Model-Predictive Trajectory Generation for Aerial Search and Coverage

2024-03-09

AI Summary

This work addresses the search-and-cover problem for unmanned aerial vehicles (UAVs) operating in environments with prior uncertainty maps modeled by Gaussian Mixture Models (GMMs). We formulate the task as an optimal control problem (OCP) aimed at maximizing uncertainty reduction. To solve it, we propose an uncertainty-driven real-time trajectory planning framework based on model predictive control (MPC) with a relaxed objective function. Crucially, we introduce a visibility-region overlap penalty into the MPC cost—first such incorporation—to promote efficient exploration while avoiding redundant sensing. Unlike conventional approaches relying on spatial discretization or mixed-integer programming, our method directly solves the problem via nonlinear programming (NLP), enabling millisecond-scale online replanning. Extensive simulations and real-world outdoor flight experiments demonstrate that the generated trajectories are smooth and highly efficient, achieving significantly higher coverage performance than baseline methods. The approach exhibits strong robustness and practical engineering applicability.

Technology Category

• Planning, Routing, and Scheduling: Planning under Uncertainty
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• User Modeling, Personalization and Recommendation: ML for personalized search and recommendations
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

This paper introduces a trajectory planning algorithm for search and coverage missions with an Unmanned Aerial Vehicle (UAV) based on an uncertainty map that represents prior knowledge of the target region, modeled by a Gaussian Mixture Model (GMM). The trajectory planning problem is formulated as an Optimal Control Problem (OCP), which aims to maximize the uncertainty reduction within a specified mission duration. However, this results in an intractable OCP whose objective functional cannot be expressed in closed form. To address this, we propose a Model Predictive Control (MPC) algorithm based on a relaxed formulation of the objective function to approximate the optimal solutions. This relaxation promotes efficient map exploration by penalizing overlaps in the UAV's visibility regions along the trajectory. The algorithm can produce efficient and smooth trajectories, and it can be efficiently implemented using standard Nonlinear Programming solvers, being suitable for real-time planning. Unlike traditional methods, which often rely on discretizing the mission space and using complex mixed-integer formulations, our approach is computationally efficient and easier to implement. The MPC algorithm is initially assessed in MATLAB, followed by Gazebo simulations and actual experimental tests conducted in an outdoor environment. The results demonstrate that the proposed strategy can generate efficient and smooth trajectories for search and coverage missions.

Problem

• Develop UAV trajectory planning for search and coverage missions
• Maximize uncertainty reduction using Model Predictive Control
• Overcome intractable Optimal Control Problem with relaxed formulation

Innovation

• UAV trajectory planning with Gaussian Mixture Model
• Model Predictive Control for optimal solutions
• Efficient real-time planning using Nonlinear Programming