arXiv subjects

Swaroop Darbha

Publications and source records attributed to Swaroop Darbha.

At least 37 records · Page 2Linked to original sources

arXiv2024

Optimal Geodesic Curvature Constrained Dubins' Path on Sphere with Free Terminal Orientation

In this paper, motion planning for a vehicle moving on a unit sphere with unit speed is considered, wherein the desired terminal location is fixed, but the terminal orientation is free. The motion of the vehicle is modeled to be constrained by a maximum geodesic curvature $U_{max},$ which controls the rate of change of heading of the vehicle such that the maximum heading change occurs when the vehicle travels on a tight circular arc of radius $r = \frac{1}{\sqrt{1 + U_{max}^2}}$. Using Pontryagin's Minimum Principle, the main result of this paper shows that for $r \leq \frac{1}{2}$, the optimal path connecting a given initial configuration and a final location on the sphere belongs to a set of at most seven paths. The candidate paths are of type $CG, CC,$ and degenerate paths of the same, where $C \in \{L, R\}$ denotes a tight left or right turn, respectively, and $G$ denotes a great circular arc.

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arXiv2024

The Persistent Robot Charging Problem for Long-Duration Autonomy

This paper introduces a novel formulation aimed at determining the optimal schedule for recharging a fleet of $n$ heterogeneous robots, with the primary objective of minimizing resource utilization. This study provides a foundational framework applicable to Multi-Robot Mission Planning, particularly in scenarios demanding Long-Duration Autonomy (LDA) or other contexts that necessitate periodic recharging of multiple robots. A novel Integer Linear Programming (ILP) model is proposed to calculate the optimal initial conditions (partial charge) for individual robots, leading to the minimal utilization of charging stations. This formulation was further generalized to maximize the servicing time for robots given adequate charging stations. The efficacy of the proposed formulation is evaluated through a comparative analysis, measuring its performance against the thrift price scheduling algorithm documented in the existing literature. The findings not only validate the effectiveness of the proposed approach but also underscore its potential as a valuable tool in optimizing resource allocation for a range of robotic and engineering applications.

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arXiv2024

Equivalence of Dubins Path on Sphere with Geographic Coordinates and Moving Frames

In this article, two methods of addressing path planning for a Dubins vehicle moving on a sphere are considered, wherein either spherical coordinates or a moving frame are considered to describe the vehicle's motion. The primary contribution of this article is to show the equivalence of these two approaches, which in turn shows that the results known for the moving frame-based description transfer to the model utilizing spherical coordinates.

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arXiv2024

Assessing the safety benefits of CACC+ based coordination of connected and autonomous vehicle platoons in emergency braking scenarios

Ensuring safety is the most important factor in connected and autonomous vehicles, especially in emergency braking situations. As such, assessing the safety benefits of one information topology over other is a necessary step towards evaluating and ensuring safety. In this paper, we compare the safety benefits of a cooperative adaptive cruise control which utilizes information from one predecessor vehicle (CACC) with the one that utilizes information from multiple predecessors (CACC+) for the maintenance of spacing under an emergency braking scenario. A constant time headway policy is employed for maintenance of spacing (that includes a desired standstill spacing distance and a velocity dependent spacing distance) between the vehicles in the platoon. The considered emergency braking scenario consists of braking of the leader vehicle of the platoon at its maximum deceleration and that of the following vehicles to maintain the spacing as per CACC or CACC+. By focusing on the standstill spacing distance and utilizing Monte Carlo simulations, we assess the safety benefits of CACC+ over CACC by utilizing the following safety metrics: (1) probability of collision, (2) expected number of collisions, and (3) severity of collision (defined as the relative velocity of the two vehicles at impact). We present and provide discussion of these results.

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arXiv2024

Selection of Time Headway in Connected and Autonomous Vehicle Platoons under Noisy V2V Communication

In this paper, we investigate the selection of time headway to ensure robust string stability in connected and autonomous vehicle platoons in the presence of signal noise in Vehicle-to-Vehicle (V2V) communication. In particular, we consider the effect of noise in communicated vehicle acceleration from the predecessor vehicle to the follower vehicle on the selection of the time headway in predecessor-follower type vehicle platooning with a Constant Time Headway Policy (CTHP). Employing a CTHP based control law for each vehicle that utilizes on-board sensors for measurement of position and velocity of the predecessor vehicle and wireless communication network for obtaining the acceleration of the predecessor vehicle, we investigate how time headway is affected by communicated signal noise. We derive constraints on the CTHP controller gains for predecessor acceleration, velocity error and spacing error and a lower bound on the time headway which will ensure robust string stability of the platoon against signal noise. We provide comparative numerical simulations on an example to illustrate the main result.

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arXiv2024

Optimal Robust Network Design: Formulations and Algorithms for Maximizing Algebraic Connectivity

This paper focuses on designing edge-weighted networks, whose robustness is characterized by maximizing algebraic connectivity, or the second smallest eigenvalue of the Laplacian matrix. This problem is motivated by cooperative vehicle localization, where accurately estimating relative position measurements and establishing communication links are essential. We also examine an associated problem where every robot is limited by payload, budget, and communication to pick no more than a specified number of relative position measurements. The basic underlying formulation for these problems is nonlinear and is known to be NP-hard. Our approach formulates this problem as a Mixed Integer Semi-Definite Program (MISDP), later reformulated into a Mixed Integer Linear Program (MILP) for obtaining optimal solutions using cutting plane algorithms. We introduce a novel upper-bounding algorithm based on principal minor characterization of positive semi-definite matrices and discuss a degree-constrained lower bounding formulation inspired by robust network structures. In addition, we propose a maximum cost heuristic with low computational complexity to identify high-quality feasible solutions for instances involving up to one hundred nodes. We show extensive computational results corroborating our proposed methods.

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arXiv2023

Heuristic for Min-Max Heterogeneous Multi-Vehicle Multi-Depot Traveling Salesman Problem

In this article, a heuristic is proposed for a min-max heterogeneous multi-vehicle multi-depot traveling salesman problem (TSP), wherein heterogeneous vehicles start from given depot positions and need to cover a given set of targets. The vehicles should cover given targets such that the maximum tour time is minimized. In the considered problem, vehicles considered can be functionally heterogeneous, wherein specific targets must be covered by a particular vehicle, structurally heterogeneous, wherein the vehicles can travel at different speeds, or both. The proposed heuristic generalizes the MD heuristic for the min-max homogeneous multi-vehicle multi-depot TSP and has three stages: an initialization stage to generate a feasible solution, a local search stage in which the vehicle with the maximum tour time is improved, and a perturbation stage to break from a local minimum. The proposed heuristic is benchmarked with the optimal solution obtained by solving a mixed integer linear program using branch and cut for instances considering three vehicles covering thirty targets. Variations in the percentage of vehicle-target assignments and the number of vehicles starting at the same depot are studied to show the heuristic's effectiveness in producing high-quality solutions. It was observed that the heuristic generated feasible solutions within 4% of the optimum on average for the considered instances.

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arXiv2023

Assisted Path Planning for a UGV-UAV Team Through a Stochastic Network

In this article, we consider a multi-agent path planning problem in a stochastic environment. The environment, which can be an urban road network, is represented by a graph where the travel time for selected road segments (impeded edges) is a random variable because of traffic congestion. An unmanned ground vehicle (UGV) wishes to travel from a starting location to a destination while minimizing the arrival time at the destination. UGV can traverse through an impeded edge but the true travel time is only realized at the end of that edge. This implies that the UGV can potentially get stuck in an impeded edge with high travel time. A support vehicle, such as an unmanned aerial vehicle (UAV) is simultaneously deployed from its starting position to assist the UGV by inspecting and realizing the true cost of impeded edges. With the updated information from UAV, UGV can efficiently reroute its path to the destination. The UGV does not wait at any time until it reaches the destination. The UAV is permitted to terminate its path at any vertex. The goal is then to develop an online algorithm to determine efficient paths for the UGV and the UAV based on the current information so that the UGV reaches the destination in minimum time. We refer to this problem as Stochastic Assisted Path Planning (SAPP). We present Dynamic $k$-Shortest Path Planning (D*KSPP) algorithm for the UGV planning and Rural Postman Problem (RPP) formulation for the UAV planning. Due to the scalability challenges of RPP, we also present a heuristic based Priority Assignment Algorithm (PAA) for the UAV planning. Computational results are presented to corroborate the effectiveness of the proposed algorithm to solve SAPP.

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arXiv2023

UAV Routing for Enhancing the Performance of a Classifier-in-the-loop

Some human-machine systems are designed so that machines (robots) gather and deliver data to remotely located operators (humans) through an interface in order to aid them in classification. The performance of a human as a (binary) classifier-in-the-loop is characterized by probabilities of correctly classifying objects of type $T$ and $F$. These two probabilities depend on the dwell time, $d$, spent collecting information at a point of interest (POI or interchangeably, target). The information gain associated with collecting information at a target is then a function of dwell time $d$ and discounted by the revisit time, $R$, i.e., the duration between consecutive revisits to the same target. The objective of the problem of routing for classification is to optimally route the vehicles and determine the optimal dwell time at each target so as to maximize the total discounted information gain while visiting every target at least once. In this paper, we make a simplifying assumption that the information gain is discounted exponentially by the revisit time; this assumption enables one to decouple the problem of routing with the problem of determining optimal dwell time at each target for a single vehicle problem. For the multi-vehicle problem, we provide a fast heuristic to obtain the allocation of targets to each vehicle and the corresponding dwell time.

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arXiv2022

The Weighted Markov-Dubins Problem

In this article, a variation of the classical Markov-Dubins problem is considered, which deals with curvature-constrained least-cost paths in a plane with prescribed initial and final configurations, different bounds for the sinistral and dextral curvatures, and penalties $μ_L$ and $μ_R$ for the sinistral and dextral turns, respectively. The addressed problem generalizes the classical Markov-Dubins problem and the asymmetric sinistral/dextral Markov-Dubins problem. The proposed formulation can be used to model an Unmanned Aerial Vehicle (UAV) with a penalty associated with a turn due to a loss in altitude while turning or a UAV with different costs for the sinistral and dextral turns due to hardware failures or environmental conditions. Using optimal control theory, the main result of this paper shows that the optimal path belongs to a set of at most $21$ candidate paths, each comprising of at most five segments. Unlike in the classical Markov-Dubins problem, the $CCC$ path, which is a candidate path for the classical Markov-Dubins problem, is not optimal for the weighted Markov-Dubins problem. Moreover, the obtained list of candidate paths for the weighted Markov-Dubins problem reduces to the standard $CSC$ and $CCC$ paths and the corresponding degenerate paths when $μ_L$ and $μ_R$ approach zero.

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arXiv2022

Cooperative Coverage with a Leader and a Wingmate in Communication-Constrained Environments

We consider a mission framework in which two unmanned vehicles (UVs), a leader and a wingmate, are required to provide cooperative coverage of an environment while being within a short communication range. This framework finds applications in underwater and/or military domains, where certain constraints are imposed on communication by either the application or the environment. An important objective of missions within this framework is to minimize the total travel and communication costs of the leader-wingmate duo. In this paper, we propose and formulate the problem of finding routes for the UVs that minimize the sum of their travel and communication costs as a network optimization problem of the form of a binary program (BP). The BP is computationally expensive, with the time required to compute optimal solutions increasing rapidly with the problem size. To address this challenge, here, we propose two algorithms, an approximation algorithm and a heuristic algorithm, to solve large-scale instances of the problem swiftly. We demonstrate the effectiveness and the scalability of these algorithms through an analysis of extensive numerical simulations performed over 500 instances, with the number of targets in the instances ranging from 6 to 100.

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arXiv2022

Path Planning and Energy Management of Hybrid Air Vehicles for Urban Air Mobility

A novel coupled path planning and energy management problem for a hybrid unmanned air vehicle is considered, where the hybrid vehicle is powered by a dual gas/electric system. Such an aerial robot is envisioned for use in an urban setting where noise restrictions are in place in certain zones necessitating battery only operation. We consider the discrete version of this problem, where a graph is constructed by sampling the boundaries of the restricted zones, and develop a path planning algorithm. The planner simultaneously solves the path planing along with the energy mode switching control, under battery constraints and noise restrictions. This is a coupled problem involving discrete decision making to find the path to travel, and determining the state of charge of the battery along the path, which is a continuous variable. A sampling based algorithm to find near optimal solution to this problem is presented. To quantify the efficacy of the solution, an algorithm that computes tight lower bounds is also presented. The algorithms presented are verified using numerical simulations, and the average gap between the feasible solutions (upper bounds) and the lower bounds are, empirically, shown to be within 15% of each other.

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arXiv2022

Assisted Shortest Path Planning for a Convoy through a Repairable Network

In this article, we consider a multi-agent path planning problem in a partially impeded environment. The impeded environment is represented by a graph with select road segments (edges) in disrepair impeding vehicular movement in the road network. A convoy wishes to travel from a starting location to a destination while minimizing some accumulated cost. The convoy may traverse an impeded edge for an additional cost (associated with repairing the edge) than if it were unimpeded. A second vehicle, referred to as a service vehicle, is simultaneously deployed with the convoy. The service vehicle assists the convoy by repairing an edge, reducing the cost for the convoy to traverse that edge. The convoy is permitted to wait at any vertex to allow the service vehicle to complete repairing an edge. The service vehicle is permitted to terminate its path at any vertex. The goal is then to find a pair of paths so the convoy reaches its destination while minimizing the total time (cost) the two vehicles are active, including any time the convoy waits. We refer to this problem as the Assisted Shortest Path Problem (ASPP). We present a generalized permanent labeling algorithm to find an optimal solution for the ASPP. We also introduce additional modifications to the labeling algorithm to significantly improve the computation time and refer to the modified labeling algorithm as $GPLA^*$. Computational results are presented to illustrate the effectiveness of $GPLA^*$ in solving the ASPP. We then give concluding remarks and briefly discuss potential variants of the ASPP for future work.

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arXiv2022

Optimal Geodesic Curvature Constrained Dubins' Paths on a Sphere

In this article, we consider the motion planning of a rigid object on the unit sphere with a unit speed. The motion of the object is constrained by the maximum absolute value, $U_{max}$ of geodesic curvature of its path; this constrains the object to change the heading at the fastest rate only when traveling on a tight smaller circular arc of radius $r <1$, where $r$ depends on the bound, $U_{max}$. We show in this article that if $0 \frac{1}{2}$, while paths of the above type may cease to exist depending on the boundary conditions and the value of $r$, optimal paths may be concatenations of more than three circular arcs.

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arXiv2021

String Stability of Connected Vehicle Platoons under Lossy V2V Communication

Recent advances in vehicle connectivity have allowed formation of autonomous vehicle platoons for improved mobility and traffic throughput. In order to avoid a pile-up in such platoons, it is important to ensure platoon (string) stability, which is the focus of this work. As per conventional definition of string stability, the power (2-norm) of the spacing error signals should not amplify downstream in a platoon. But in practice, it is the infinity-norm of the spacing error signal that dictates whether a collision occurs. We address this discrepancy in the first part of our work, where we reconsider string stability from a safety perspective and develop an upper limit on the maximum spacing error in a homogeneous platoon as a function of the acceleration maneuver of the lead vehicle. In the second part of this paper, we extend our previous results by providing the minimum achievable time headway for platoons with two-predecessor lookup schemes experiencing burst-noise packet losses. Finally, we utilize throttle and brake maps to develop a longitudinal vehicle model and validate it against a Lincoln MKZ which is then used for numerical corroboration of the proposed time headway selection algorithms.

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arXiv2021

Bounds on Optimal Revisit Times in Persistent Monitoring Missions with a Distinct \& Remote Service Station

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.

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arXiv2020

Mobility and Safety Benefits of Connectivity in CACC Vehicle Strings

In this paper, we re-examine the notion of string stability as it relates to safety by providing an upper bound on the maximum spacing error of any vehicle in a homogeneous platoon in terms of the input of the leading vehicle. We reinforce our previous work on lossy CACC platoons by accommodating for burst-noise behavior in the V2V link. Further, through Monte Carlo type simulations, we demonstrate that connectivity can enhance traffic mobility and safety in a CACC string even when the deceleration capabilities of the vehicles in the platoon are heterogeneous.

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arXiv2019

Estimation of Location and Orientation for Underwater Vehicles from Range Measurements

Localization is an important required task for enabling vehicle autonomy for underwater vehicles. Localization entails the determination of position of the center of mass and orientation of a vehicle from the available measurements. In this paper, we focus on localization by using One-Way Travel Time (OWTT) measurements available to a vehicle from the communication of its multiple on-board receivers with acoustic beacons, more specifically, long baseline (LBL) beacons. Range can be inferred by multiplying the OWTT with speed of sound; however, water conditions can change spatially and temporally resulting in uncertainty in range measurement. The farther a beacon is from a receiver, the larger is the uncertainty. The proposed method for localization accounts captures this uncertainty by bounding the true distance with an increasing (calibrating) function of the range measurement. Determination of this calibration function is formulated as polynomial optimization problem and is a crucial step for localization. The proposed two-step procedure for localization is as follows: based on the range measurements specific to a receiver from the beacons, a convex optimization problem is proposed to estimate the location of the receiver. The estimate is essentially a center of the set of possible locations of the receiver. In the second step, the location estimates of the vehicle are corrected using rigid body motion constraints and the orientation of the rigid body is thus determined. Numerical examples and experimental results provided at the end corroborate the procedures developed in this paper.

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