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Multi-AAV Cooperative Path Planning using Nonlinear Model Predictive Control with Localization Constraints

Amith Manoharan, Rajnikanth Sharma, P. B. Sujit

TL;DR

The paper tackles joint cooperative localization and path planning for multiple AAVs in GPS-denied environments by marrying nonlinear model predictive control (NMPC) with moving horizon estimation (MHE). It introduces an analytical, closed-form covariance approximation derived from the vehicle-landmark graph to predict localization uncertainty within the NMPC prediction window, enabling real-time planning with localization constraints. Through extensive simulations, the approach demonstrates near-optimal paths, superior localization accuracy compared with EKF-based estimation, and clear benefits from inter-vehicle cooperation, while also showing scalability to larger teams. These results suggest practical viability for coordinated AAV missions in urban canyons and similar GPS-denied scenarios, with avenues for future enhancements such as obstacle avoidance and landmark management.

Abstract

In this paper, we solve a joint cooperative localization and path planning problem for a group of Autonomous Aerial Vehicles (AAVs) in GPS-denied areas using nonlinear model predictive control (NMPC). A moving horizon estimator (MHE) is used to estimate the vehicle states with the help of relative bearing information to known landmarks and other vehicles. The goal of the NMPC is to devise optimal paths for each vehicle between a given source and destination while maintaining desired localization accuracy. Estimating localization covariance in the NMPC is computationally intensive, hence we develop an approximate analytical closed form expression based on the relationship between covariance and path lengths to landmarks. Using this expression while computing NMPC commands reduces the computational complexity significantly. We present numerical simulations to validate the proposed approach for different numbers of vehicles and landmark configurations. We also compare the results with EKF-based estimation to show the superiority of the proposed closed form approach.

Multi-AAV Cooperative Path Planning using Nonlinear Model Predictive Control with Localization Constraints

TL;DR

The paper tackles joint cooperative localization and path planning for multiple AAVs in GPS-denied environments by marrying nonlinear model predictive control (NMPC) with moving horizon estimation (MHE). It introduces an analytical, closed-form covariance approximation derived from the vehicle-landmark graph to predict localization uncertainty within the NMPC prediction window, enabling real-time planning with localization constraints. Through extensive simulations, the approach demonstrates near-optimal paths, superior localization accuracy compared with EKF-based estimation, and clear benefits from inter-vehicle cooperation, while also showing scalability to larger teams. These results suggest practical viability for coordinated AAV missions in urban canyons and similar GPS-denied scenarios, with avenues for future enhancements such as obstacle avoidance and landmark management.

Abstract

In this paper, we solve a joint cooperative localization and path planning problem for a group of Autonomous Aerial Vehicles (AAVs) in GPS-denied areas using nonlinear model predictive control (NMPC). A moving horizon estimator (MHE) is used to estimate the vehicle states with the help of relative bearing information to known landmarks and other vehicles. The goal of the NMPC is to devise optimal paths for each vehicle between a given source and destination while maintaining desired localization accuracy. Estimating localization covariance in the NMPC is computationally intensive, hence we develop an approximate analytical closed form expression based on the relationship between covariance and path lengths to landmarks. Using this expression while computing NMPC commands reduces the computational complexity significantly. We present numerical simulations to validate the proposed approach for different numbers of vehicles and landmark configurations. We also compare the results with EKF-based estimation to show the superiority of the proposed closed form approach.
Paper Structure (14 sections, 4 theorems, 73 equations, 8 figures)

This paper contains 14 sections, 4 theorems, 73 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Problem formulation
  3. Moving horizon estimation
  4. Covariance calculation
  5. Range measurements
  6. Bearing measurements
  7. NMPC formulation
  8. Results and Discussion
  9. Simulation setup
  10. Effect of NMPC horizon length
  11. Effect of cooperation
  12. MHE vs EKF
  13. 10 vehicles
  14. Conclusions

Key Result

Theorem 1

If the Assumptions assump:MHE1,assump:MHE2 are satisfied and the Remarks rem:MHE1,rem:MHE2 hold, then there exists an upper bound defined by where $\zeta_m$ is found using the equation $c_1,c_2$, and $c_3$ are positive constants. Let and if $p$ is selected such that $a(p,\delta) <1$, then the dynamics of (eq:bound) is asymptotically stable.

Figures (8)

  • Figure 1: (a) Path planning scenario. (b) Relative position measurement graph with vehicles and landmarks as nodes and measurements as edges.
  • Figure 2: Block diagram and a graphical representation of the proposed NMPC-MHE control scheme.
  • Figure 3: (a) Different configurations of two vehicles and two landmarks. (b) Different configuration of the system with 3 vehicles and 2 landmarks (c) Notations for a general multi-vehicle-landmark RPMG.
  • Figure 4: The average computational time taken per iteration for different $\tau_h$. (a) 0.05 s (b) 0.42 s (c) 1.21 s (d) 3.43 s.
  • Figure 5: Monte-Carlo simulation for prediction horizon $\tau_h=1,25,40$. (a) Average computational time per iteration (b) Average time taken by all the agents to reach their destinations.
  • ...and 3 more figures

Theorems & Definitions (11)

  • Definition 1
  • Definition 2
  • Remark 1
  • Remark 2
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Corollary 1
  • Corollary 2
  • ...and 1 more