent planner, which plans for a single agent while paying attention to both the structure of the map and other agents with whom conflicts may happen. We then develop a novel multi-agent planner called LM* by integrating this learning-based single-agent planner with M*. Our results show that for both "seen" and "unseen" maps, in comparison with M*, LM* has fewer conflicts to be resolved and thus, runs faster and enjoys higher success rates. We empirically show that MAPF solutions computed by LM* are near-optimal. Our code is available at https://github.com/lakshayvirmani/learning-assisted-mstar .

Allen George Philip, Zhongqiang Ren, Sivakumar Rathinam et al.

This paper introduces a new formulation that finds the optimum for the Moving-Target Traveling Salesman Problem (MT-TSP), which seeks to find a shortest path for an agent, that starts at a depot, visits a set of moving targets exactly once within their assigned time-windows, and returns to the depot. The formulation relies on the key idea that when the targets move along lines, their trajectories become convex sets within the space-time coordinate system. The problem then reduces to finding the shortest path within a graph of convex sets, subject to some speed constraints. We compare our formulation with the current state-of-the-art Mixed Integer Conic Program (MICP) solver for the MT-TSP. The experimental results show that our formulation outperforms the MICP for instances with up to 20 targets, with up to two orders of magnitude reduction in runtime, and up to a 60\% tighter optimality gap. We also show that the solution cost from the convex relaxation of our formulation provides significantly tighter lower bounds for the MT-TSP than the ones from the MICP.

Zhongqiang Ren, Anushtup Nandy, Sivakumar Rathinam et al.

Multi-Agent Combinatorial Path Finding (MCPF) seeks collision-free paths for multiple agents from their initial to goal locations, while visiting a set of intermediate target locations in the middle of the paths. MCPF is challenging as it involves both planning collision-free paths for multiple agents and target sequencing, i.e., solving traveling salesman problems to assign targets to and find the visiting order for the agents. Recent work develops methods to address MCPF while minimizing the sum of individual arrival times at goals. Such a problem formulation may result in paths with different arrival times and lead to a long makespan, the maximum arrival time, among the agents. This paper proposes a min-max variant of MCPF, denoted as MCPF-max, that minimizes the makespan of the agents. While the existing methods (such as MS*) for MCPF can be adapted to solve MCPF-max, we further develop two new techniques based on MS* to defer the expensive target sequencing during planning to expedite the overall computation. We analyze the properties of the resulting algorithm Deferred MS* (DMS*), and test DMS* with up to 20 agents and 80 targets. We demonstrate the use of DMS* on differential-drive robots.

Zhongqiang Ren, Richard Zhan, Sivakumar Rathinam et al.

This work addresses a Multi-Objective Shortest Path Problem (MO-SPP) on a graph where the goal is to find a set of Pareto-optimal solutions from a start node to a destination in the graph. A family of approaches based on MOA* have been developed to solve MO-SPP in the literature. Typically, these approaches maintain a "frontier" set at each node during the search process to keep track of the non-dominated, partial paths to reach that node. This search process becomes computationally expensive when the number of objectives increases as the number of Pareto-optimal solutions becomes large. In this work, we introduce a new method to efficiently maintain these frontiers for multiple objectives by incrementally constructing balanced binary search trees within the MOA* search framework. We first show that our approach correctly finds the Pareto-optimal front, and then provide extensive simulation results for problems with three, four and five objectives to show that our method runs faster than existing techniques by up to an order of magnitude.

Zhongqiang Ren, Sivakumar Rathinam, Howie Choset

This work considers a Motion Planning Problem with Dynamic Obstacles (MPDO) in 2D that requires finding a minimum-arrival-time collision-free trajectory for a point robot between its start and goal locations amid dynamic obstacles moving along known trajectories. Existing methods, such as continuous Dijkstra paradigm, can find an optimal solution by restricting the shape of the obstacles or the motion of the robot, while this work makes no such assumptions. Other methods, such as search-based planners and sampling-based approaches can compute a feasible solution to this problem but do not provide approximation bounds. Since finding the optimum is challenging for MPDO, this paper develops a framework that can provide tight lower bounds to the optimum. These bounds act as proxies for the optimum which can then be used to bound the deviation of a feasible solution from the optimum. To accomplish this, we develop a framework that consists of (i) a bi-level discretization approach that converts the MPDO to a relaxed path planning problem, and (ii) an algorithm that can solve the relaxed problem to obtain lower bounds. We also present numerical results to corroborate the performance of the proposed framework. These results show that the bounds obtained by our approach for some instances are up to twice tighter than a baseline approach showcasing potential advantages of the proposed approach.

Stephen Ninan, Sivakumar Rathinam

Accurate pose estimation is a fundamental ability that all mobile robots must posses in order to traverse robustly in a given environment. Much like a human, this ability is dependent on the robot's understanding of a given scene. For Autonomous Vehicles (AV's), detailed 3D maps created beforehand are widely used to augment the perceptive abilities and estimate pose based on current sensor measurements. This approach however is less suited for rural communities that are sparsely connected and cover large areas. To deal with the challenge of localizing a vehicle in a rural setting, this paper presents a data-set of rural road scenes, along with an approach for fast segmentation of roads using LIDAR point clouds. The segmented point cloud in concert with road network information from Open Street Maps (OSM) is used for pose estimation. We propose two measurement models which are compared with state of the art methods for localization on OSM for tracking as well as global localization. The results show that the proposed algorithm is able to estimate pose within a 2 sq. km area with mean accuracy of 6.5 meters.

Zhongqiang Ren, Sivakumar Rathinam, Maxim Likhachev et al.

This paper addresses a generalization of the well known multi-agent path finding (MAPF) problem that optimizes multiple conflicting objectives simultaneously such as travel time and path risk. This generalization, referred to as multi-objective MAPF (MOMAPF), arises in several applications ranging from hazardous material transportation to construction site planning. In this paper, we present a new multi-objective conflict-based search (MO-CBS) approach that relies on a novel multi-objective safe interval path planning (MO-SIPP) algorithm for its low-level search. We first develop the MO-SIPP algorithm, show its properties and then embed it in MO-CBS. We present extensive numerical results to show that (1) there is an order of magnitude improvement in the average low level search time, and (2) a significant improvement in the success rates of finding the Pareto-optimal front can be obtained using the proposed approach in comparison with the previous MO-CBS.

Zhongqiang Ren, Sivakumar Rathinam, Maxim Likhachev et al.

Incremental graph search algorithms such as D* Lite reuse previous, and perhaps partial, searches to expedite subsequent path planning tasks. In this article, we are interested in developing incremental graph search algorithms for path finding problems to simultaneously optimize multiple objectives such as travel risk, arrival time, etc. This is challenging because in a multi-objective setting, the number of "Pareto-optimal" solutions can grow exponentially with respect to the size of the graph. This article presents a new multi-objective incremental search algorithm called Multi-Objective Path-Based D* Lite (MOPBD*) which leverages a path-based expansion strategy to prune dominated solutions. Additionally, we introduce a sub-optimal variant of MOPBD* to improve search efficiency while approximating the Pareto-optimal front. We numerically evaluate the performance of MOPBD* and its variants in various maps with two and three objectives. Results show that our approach is more efficient than search from scratch, and runs up to an order of magnitude faster than the existing incremental method for multi-objective path planning.

Sai Krishna Kanth Hari, Sivakumar Rathinam, Swaroop Darbha et al.

Persistent monitoring missions require an up-to-date knowledge of the changing state of the underlying environment. UAVs can be gainfully employed to continually visit a set of targets representing tasks (and locations) in the environment and collect data therein for long time periods. The enduring nature of these missions requires the UAV to be regularly recharged at a service station. In this paper, we consider the case in which the service station is not co-located with any of the targets. An efficient monitoring requires the revisit time, defined as the maximum of the time elapsed between successive revisits to targets, to be minimized. Here, we consider the problem of determining UAV routes that lead to the minimum revisit time. The problem is NP-hard, and its computational difficulty increases with the fuel capacity of the UAV. We develop an algorithm to construct near-optimal solutions to the problem quickly, when the fuel capacity exceeds a threshold. We also develop lower bounds to the optimal revisit time and use these bounds to demonstrate (through numerical simulations) that the constructed solutions are, on an average, at most 0.01% away from the optimum.

Zhongqiang Ren, Sivakumar Rathinam, Howie Choset

In multi-agent applications such as surveillance and logistics, fleets of mobile agents are often expected to coordinate and safely visit a large number of goal locations as efficiently as possible. The multi-agent planning problem in these applications involves allocating and sequencing goals for each agent while simultaneously producing conflict-free paths for the agents. In this article, we introduce a new algorithm called MS* which computes an optimal solution for this multi-agent problem by fusing and advancing state of the art solvers for multi-agent path finding (MAPF) and multiple travelling salesman problem (mTSP). MS* leverages our prior subdimensional expansion approach for MAPF and embeds the mTSP solvers to optimally allocate and sequence goals for agents. Numerical results show that our new algorithm can solve the multi-agent problem with 20 agents and 50 goals in a minute of CPU time on a standard laptop.

Kenny Chour, Sivakumar Rathinam, Ramamoorthi Ravi

We combine ideas from uni-directional and bi-directional heuristic search, and approximation algorithms for the Traveling Salesman Problem, to develop a novel framework for a Multi-Goal Path Finding (MGPF) problem that provides a 2-approximation guarantee. MGPF aims to find a least-cost path from an origin to a destination such that each node in a given set of goals is visited at least once along the path. We present numerical results to illustrate the advantages of our framework over conventional alternates in terms of the number of expanded nodes and run time.

Zhongqiang Ren, Sivakumar Rathinam, Howie Choset

Multi-agent path finding (MAPF) determines an ensemble of collision-free paths for multiple agents between their respective start and goal locations. Among the available MAPF planners for workspace modeled as a graph, A*-based approaches have been widely investigated due to their guarantees on completeness and solution optimality, and have demonstrated their efficiency in many scenarios. However, almost all of these A*-based methods assume that each agent executes an action concurrently in that all agents start and stop together. This article presents a natural generalization of MAPF with asynchronous actions (MAPF-AA) where agents do not necessarily start and stop concurrently. The main contribution of the work is a proposed approach called Loosely Synchronized Search (LSS) that extends A*-based MAPF planners to handle asynchronous actions. We show LSS is complete and finds an optimal solution if one exists. We also combine LSS with other existing MAPF methods that aims to trade-off optimality for computational efficiency. Numerical results are presented to corroborate the performance of LSS and the applicability of the proposed method is verified in the Robotarium, a remotely accessible swarm robotics research platform.

Zhongqiang Ren, Sivakumar Rathinam, Howie Choset

Conventional multi-agent path planners typically determine a path that optimizes a single objective, such as path length. Many applications, however, may require multiple objectives, say time-to-completion and fuel use, to be simultaneously optimized in the planning process. Often, these criteria may not be readily compared and sometimes lie in competition with each other. Simply applying standard multi-objective search algorithms to multi-agent path finding may prove to be inefficient because the size of the space of possible solutions, i.e., the Pareto-optimal set, can grow exponentially with the number of agents (the dimension of the search space). This paper presents an approach that bypasses this so-called curse of dimensionality by leveraging our prior multi-agent work with a framework called subdimensional expansion. One example of subdimensional expansion, when applied to A*, is called M* and M* was limited to a single objective function. We combine principles of dominance and subdimensional expansion to create a new algorithm named multi-objective M* (MOM*), which dynamically couples agents for planning only when those agents have to "interact" with each other. MOM* computes the complete Pareto-optimal set for multiple agents efficiently and naturally trades off sub-optimal approximations of the Pareto-optimal set and computational efficiency. Our approach is able to find the complete Pareto-optimal set for problem instances with hundreds of solutions which the standard multi-objective A* algorithms could not find within a bounded time.

Zhongqiang Ren, Sivakumar Rathinam, Howie Choset

Conventional multi-agent path planners typically compute an ensemble of paths while optimizing a single objective, such as path length. However, many applications may require multiple objectives, say fuel consumption and completion time, to be simultaneously optimized during planning and these criteria may not be readily compared and sometimes lie in competition with each other. The goal of the problem is thus to find a Pareto-optimal set of solutions instead of a single optimal solution. Naively applying existing multi-objective search algorithms, such as multi-objective A* (MOA*), to multi-agent path finding may prove to be inefficient as the dimensionality of the search space grows exponentially with the number of agents. This article presents an approach named Multi-Objective Conflict-Based Search (MO-CBS) that attempts to address this so-called curse of dimensionality by leveraging prior Conflict-Based Search (CBS), a well-known algorithm for single-objective multi-agent path finding, and principles of dominance from multi-objective optimization literature. We also develop several variants of MO-CBS to improve its performance. We prove that MO-CBS and its variants can compute the entire Pareto-optimal set. Numerical results show that MO-CBS outperforms MOM*, a recently developed state-of-the-art multi-objective multi-agent planner.

Sai Krishna Hari, Abhishek Nayak, Sivakumar Rathinam

This article presents an approximation algorithm for a task allocation, sequencing and scheduling problem involving a team of human operators and robots. Specifically, we present an algorithm with an approximation ratio as a function of the number of human operators ($m$) and the number of robots ($k$) in the team. The approximation ratios are $\frac{7}{2} -\frac{5}{2k}$, $\frac{5}{2} -\frac{1}{k}$ and $\frac{7}{2} -\frac{1}{k}$ when $m=1$, $m\geq k\geq 2$ and $k>m\geq 2$ respectively. We also present computational results to corroborate the performance of the proposed approximation algorithm.

Sivakumar Rathinam, Satyanarayana Gupta Manyam, Yuntao Zhang

This article considers two variants of a shortest path problem for a car-like robot visiting a set of waypoints. The sequence of waypoints to be visited is specified in the first variant while the robot is allowed to visit the waypoints in any sequence in the second variant. Field of view constraints are also placed when the robot arrives at a waypoint, i.e., the orientation of the robot at any waypoint is restricted to belong to a given interval of angles at the waypoint. The shortest path problem is first solved for two waypoints with the field of view constraints using Pontryagin's minimum principle. Using the results for the two point problem, tight lower and upper bounds on the length of the shortest path are developed for visiting n points by relaxing the requirement that the arrival angle must be equal to the departure angle of the robot at each waypoint. Theoretical bounds are also provided on the length of the feasible solutions obtained by the proposed algorithm. Simulation results verify the performance of the bounds for instances with 20 waypoints.

Sai Krishna Kanth Hari, Sivakumar Rathinam, Swaroop Darbha et al.

We consider the problem of planning a closed walk $\mathcal W$ for a UAV to persistently monitor a finite number of stationary targets with equal priorities and dynamically changing properties. A UAV must physically visit the targets in order to monitor them and collect information therein. The frequency of monitoring any given target is specified by a target revisit time, $i.e.$, the maximum allowable time between any two successive visits to the target. The problem considered in this paper is the following: Given $n$ targets and $k \geq n$ allowed visits to them, find an optimal closed walk $\mathcal W^*(k)$ so that every target is visited at least once and the maximum revisit time over all the targets, $\mathcal R(\mathcal W(k))$, is minimized. We prove the following: If $k \geq n^2-n$, $\mathcal R(\mathcal W^*(k))$ (or simply, $\mathcal R^*(k)$) takes only two values: $\mathcal R^*(n)$ when $k$ is an integral multiple of $n$, and $\mathcal R^*(n+1)$ otherwise. This result suggests significant computational savings - one only needs to determine $\mathcal W^*(n)$ and $\mathcal W^*(n+1)$ to construct an optimal solution $\mathcal W^*(k)$. We provide MILP formulations for computing $\mathcal W^*(n)$ and $\mathcal W^*(n+1)$. Furthermore, for {\it any} given $k$, we prove that $\mathcal R^*(k) \geq \mathcal R^*(k+n)$.

Parikshit Maini, Kaarthik Sundar, Sivakumar Rathinam et al.

Low cost Unmanned Aerial Vehicles (UAVs) need multiple refuels to accomplish large area coverage. The number of refueling stations and their placement plays a vital role in determining coverage efficiency. In this paper, we propose the use of a ground-based refueling vehicle (RV) to increase the operational range of a UAV in both spatial and temporal domains. Determining optimal routes for the UAV and RV, and selecting optimized locations for refueling to aid in minimizing coverage time is a challenging problem due to different vehicle speeds, coupling between refueling location placement, and the coverage area at each location. We develop a two-stage strategy for coupled route planning for UAV and RV to perform a coverage mission. The first stage computes a minimal set of refueling sites that permit a feasible UAV route. In the second stage, multiple Mixed-Integer Linear Programming (MILP) formulations are developed to plan optimal routes for the UAV and the refueling vehicle taking into account the feasible set of refueling sites generated in stage one. The performance of different formulations is compared empirically. In addition, computationally efficient heuristics are developed to solve the routing problem. Extensive simulations are conducted to corroborate the effectiveness of proposed approaches.

Abhishek Nayak, Kenny Chour, Tyler Marr et al.

Infrastructure Enabled Autonomy (IEA) is a new paradigm that employs a distributed intelligence architecture for connected autonomous vehicles by offloading core functionalities to the infrastructure. In this paper, we develop a simulation framework that can be used to study the concept. A key challenge for such a simulation is the rapid increase in the scale of the computations with the size of the infrastructure to be considered. Our simulation framework is designed to be distributed and scales proportionally with the infrastructure. By integrally using both the hardware controllers and communication devices as part of the simulation framework, we achieve an optimal balance between modeling of the dynamics and sensors, and reusing real hardware for simulation of proprietary or complex communication methods. Multiple cameras on the infrastructure are simulated. The simulation of the camera image processing is done in distributed hardware and the resultant position information is transmitted wirelessly to the computer simulating the autonomous vehicle. We demonstrate closed loop control of a single vehicle following given waypoints using information from multiple cameras located on Road-Side-Units.

Swaminathan Gopalswamy, Sivakumar Rathinam

Multiple studies have illustrated the potential for dramatic societal, environmental and economic benefits from significant penetration of autonomous driving. However, all the current approaches to autonomous driving require the automotive manufacturers to shoulder the primary responsibility and liability associated with replacing human perception and decision making with automation, potentially slowing the penetration of autonomous vehicles, and consequently slowing the realization of the societal benefits of autonomous vehicles. We propose here a new approach to autonomous driving that will re-balance the responsibility and liabilities associated with autonomous driving between traditional automotive manufacturers, infrastructure players, and third-party players. Our proposed distributed intelligence architecture leverages the significant advancements in connectivity and edge computing in the recent decades to partition the driving functions between the vehicle, edge computers on the road side, and specialized third-party computers that reside in the vehicle. Infrastructure becomes a critical enabler for autonomy. With this Infrastructure Enabled Autonomy (IEA) concept, the traditional automotive manufacturers will only need to shoulder responsibility and liability comparable to what they already do today, and the infrastructure and third-party players will share the added responsibility and liabilities associated with autonomous functionalities. We propose a Bayesian Network Model based framework for assessing the risk benefits of such a distributed intelligence architecture. An additional benefit of the proposed architecture is that it enables "autonomy as a service" while still allowing for private ownership of automobiles.

Kaarthik Sundar, Sohum Misra, Sivakumar Rathinam et al.

Most of the routing algorithms for unmanned vehicles, that arise in data gathering and monitoring applications in the literature, rely on the Global Positioning System (GPS) information for localization. However, disruption of GPS signals either intentionally or unintentionally could potentially render these algorithms not applicable. In this article, we present a novel method to address this difficulty by combining methods from cooperative localization and routing. In particular, the article formulates a fundamental combinatorial optimization problem to plan routes for an unmanned vehicle in a GPS-restricted environment while enabling localization for the vehicle. We also develop algorithms to compute optimal paths for the vehicle using the proposed formulation. Extensive simulation results are also presented to corroborate the effectiveness and performance of the proposed formulation and algorithms.

Kaarthik Sundar, Saravanan Venkatachalam, Sivakumar Rathinam

This paper addresses a fuel-constrained, autonomous vehicle path planning problem in the presence of multiple refueling stations. We are given a set of targets, a set of refueling stations, and a depot where $m$ vehicles are stationed. The vehicles are allowed to refuel at any refueling station, and the objective of the problem is to determine a route for each vehicle starting and terminating at the depot, such that each target is visited by at least one vehicle, the vehicles never run out of fuel while traversing their routes, and the total travel cost of all the routes is a minimum. We present four new mixed-integer linear programming formulations for the problem. These formulations are compared both analytically and empirically, and a branch-and-cut algorithm is developed to compute an optimal solution. Extensive computational results on a large class of test instances that corroborate the effectiveness of the algorithm are also presented.

Sivakumar Rathinam, Pramod Khargonekar

The problem of finding the shortest path for a vehicle visiting a given sequence of target points subject to the motion constraints of the vehicle is an important problem that arises in several monitoring and surveillance applications involving unmanned aerial vehicles. There is currently no algorithm that can find an optimal solution to this problem. Therefore, heuristics that can find approximate solutions with guarantees on the quality of the solutions are useful. The best approximation algorithm currently available for the case when the distance between any two adjacent target points in the sequence is at least equal to twice the minimum radius of the vehicle has a guarantee of 3.04. This article provides a new approximation algorithm which improves this guarantee to 2.04. The developed algorithm is also implemented for hundreds of typical instances involving at most 30 points to corroborate the performance of the proposed approach.

Satyanarayana Manyam, Sivakumar Rathinam, David Casbeer et al.

The Dubins interval problem aims to find the shortest path of bounded curvature between two targets such that the departure angle from the first target and the arrival angle at the second target are constrained to two respective intervals. We propose a new and a simple algorithm to this problem based on the minimum principle of Pontryagin.

Satyanarayana Manyam, Sivakumar Rathinam

The Dubins Traveling Salesman Problem (DTSP) has generated significant interest over the last decade due to its occurrence in several civil and military surveillance applications. Currently, there is no algorithm that can find an optimal solution to the problem. In addition, relaxing the motion constraints and solving the resulting Euclidean TSP (ETSP) provides the only lower bound available for the problem. However, in many problem instances, the lower bound computed by solving the ETSP is far below the cost of the feasible solutions obtained by some well-known algorithms for the DTSP. This article addresses this fundamental issue and presents the first systematic procedure for developing tight lower bounds for the DTSP.