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Distributed Spatial-Temporal Trajectory Optimization for Unmanned-Aerial-Vehicle Swarm

Xiaobo Zheng, Pan Tang, Defu Lin, Shaoming He

TL;DR

This work introduces a fully distributed framework for spatial–temporal trajectory optimization of UAV swarms by coupling Parameterized DDP (PDDP) with ADMM in a two-layer architecture (D-PDDP). The method jointly optimizes trajectories and final times while enforcing local dynamics and inter-agent constraints through a consensus mechanism, removing the need to predefine terminal times. A spectral-gradient-based adaptive penalty scheme accelerates ADMM convergence, reducing iterations and computation time. The approach is validated on multi-UAV scenarios with obstacle avoidance, collision and communication constraints, and time-sequencing requirements, demonstrating scalable, distributed optimization with robust performance. Although demonstrated in simulation, the framework shows potential for real-time deployment in large-scale UAV swarms, pending considerations of communication delays and network unreliability.

Abstract

Swarm trajectory optimization problems are a well-recognized class of multi-agent optimal control problems with strong nonlinearity. However, the heuristic nature of needing to set the final time for agents beforehand and the time-consuming limitation of the significant number of iterations prohibit the application of existing methods to large-scale swarm of Unmanned Aerial Vehicles (UAVs) in practice. In this paper, we propose a spatial-temporal trajectory optimization framework that accomplishes multi-UAV consensus based on the Alternating Direction Multiplier Method (ADMM) and uses Differential Dynamic Programming (DDP) for fast local planning of individual UAVs. The introduced framework is a two-level architecture that employs Parameterized DDP (PDDP) as the trajectory optimizer for each UAV, and ADMM to satisfy the local constraints and accomplish the spatial-temporal parameter consensus among all UAVs. This results in a fully distributed algorithm called Distributed Parameterized DDP (D-PDDP). In addition, an adaptive tuning criterion based on the spectral gradient method for the penalty parameter is proposed to reduce the number of algorithmic iterations. Several simulation examples are presented to verify the effectiveness of the proposed algorithm.

Distributed Spatial-Temporal Trajectory Optimization for Unmanned-Aerial-Vehicle Swarm

TL;DR

This work introduces a fully distributed framework for spatial–temporal trajectory optimization of UAV swarms by coupling Parameterized DDP (PDDP) with ADMM in a two-layer architecture (D-PDDP). The method jointly optimizes trajectories and final times while enforcing local dynamics and inter-agent constraints through a consensus mechanism, removing the need to predefine terminal times. A spectral-gradient-based adaptive penalty scheme accelerates ADMM convergence, reducing iterations and computation time. The approach is validated on multi-UAV scenarios with obstacle avoidance, collision and communication constraints, and time-sequencing requirements, demonstrating scalable, distributed optimization with robust performance. Although demonstrated in simulation, the framework shows potential for real-time deployment in large-scale UAV swarms, pending considerations of communication delays and network unreliability.

Abstract

Swarm trajectory optimization problems are a well-recognized class of multi-agent optimal control problems with strong nonlinearity. However, the heuristic nature of needing to set the final time for agents beforehand and the time-consuming limitation of the significant number of iterations prohibit the application of existing methods to large-scale swarm of Unmanned Aerial Vehicles (UAVs) in practice. In this paper, we propose a spatial-temporal trajectory optimization framework that accomplishes multi-UAV consensus based on the Alternating Direction Multiplier Method (ADMM) and uses Differential Dynamic Programming (DDP) for fast local planning of individual UAVs. The introduced framework is a two-level architecture that employs Parameterized DDP (PDDP) as the trajectory optimizer for each UAV, and ADMM to satisfy the local constraints and accomplish the spatial-temporal parameter consensus among all UAVs. This results in a fully distributed algorithm called Distributed Parameterized DDP (D-PDDP). In addition, an adaptive tuning criterion based on the spectral gradient method for the penalty parameter is proposed to reduce the number of algorithmic iterations. Several simulation examples are presented to verify the effectiveness of the proposed algorithm.
Paper Structure (17 sections, 80 equations, 5 figures, 7 tables, 3 algorithms)

This paper contains 17 sections, 80 equations, 5 figures, 7 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Backgrounds and Preliminaries
  3. Multi-Agent Optimal Control Problem
  4. Parameterized Differential Dynamic Programming
  5. Alternating Direction Method of Multiplier
  6. Distributed Parameterized Differential Dynamic Programming
  7. Problem Reformulation
  8. Problem Solution
  9. Adaptive Penalty Parameter Based Acceleration for D-PDDP
  10. Derivition of Spectral Stepsize
  11. Local Curvature Estimation
  12. Adaptive Penalty Parameter Update
  13. Application Example: UAV Swarm Distributed Optimization
  14. Mission Scenario Setting
  15. Characteristics of Proposed Algorithm
  16. ...and 2 more sections

Figures (5)

  • Figure 1: Schematic diagram of a two-layer structure for distributed spatial-temporal optimization.
  • Figure 2: Distributed spatial-temporal joint optimization results for Scenario 1.
  • Figure 3: Distributed spatial-temporal joint optimization results for Scenario 2.
  • Figure 4: Distributed spatial-temporal joint optimization results for Scenario 3.
  • Figure 5: Distributed spatial-temporal joint optimization results for Scenario 4.

Theorems & Definitions (9)

  • Definition 1
  • Definition 2
  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Remark 5
  • Remark 6
  • Remark 7