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Energy-Efficient UAV-Assisted Mobile Edge Computing: Resource Allocation and Trajectory Optimization

Mushu Li, Nan Cheng, Jie Gao, Yinlu Wang, Lian Zhao, Xuemin, Shen

arXiv:2007.15105v1cs.NIeess.SPeess.SY

TL;DR

The paper studies how to maximize UAV energy efficiency in UAV-assisted MEC while meeting user service requirements through joint trajectory and resource optimization. It solves the resulting nonconvex fractional problem with iterative convex-approximation and fractional-programming methods, extends optimization to distributed operation and limited mobility knowledge, and reports an effective energy-efficiency maximization approach.

  • Problem

    UAV-assisted MEC must jointly handle limited UAV energy, trajectory design, and computation-load allocation for energy-efficient task offloading.

  • Method

    The approach jointly optimizes UAV trajectory and resource allocation, using SCA, Dinkelbach optimization, distributed decomposition, and spatial distribution estimation for limited mobility knowledge.

  • Results

    The proposed optimization approach maximizes UAV energy efficiency and provides an energy-efficient trajectory when user mobility knowledge is limited.

  • Takeaways & Limitations

    UAV trajectory and resource allocation can be optimized together for on-demand edge computing, including when mobility and offloading requests are ambiguous at cycle start.

Abstract

from arXiv · show

In this paper, we study unmanned aerial vehicle (UAV) assisted mobile edge computing (MEC) with the objective to optimize computation offloading with minimum UAV energy consumption. In the considered scenario, a UAV plays the role of an aerial cloudlet to collect and process the computation tasks offloaded by ground users. Given the service requirements of users, we aim to maximize UAV energy efficiency by jointly optimizing the UAV trajectory, the user transmit power, and computation load allocation. The resulting optimization problem corresponds to nonconvex fractional programming, and the Dinkelbach algorithm and the successive convex approximation (SCA) technique are adopted to solve it. Furthermore, we decompose the problem into multiple subproblems for distributed and parallel problem solving. To cope with the case when the knowledge of user mobility is limited, we adopt a spatial distribution estimation technique to predict the location of ground users so that the proposed approach can still be applied. Simulation results demonstrate the effectiveness of the proposed approach for maximizing the energy efficiency of UAV.

I. INTRODUCTION

The paper addresses energy-efficient UAV-assisted MEC for remote or challenging IoT deployments where terrestrial infrastructure cannot reliably support computation offloading. It jointly optimizes UAV trajectory and communication/computing resources, while also addressing distributed solution and limited mobility knowledge.

  • Motivation: Sparse terrestrial infrastructure cannot reliably communicate with IoT nodes in remote or challenging areas, motivating UAV-supported communication and computing.UAV-mounted cloudlets can be dispatched flexibly to collect and process tasks from ground users.
  • Challenges: Limited UAV energy, substantial mechanical flight consumption, and cubic growth of computing energy with allocated load make trajectory and load design necessary.Improper computation-load allocation can increase energy consumption or prevent tasks from finishing on time.
  • Research gap: UAV trajectory, computation-load allocation, and communication-resource management are coupled, and their joint energy-efficiency optimization was identified as uninvestigated in UAV-assisted MEC.The paper formulates an energy-constrained UAV-assisted MEC system with service and mechanical-operation constraints.
  • Approach: The proposed model jointly optimizes UAV movement, communication resources, and computing resources to maximize the ratio of offloaded data to UAV energy consumption.The UAV collects offloading data, processes tasks, and returns computing results during each cycle.
  • Solution method: Dinkelbach and SCA methods transform the nonconvex fractional problem, while ADMM decomposes it for distributed and parallel optimization without sharing local information.Users and the UAV obtain resource-allocation results iteratively through cooperative optimization.
  • Limited mobility knowledge: Gaussian kernel density estimation predicts ground-user locations when mobility knowledge is limited, enabling energy-efficient trajectory decisions despite ambiguous mobility and offloading requests.The strategy operates at the beginning of each optimization cycle using predicted location information.

II. RELATED WORKS

Prior MEC studies address energy, delay, offloading, and radio-resource allocation mainly for fixed infrastructures or related UAV communication settings. This paper focuses on UAV-mounted cloudlets that introduce dynamic channels and mechanical constraints, with multi-user energy-efficient resource management.

  • MEC resource allocation: Earlier MEC research studied energy minimization, delay, task dropping, partial offloading, and radio-resource allocation, generally with fixed edge infrastructures.These studies include binary or partial offloading and Lyapunov-based management for energy-harvesting devices.
  • UAV-assisted MEC: UAVs have also served as communication relays or aerial cloudlets for offloading, recommendation, path planning, and predefined-trajectory strategies.Existing cloudlet studies addressed communication energy, traffic or computing-load reduction, and joint delay or cost objectives.
  • UAV communications: UAV communication studies considered throughput, trajectory design, power control, channel assignment, and single-terminal energy efficiency, rather than the paper’s multi-user resource-management setting.The cited single-ground-terminal work designs a trajectory for hovering above one communication terminal.
  • Research gap: Existing work did not investigate the energy consumption of the UAV-mounted cloudlet in the cited IoT offloading strategy, leaving UAV energy efficiency insufficiently addressed.The present setting instead considers dynamic channel conditions and mechanical operation constraints.
  • Network model: The system model uses a single UAV-mounted cloudlet deployed over area A to provide edge computing service for ground users.Users with computation tasks send offloading requests at the beginning of each cycle.

B. Communication Model

The model represents UAV–user communication through distance-dependent channels and considers both orthogonal and non-orthogonal access. It jointly represents UAV trajectory, transmit-power allocation, task partitioning, and computation execution constraints.

  • UAV mobility: The UAV maintains a fixed altitude while its optimization-variable trajectory specifies positions throughout the computation cycle.Average velocity and acceleration are derived per slot and constrained by maximum speed and acceleration.
  • Channel model: Channel quality depends on UAV–user distance under a free-space path-loss model with high-probability line-of-sight links.The channel gain is represented for each user and time slot using the UAV–user geometry.
  • Access schemes: The system supports orthogonal access with one user per sub-channel and non-orthogonal access with shared bandwidth and inter-user interference.Noise power is defined differently for the two access schemes, while each user’s allocated power is represented by δ_i,k.
  • Task partitioning: Offloaded bits are constrained by user task requirements, with tasks not fully offloaded processed locally after the threshold requirement is satisfied.The UAV buffers received input data and executes the offloaded workload subject to reception and completion constraints.
  • Computation model: The UAV cloudlet uses DVFS, allowing its CPU-cycle frequency to vary with workload within a maximum frequency.The computation model represents workload allocation through per-user, per-slot processed data and the required cycles per bit.

D. Energy Consumption Model

The energy model accounts for communication, local and UAV computing, and UAV propulsion, while defining energy efficiency as offloaded data divided by UAV energy consumption. The resulting constrained objective is non-linear fractional programming.

  • Communication energy: Communication energy decreases when the UAV is closer to a user because the communication link becomes more favorable.The model treats downlink energy as negligible because communication energy is small relative to propulsion and computing energy, and output data are usually smaller than input data.
  • Energy components: UAV-mounted-cloudlet energy comprises mechanical-operation and computing costs, whereas user energy includes communication and local-computing costs.The model separately formulates communication energy and computing energy for users and the UAV.
  • Propulsion energy: The fixed-wing propulsion model relates slot energy consumption to instantaneous UAV velocity and acceleration, with aircraft-dependent parameters.The model uses a refined propulsion-energy formulation for fixed-wing UAVs.
  • Optimization objective: Energy efficiency is defined as overall offloaded data divided by UAV energy consumption over a cycle, subject to offloading, computing, and mechanical constraints.The optimization seeks to maximize this ratio under user service and UAV capability constraints.
  • Problem structure: The resulting problem is challenging because it is non-linear fractional and includes interference-related and propulsion-energy non-convexities.The authors therefore seek an efficient local-optimum approach rather than direct global optimization.

V. PROPOSED OPTIMIZATION APPROACH

The proposed approach combines SCA and Dinkelbach optimization, then uses ADMM to decompose the problem for scalable distributed solving. The approximation yields a local maximizer and a lower bound on maximum energy efficiency.

  • SCA: SCA replaces non-convex functions and constraints with solvable convex approximations and iterates until reaching a local optimizer.The approximations use first-order Taylor expansions and updated auxiliary variables from the previous iteration.
  • Fractional optimization: Dinkelbach’s algorithm solves the fractional programming problem embedded within each SCA iteration.The inner fractional problem remains non-convex after approximation, so it is handled separately by Dinkelbach iterations.
  • Distributed solution: ADMM decomposes the optimization into subproblems, assigning power allocation to users and computation-load allocation and trajectory planning to the UAV.This decomposition is introduced to improve scalability through distributed and parallel problem solving.
  • Solution guarantee: The convex approximation solution is a local maximizer of the original problem and provides a lower bound on its maximum energy efficiency.The result follows from the stated lemma for the approximated constraints.

B. Dinkelbach Algorithm

The Dinkelbach procedure converts the fractional objective into a parameterized problem whose parameter is updated until the transformed objective reaches zero. Reusing the previous SCA iteration’s parameter improves computational efficiency.

  • Parameterization: Dinkelbach’s method solves a parameterized optimization problem and identifies the optimum when the monotone decreasing transformed function equals zero.The optimal parameter equals the optimal energy-efficiency value of the approximated problem.
  • Iteration behavior: The optimal Dinkelbach parameter is nondecreasing across consecutive SCA iterations.The paper states α∗(t−1) ≤ α∗(t), while the transformed objective at the newer parameter is zero.
  • Initialization: Initializing each Dinkelbach loop with the previous SCA iteration’s optimal parameter instead of zero reduces optimization computation effort.This warm start is justified by the monotonicity relation between consecutive parameters.

C. Sub-problem Decomposition by ADMM

ADMM decomposes the UAV-assisted computation offloading problem into user-side and UAV-side subproblems, enabling distributed and parallel optimization while coordinating shared trajectory and workload variables.

  • Users maximize their offloaded computation tasks in parallel, while the UAV minimizes energy consumption under shared coordination variables.
  • The original problem is decomposed into several subproblems without losing optimality.
  • ADMM introduces auxiliary matrices so users provide expected UAV trajectories and loads, while the UAV returns a unified trajectory and computation allocation.
  • The user-side and UAV-side updates exchange matrices and dual variables iteratively until the objective change satisfies a stopping threshold.
  • The decomposition avoids sharing some local user and UAV parameters and allows SOC constraints to be solved by users in parallel.

D. Convergence and Complexity Analysis

The paper analyzes convergence for the nested SCA, Dinkelbach, and ADMM procedures and characterizes complexity through the SOC programs that dominate computation.

  • The three algorithmic loops in Algorithms 1–3 are guaranteed to converge under the stated feasibility and initialization conditions.
  • The Dinkelbach algorithm reaches the optimal α∗ with a super-linear rate.
  • The computational burden is dominated by SOC programming, with decomposition reducing user-side work to smaller SOC constraints and a UAV-side set of K constraints in seven dimensions.

VI. PROACTIVE TRAJECTORY DESIGN BASED ON SPATIAL DISTRIBUTION ESTIMATION

The paper uses kernel density estimation to predict user spatial distributions when future mobility and immediate offloading requests are unavailable, then optimizes a virtual-user representation of expected workload.

  • The approach addresses users’ limited knowledge of future positions and the delay caused by sending offloading requests only at cycle beginnings.
  • Kernel density estimation predicts user mobility from periodically sampled locations within each computation cycle.
  • A Gaussian kernel estimates the spatial density, with bandwidths selected by maximum-likelihood cross-validation.
  • The working area is divided into G × G sub-areas, each represented by a virtual user at its center carrying the expected computation load.
  • As G increases, the performance of the spatial-distribution estimation improves correspondingly.

VII. NUMERICAL RESULTS

Numerical experiments evaluate trajectory, convergence, offloading, and energy-allocation behavior in three-node and four-node scenarios. The proposed approach adapts trajectories and resource allocation to user demands and energy constraints, outperforming the circular benchmark in supported comparisons.

  • Experimental settings: The proposed trajectories serve both three-node and four-node scenarios with stationary or mobile users and fixed-wing UAV motion constraints.
  • Convergence: The three-node energy-efficiency computation converges at t = 30 SCA iterations, while the four-node case requires more iterations.
  • Energy efficiency: Loose offloading requirements improve energy efficiency, whereas tight requirements decrease it because the UAV consumes more energy moving closer to users.
  • Offloading: The proposed approach achieves the minimum offloading requirement in all tested scenarios, unlike the circular trajectory scheme.
  • Energy trade-offs: Increasing maximum communication energy initially raises energy efficiency, after which it reaches a ceiling when all users’ computing data is collected.
  • Benchmark comparison: The proposed approach improves energy efficiency significantly compared with the circular trajectory and balances computation workload to reduce computing energy consumption.

VIII. CONCLUSIONS

The paper jointly optimizes UAV trajectory design and resource allocation to maximize energy efficiency in UAV-assisted MEC, using distributed optimization and mobility estimation when user trajectories are limited.

  • The proposed approach jointly considers UAV trajectory design and resource allocation in a UAV-assisted MEC system.
  • The resulting non-convex and non-linear energy-efficiency maximization problem is solved in a distributed manner.
  • Node mobility estimation enables proactive UAV trajectory design when knowledge of user trajectories is limited.
  • The work provides insights into optimal UAV trajectory design for on-demand edge computing services for remote IoT nodes.
  • Future work will address online resource management under dynamic channel environments and uncertainty in user mobility and computation demand.

APPENDIX A: PROOF OF LEMMA 1

The proof reformulates the energy-efficiency optimization using auxiliary variables and successive convex approximations, establishing bounds and local-optimality behavior for the resulting procedure.

  • The non-linear numerator and denominator terms are handled with auxiliary variables and equivalent reformulations of the optimization problem.
  • Auxiliary variables represent lower bounds on user data rates and upper bounds on UAV propulsion energy.
  • Additional variables transform nonconvex rate constraints through relations involving ξ_i,k, δ_i,kP/l_i,k, and l_i,k ≥ N_0/h_i,k.
  • First-order Taylor expansions and cone expressions approximate constraints to obtain lower bounds on the relevant terms.
  • The approximated constraints are stricter than the originals, so the approximated solution is strictly smaller than the original optimum.
  • Gradient consistency causes the SCA algorithm to stop when a local optimizer is found.
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