arXiv subjects

Satyanarayana G. Manyam

Publications and source records attributed to Satyanarayana G. Manyam.

14 recordsLinked to original sources

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

Multi Agent Pathfinding for Noise Restricted Hybrid Fuel Unmanned Aerial Vehicles

Multi Agent Path Finding (MAPF) seeks the optimal set of paths for multiple agents from respective start to goal locations such that no paths conflict. We address the MAPF problem for a fleet of hybrid-fuel unmanned aerial vehicles which are subject to location-dependent noise restrictions. We solve this problem by searching a constraint tree for which the subproblem at each node is a set of shortest path problems subject to the noise and fuel constraints and conflict zone avoidance. A labeling algorithm is presented to solve this subproblem, including the conflict zones which are treated as dynamic obstacles. We present the experimental results of the algorithms for various graph sizes and number of agents.

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arXiv2024

Pursuit-Evasion on a Sphere and When It Can Be Considered Flat

In classical works on a planar differential pursuit-evasion game with a faster pursuer, the intercept point resulting from the equilibrium strategies lies on the Apollonius circle. This property was exploited for the construction of the equilibrium strategies for two faster pursuers against one evader. Extensions for planar multiple-pursuer single-evader scenarios have been considered. We study a pursuit-evasion game on a sphere and the relation of the equilibrium intercept point to the Apollonius domain on the sphere. The domain is a generalization of the planar Apollonius circle set. We find a condition resulting in the intercept point belonging to the Apollonius domain, which is the characteristic of the planar game solution. Finally, we use this characteristic to discuss pursuit and evasion strategies in the context of two pursuers and a single slower evader on the sphere and illustrate it using numerical simulations.

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arXiv2024

Sampling-Based Risk-Aware Path Planning Around Dynamic Engagement Zones

Existing methods for avoiding dynamic engagement zones (EZs) and minimizing risk leverage the calculus of variations to obtain optimal paths. While such methods are deterministic, they scale poorly as the number of engagement zones increases. Furthermore, optimal-control based strategies are sensitive to initial guesses and often converge to local, rather than global, minima. This paper presents a novel sampling-based approach to obtain a feasible flight plan for a Dubins vehicle to reach a desired location in a bounded operating region in the presence of a large number of engagement zones. The dynamic EZs are coupled to the vehicle dynamics through its heading angle. Thus, the dynamic two-dimensional obstacles in the (x,y) plane can be transformed into three-dimensional static obstacles in a lifted (x,y,ψ) space. This insight is leveraged in the formulation of a Rapidly-exploring Random Tree (RRT*) algorithm. The algorithm is evaluated with a Monte Carlo experiment that randomizes EZ locations to characterize the success rate and average path length as a function of the number of EZs and as the computation time made available to the planner is increased.

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arXiv2024

Noise Aware Path Planning and Power Management of Hybrid Fuel UAVs

Hybrid fuel Unmanned Aerial Vehicles (UAV), through their combination of multiple energy sources, offer several advantages over the standard single fuel source configuration, the primary one being increased range and efficiency. Multiple power or fuel sources also allow the distinct pitfalls of each source to be mitigated while exploiting the advantages within the mission or path planning. We consider here a UAV equipped with a combustion engine-generator and battery pack as energy sources. We consider the path planning and power-management of this platform in a noise-aware manner. To solve the path planning problem, we first present the Mixed Integer Linear Program (MILP) formulation of the problem. We then present and analyze a label-correcting algorithm, for which a pseudo-polynomial running time is proven. Results of extensive numerical testing are presented which analyze the performance and scalability of the labeling algorithm for various graph structures, problem parameters, and search heuristics. It is shown that the algorithm can solve instances on graphs as large as twenty thousand nodes in only a few seconds.

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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

Virtual Target Selection for a Multiple-Pursuer Multiple-Evader Scenario

This paper considers an M-pursuer N-evader scenario involving virtual targets. The virtual targets serve as an intermediary target for the pursuers, allowing the pursuers to delay their final assignment to the evaders. However, upon reaching the virtual target, the pursuers must decide which evader to capture. It is assumed that there are more pursuers than evaders and that the pursuers are faster than the evaders. The objective is two-part: first, assign each pursuer to a virtual target and evader such that the pursuer team's energy is minimized, and second, choose the virtual targets' locations for this minimization problem. The approach taken is to consider the Apollonius geometry between each pursuer's virtual target location and each evader. Using the constructed Apollonius circles, the pursuer's travel distance and maneuver at a virtual target are obtained. These metrics serve as a gauge for the total energy required to capture a particular evader and are used to solve the joint virtual target selection and pursuer-evader assignment problem. This paper provides a mathematical definition of this problem, the solution approach taken, and an example.

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arXiv2022

Development of Linear Battery Model for Path Planning with Mixed Integer Linear Programming: Simulated and Experimental Validation

Mixed Integer Linear Programs (MILPs) are often used in the path planning of both ground and aerial vehicles. Such a formulation of the path planning problem requires a linear objective function and constraints, limiting the fidelity of the the tracking of vehicle states. One such parameter is the state of charge of the battery used to power the vehicle. Accurate battery state estimation requires nonlinear differential equations to be solved. This state estimation is important in path planning to ensure flyable paths, however when using MILPs to formulate the path planning problem these nonlinear equations cannot be implemented. Poor accuracy in battery estimation during the path planning runs the risk of the planned path being feasible by the estimation model but in reality will deplete the battery to a critical level. To the end of higher accuracy battery estimation within a MILP, we present here a simple linear battery model which predicts the change in state-of-charge (SOC) of a battery given a power draw and duration. This model accounts for changes in battery voltage due to applied electrical load and changes in battery SOC. The battery model is presented and then tested against alternate battery models in numerical and in experimental tests. Further, the effect the proposed linear model has over a simpler SOC estimation on the time-to-solve a resource constrained shortest path problem is also evaluated, implemented in two different algorithms. It is seen that the linear model performs well in battery state estimation while remaining implementable in a Linear Program or MILP, with little affect on the time-to-solve.

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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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arXiv2019

Cooperative Routing for an Air-Ground Vehicle Team -- Exact Algorithm, Transformation Method, and Heuristics

This article considers a cooperative vehicle routing problem for an intelligence, surveillance, and reconnaissance mission in the presence of communication constraints between the vehicles. The proposed framework uses a ground vehicle and an Unmanned Aerial Vehicle (UAV) that travel cooperatively and visit a set of targets while satisfying the communication constraints. The problem is formulated as a mixed-integer linear program, and a branch-and-cut algorithm is developed to solve the problem to optimality. Furthermore, a transformation method and a heuristic are also developed for the problem. The effectiveness of all the algorithms is corroborated through extensive computational experiments on several randomly generated instances.

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arXiv2017

Multi-UAV Routing for Persistent Intelligence Surveillance & Reconnaissance Missions

We consider a Persistent Intelligence, Surveillance and Reconnaissance (PISR) routing problem, which includes collecting data from a set of specified task locations and delivering that data to a control station. Each task is assigned a refresh rate based on its priority, where higher priority tasks require higher refresh rates. The UAV team's objective is to minimize the maximum of the delivery times of all the tasks' data to the control station, while simultaneously, satisfying each task's revisit period constraint. The centralized path planning problem for this PISR routing problem is formulated using mixed integer linear programming and solved using a branch-and-cut algorithm. Heuristics are presented to find sub-optimal feasible solutions that require much less computation time. The algorithms are tested on several instances and their performance is compared with respect to the optimal cost and computation time.

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arXiv2017

Path Planning for Multiple Heterogeneous Unmanned Vehicles with Uncertain Service Times

This article presents a framework and develops a formulation to solve a path planning problem for multiple heterogeneous Unmanned Vehicles (UVs) with uncertain service times for each vehicle--target pair. The vehicles incur a penalty proportional to the duration of their total service time in excess of a preset constant. The vehicles differ in their motion constraints and are located at distinct depots at the start of the mission. The vehicles may also be equipped with disparate sensors. The objective is to find a tour for each vehicle that starts and ends at its respective depot such that every target is visited and serviced by some vehicle while minimizing the sum of the total travel distance and the expected penalty incurred by all the vehicles. We formulate the problem as a two-stage stochastic program with recourse, present the theoretical properties of the formulation and advantages of using such a formulation, as opposed to a deterministic expected value formulation, to solve the problem. Extensive numerical simulations also corroborate the effectiveness of the proposed approach.

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