PaperlayerView exact revision on arXiv

Source-linked AI summary

Energy Minimization for Wireless Communication with Rotary-Wing UAV

Yong Zeng, Jie Xu, Rui Zhang

arXiv:1804.02238v1cs.IT

TL;DR

The paper addresses minimizing rotary-wing UAV energy consumption while meeting multiple ground nodes’ communication requirements. It derives a rotary-wing propulsion model and develops fly-hover-communicate and general flying-communication optimizations using TSP, convex optimization, path discretization, and SCA. Numerical results show significant performance gains over benchmark schemes for energy-efficient rotary-wing UAV communication.

  • Problem

    The paper seeks to minimize total propulsion and communication energy while satisfying each ground node’s communication throughput requirement in rotary-wing UAV communication.

  • Method

    The paper derives a rotary-wing propulsion power model and develops fly-hover-communicate and flying-communication solutions using TSP, convex optimization, path discretization, and SCA.

  • Results

    Numerical results show that the proposed designs achieve significant energy savings over benchmark schemes for rotary-wing UAV-enabled wireless communication.

  • Takeaways & Limitations

    The proposed designs provide energy-efficient communication approaches for rotary-wing UAV systems while meeting individual ground-node throughput requirements.

Abstract

from arXiv · show

This paper studies unmanned aerial vehicle (UAV) enabled wireless communication, where a rotarywing UAV is dispatched to send/collect data to/from multiple ground nodes (GNs). We aim to minimize the total UAV energy consumption, including both propulsion energy and communication related energy, while satisfying the communication throughput requirement of each GN. To this end, we first derive an analytical propulsion power consumption model for rotary-wing UAVs, and then formulate the energy minimization problem by jointly optimizing the UAV trajectory and communication time allocation among GNs, as well as the total mission completion time. The problem is difficult to be optimally solved, as it is non-convex and involves infinitely many variables over time. To tackle this problem, we first consider the simple fly-hover-communicate design, where the UAV successively visits a set of hovering locations and communicates with one corresponding GN when hovering at each location. For this design, we propose an efficient algorithm to optimize the hovering locations and durations, as well as the flying trajectory connecting these hovering locations, by leveraging the travelling salesman problem (TSP) and convex optimization techniques. Next, we consider the general case where the UAV communicates also when flying. We propose a new path discretization method to transform the original problem into a discretized equivalent with a finite number of optimization variables, for which we obtain a locally optimal solution by applying the successive convex approximation (SCA) technique. Numerical results show the significant performance gains of the proposed designs over benchmark schemes, in achieving energy-efficient communication with rotary-wing UAVs.

I. INTRODUCTION

The paper targets energy-efficient wireless communication with rotary-wing UAVs, whose propulsion energy differs fundamentally from fixed-wing UAVs. It develops fly-hover-communicate and general flying-communication designs by jointly optimizing trajectory, communication allocation, and mission time.

  • Motivation: UAV-enabled wireless communication offers on-demand deployment, shorter-distance LoS links, and flexible 3D movement for serving ground nodes.The paper identifies applications including public safety, traffic offloading, IoT data collection, emergency response, and service recovery.
  • Motivation: Limited onboard energy is critical because rotary-wing UAVs consume propulsion energy to remain airborne and move, often exceeding communication-related power.Consequently, UAV energy-efficient communication design differs significantly from conventional terrestrial systems.
  • Research gap: Fixed-wing UAV energy results do not apply to rotary-wing UAVs because their fundamentally different mechanical designs yield drastically different propulsion energy models.This motivates deriving a rotary-wing propulsion power model for the paper’s communication setting.
  • Problem formulation: The paper formulates total UAV energy minimization, including propulsion and communication energy, while satisfying each ground node’s communication requirement.The optimization jointly covers UAV trajectory, communication time allocation among multiple ground nodes, and total mission completion time.
  • Proposed designs: The fly-hover-communicate design optimizes hovering locations, durations, visiting order, and flight speed using TSP-solving and convex optimization techniques.The resulting method provides an efficient high-quality approximate solution despite the embedded NP-hard visiting-order problem.
  • Proposed designs: For communication during flight, path discretization converts infinitely many time-dependent variables into finitely many variables without pre-specifying mission completion time.Successive convex approximation then produces a solution that converges to at least a locally optimal solution satisfying KKT conditions.

II. SYSTEM MODEL AND PROBLEM FORMULATION

The system models rotary-wing UAV communication with LoS channels, TDMA scheduling, a bounded trajectory, and throughput requirements for multiple ground nodes.

  • A. System Model: The UAV serves K ground nodes at a fixed altitude H while communicating a required number of bits with each node.
  • A. System Model: The horizontal trajectory q(t) is defined over the mission time Tt and must satisfy the maximum-speed constraint ∥q̇(t)∥≤Vmax.
  • A. System Model: Wireless channels are assumed to be LoS-dominated, with channel gain modeled using free-space path loss and reference gain β0.
  • A. System Model: The transmitter uses fixed power P, and the achievable rate depends on bandwidth B, receiver noise σ2, coding gap Γ, and received reference SNR γ0.
  • A. System Model: TDMA scheduling uses binary indicators λk(t), with at most one ground node scheduled at any instant.
  • A. System Model: Each node’s aggregated throughput is determined by mission time, trajectory, and scheduling, and must meet its target requirement.

B. Energy Consumption Model for Rotary-Wing UAV

The energy model combines communication and rotary-wing propulsion consumption, whose speed dependence makes hovering generally nonoptimal and complicates optimization.

  • Total UAV energy comprises communication-related energy and propulsion energy required to keep the aircraft aloft and support movement.
  • The communication-related power is modeled as constant, while acceleration-induced energy is ignored for typical communication applications.
  • Rotary-wing propulsion power contains blade-profile, induced, and parasite components with distinct speed dependencies.
  • Blade-profile and parasite power increase quadratically and cubically with speed, whereas induced power decreases with speed.
  • Hovering consumes finite power Ph=P0+Pi, but P(V) first decreases and then increases as speed grows, so hovering is generally not most power-conserving.
  • The propulsion power function is neither convex nor concave, unlike the simpler convex fixed-wing model.
  • The model defines propulsion energy by integrating P(∥v(t)∥) over the trajectory, and Fig. 1 plots this power against speed with its components and approximation.
  • Maximum-endurance speed minimizes power consumption, while maximum-range speed minimizes energy per unit distance; typically Vme≤Vmr≤Vmax.

C. Problem Formulation for UAV Energy Minimization

The paper formulates total-energy minimization over trajectory, scheduling, and mission time under throughput constraints, then develops finite-variable solution strategies.

  • C. Problem Formulation for UAV Energy Minimization: The objective minimizes total UAV energy while satisfying target communication throughput for every ground node.
  • C. Problem Formulation for UAV Energy Minimization: The formulation may include initial and final horizontal UAV locations, depending on the practical application scenario.
  • C. Problem Formulation for UAV Energy Minimization: The optimization jointly determines the continuous trajectory q(t) and communication scheduling functions λk(t).
  • C. Problem Formulation for UAV Energy Minimization: Because trajectory and scheduling are continuous in time, the problem has infinitely many optimization variables, a complicated energy objective, and nonconvex constraints.
  • C. Problem Formulation for UAV Energy Minimization: A general solution uses path discretization to obtain finitely many variables and applies SCA to find at least a locally optimal solution.
  • III. FLY-HOVER-COMMUNICATE PROTOCOL: The fly-hover-communicate protocol restricts communication to hovering locations assigned to individual ground nodes.
  • III. FLY-HOVER-COMMUNICATE PROTOCOL: Under this protocol, optimization reduces to hovering locations, communication durations, and the speed and path connecting those locations.
  • III. FLY-HOVER-COMMUNICATE PROTOCOL: The protocol is extended from one ground node to multiple ground nodes after analyzing the single-node case.

A. Optimal Fly-Hover-Communicate Scheme for One Single GN

For one ground node, fly-hover-communicate optimization balances travel energy against hovering and communication energy, yielding MR-speed travel and an optimized stopping distance.

  • A. Optimal Fly-Hover-Communicate Scheme for One Single GN: The single-node setup considers an initial UAV position, a ground node, and optional constraints on the final UAV location.
  • A. Optimal Fly-Hover-Communicate Scheme for One Single GN: Hovering at the initial location can require excessive mission time and energy when the initial link distance is large.
  • A. Optimal Fly-Hover-Communicate Scheme for One Single GN: Flying closer to the ground node increases travel energy but can raise the data rate and reduce hovering and communication energy.
  • A. Optimal Fly-Hover-Communicate Scheme for One Single GN: The optimal hovering location balances traveling energy against hovering and communication energy.
  • A. Optimal Fly-Hover-Communicate Scheme for One Single GN: For a chosen travel distance, the formulation computes travel time, achievable hovering rate, communication time, and total energy.
  • A. Optimal Fly-Hover-Communicate Scheme for One Single GN: The total energy is decomposed as Etot=Etr+Ehc and optimized over travel time, speed profile, and travel distance.
  • A. Optimal Fly-Hover-Communicate Scheme for One Single GN: The optimal travel solution uses constant maximum-range speed Vmr, reducing the problem to a univariate optimization over travel distance.
  • A. Optimal Fly-Hover-Communicate Scheme for One Single GN: Travel distance increases linearly with travel energy and decreases hovering energy, so the optimum can be found by one-dimensional search; higher throughput favors moving closer.

B. Fly-Hover-Communicate for Multiple GNs

The fly-hover-communicate protocol jointly selects hovering locations, communication durations, and a route through those locations to reduce UAV energy consumption. It uses TSP-based ordering, convex optimization, and SCA to obtain an efficient approximate solution.

  • The protocol optimizes K hovering locations, communication durations, and the traveling path and speed among those locations.Each GN is served while the UAV hovers at a corresponding location.
  • The UAV should travel at the minimum-power speed Vmr, while the route length depends on the visiting order of the hovering locations.The visiting order is represented by permutation variables π(k).
  • With fixed hovering locations, route selection reduces to a traveling salesman problem with predetermined initial and final locations, which is NP hard.Jointly optimizing locations yields the more general traveling salesman problem with neighborhoods.
  • The proposed approximation first solves a TSP over GN locations, fixes the visiting order, and then uses convex optimization with SCA to optimize hovering waypoints.The SCA subproblem is convex and is solved iteratively using global lower bounds.
  • Algorithm 1 is guaranteed to converge to at least a locally optimal solution satisfying the KKT conditions.The algorithm successively updates local points while solving convex subproblems.

IV. GENERAL SOLUTION TO (P1) WITH PATH DISCRETIZATION AND SCA

The fly-hover-communicate protocol provides an efficient solution whose variable count depends on the number of GNs, but it is strictly sub-optimal because it forbids communication during flight. The general solution removes this restriction by jointly optimizing trajectory and communication allocation.

  • The fly-hover-communicate protocol has an optimization-variable count that depends on K rather than mission completion time Tt.
  • The protocol is strictly sub-optimal because the UAV does not communicate while flying.
  • The general solution jointly optimizes the UAV trajectory and communication time allocation without assuming communication occurs only while hovering.

A. Path Discretization

Path discretization replaces time-based discretization with a finite representation of the UAV path, avoiding advance specification of mission completion time. It models each segment with constant velocity and supports communication allocation, energy computation, and convex constraints.

  • The original problem has infinitely many time-coupled optimization variables, making direct solution difficult.
  • Time discretization requires a pre-specified mission completion time Tt and may require solving many optimization problems for different assumed values.This becomes impractical when the optimal Tt is moderately large.
  • Path discretization divides the UAV path into M + 1 line segments, represented by M + 2 points, and requires only one optimization problem.The mission completion time is determined directly after segment durations are obtained.
  • Within each segment, the UAV is assumed to fly at constant velocity with approximately unchanged GN distances, while hovering is represented by setting consecutive discretization points equal.The segment size can be chosen with Δmax ≪ H, and M satisfies (M + 1)Δmax ≥ D̂.
  • Communication time variables τmk allocate TDMA service to each GN on each segment, enabling discretized throughput and energy expressions.The segment speed is determined by its length divided by duration, and the resulting problem includes speed and segment constraints.
  • The discretized problem remains non-convex because its energy objective and throughput constraint are non-convex.Consequently, a globally optimal solution is difficult to obtain.
  • An efficient locally optimal solution is obtained by applying the SCA technique to the path-discretized problem.

B. Proposed Solution to (P4)

The proposed solution handles the remaining non-convexity by replacing selected constraints with global lower bounds and iteratively solving convex approximations. The resulting SCA algorithm converges to at least a locally optimal solution satisfying KKT conditions.

  • The reformulated problem remains non-convex because constraints involving communication, slack variables, and segment durations are non-convex.
  • SCA constructs global lower bounds using first-order Taylor expansions at the current local point.These bounds replace the non-convex constraints in the iterative subproblem.
  • The lower-bound replacements produce a convex optimization problem that can be solved using standard convex optimization techniques or CVX.Its feasible region is generally a subset of the original reformulated problem's feasible region.
  • Successively updating the local point and solving the convex subproblem yields an efficient algorithm for the original energy minimization problem.
  • Algorithm 2 is guaranteed to converge to at least a locally optimal solution satisfying the KKT conditions.
  • The SCA algorithm can also be applied to other UAV communication objectives, such as mission completion time minimization, by replacing the cost function.

V. NUMERICAL RESULTS

The numerical results show that the proposed energy-minimization designs converge effectively and adapt UAV trajectories, speeds, hovering locations, and communication-time allocation to throughput requirements. They achieve performance gains over benchmark schemes while exposing trade-offs between energy consumption and mission completion time.

  • Convergence: The SCA-based algorithm converges in a few iterations, and its convex-optimization upper bound is practically tight.The upper-bound and exact energy curves match closely for a throughput requirement of 200 Mbits.
  • Trajectory and speed behavior: Optimized fly-hover-communicate locations balance communication distance against flying distance rather than placing the UAV directly above every GN.Higher throughput requirements move the optimized hovering locations closer to the GNs.
  • Trajectory and speed behavior: The fly-hover-communicate protocol uses maximum-rate flying between optimized locations and hovering at those locations for communication.Its speed therefore has two statuses: flying at the maximum-range speed Vmr and hovering.
  • Communication allocation: The SCA energy-minimization design allocates more communication time to the nearer GN at each UAV location.The allocation favors better channels, which generally provide higher spectrum efficiency.
  • Benchmark comparison: The optimized fly-hover-communicate scheme outperforms fixed geometric-center and above-GN benchmarks in energy consumption and mission completion time.The two benchmarks exchange relative advantage as throughput increases, while the optimized scheme adapts hovering locations to communication requirements.
  • Benchmark comparison: Energy minimization and time minimization generally produce different solutions, although optimizing one objective can to some extent reduce the other.Explicitly minimizing UAV energy yields further energy savings compared with heuristic time minimization.

VI. CONCLUSION

The paper develops energy-efficient communication designs for rotary-wing UAVs by combining an analytical propulsion model with optimization of trajectories and communication. Numerical results report significant energy savings over benchmark schemes.

  • Model and problem: The paper derives a rotary-wing propulsion power model and formulates total-energy minimization subject to each GN's throughput requirement.The objective includes propulsion and communication energy.
  • Proposed designs: The fly-hover-communicate solution uses TSP and convex optimization to optimize hovering locations, durations, visiting order, and speed.This provides an efficient solution for the simplified communication protocol.
  • Proposed designs: The general solution allows communication during flight through path discretization and successive convex approximation.The approach addresses the original trajectory and communication design without restricting communication to hovering.
  • Results: The proposed designs achieve significant energy savings compared with other benchmark schemes for rotary-wing UAV communication.The reported numerical results support energy-efficient communication under the formulated throughput requirements.

APPENDIX A

Appendix A derives an analytical propulsion-power model for rotary-wing aircraft in hovering and forward flight. It uses standard aerodynamic relationships and simplifying assumptions to obtain the model used in the paper.

  • Model derivation: The appendix derives the rotary-wing UAV power-consumption model from actuator-disc and blade-element theory.Most notations and results follow established aircraft textbooks, while the derivation adapts them for UAV communications.
  • Hovering flight: Hovering power is obtained from the torque coefficient, rotor parameters, and the thrust balance T = W.The derivation uses the relationship P = qcρsAΩ^3R^3 and the hovering thrust condition.
  • Forward flight: Forward-flight power is derived using the torque coefficient and mean induced velocity for a rotary-wing aircraft moving at speed V.The forward-flight derivation is more complicated than the fixed-wing counterpart and assumes, among other conditions, a constant blade-section drag coefficient.
  • Forward flight: For a given thrust, the mean induced velocity decreases as forward speed increases.This relationship is used in deriving the required forward-flight power expression.
  • Model simplification: Assuming a small rotor-disc tilt angle gives T ≈ W and κ ≈ 1, reducing the general forward-flight expression to the model in Section II-B.The force balance in straight level flight provides the approximation.
Loading 1804.02238v1…