Coordinated UAV-UGV Trajectory Optimization via Model-Algorithm Co-Design

Teaming up heterogeneous robots enables the combination of complementary capabilities that are difficult or impossible to achieve for a single robot. For example, uncrewed ground vehicles (UGVs) can carry heavy payloads that support long-duration batteries, high-power computers, and high-performance communication and sensing units. But they often struggle in chalenging terrains and suffer from slow mobility and limited viewpoints. On the other hand, uncrewed aerial vehicles (UAVs) are highly agile, largely unconstrained by terrain, and offer superior vantage points for sensing and monitoring. Yet they often have limited payload capacity, which causes short flight endurance that necessitates frequent recharging. Building a single robot that simultaneously combines the strengths of UAVs and UGVs is often prohibitively expensive, and simply scaling up numbers of homogeneous systems may not provided all necessary capabilities. In contrast, coordinating a team of UAVs and UGVs enables missions that exceed the capabilities of individual robots while providing inherent redundancy against single-robot failures.

The OptimalX Lab, directed by Prof. Yue Yu at the Department of Aerospace Engineering & Mechanics, is collaborating with Dr. James Humann from the DEVCOM Army Research Lab to develop the mathematical and algorithmic foundations for real-time, coordinated trajectory optimization for UAV-UGV systems at unprecedented scale. This collaboration is supported by a Cooperative Research and Development Agreement between DEVCOM Army Research Lab and the Minnesota Robotics Institute, with Dr. James Humann as a lead collaborator. This research aims to extend the operational reach of UAVs in cooperative missions—including environmental monitoring, persistent surveillance, advanced air mobility, and precision agriculture—by leveraging load-carrying UGVs as mobile charging stations, localization anchors, and computational support platforms. 

Realizing this vision requires coordinated trajectory optimization that accounts not only for the objectives of individual UAVs and UGVs, but also for transitions between independent and cooperative modes of operation. These transitions occur, for example, when a UGV rendezvous with a UAV to enable mobile recharging, sensor recalibration, or access to high-power onboard computation. The resulting trajectory optimization problems must therefore jointly reason over continuous decisions, such as vehicle position trajectories, and discrete decisions, such as whether to switch between individual and cooperative modes. These problems are commonly modeled as mixed-integer nonlinear programs, which are among the most challenging classes of optimization problems due to the interplay between discrete decisions and nonlinear—and often nonconvex—constraints. 

To tackle this challenge, this research proposes a novel concept termed model–algorithm co-design, which integrates the design of optimization models—used to translate robotic decision-making problems into mathematical optimization problems—with the design of optimization algorithms that compute solutions to those problems. In many practical applications of mathematical optimization, modeling choices have cascading downstream effects on algorithm design and computational performance. For example, in UAV trajectory optimization, a critical requirement is that, at any point along the trajectory, the onboard battery must be either charging or discharging. This requirement can be modeled using a discrete optimization formulation, via a binary variable indicating the charging/discharging mode, or alternatively using a continuous optimization formulation, through nonlinear complementarity constraints that enforce mutual exclusivity between charging and discharging dynamics. These modeling choices fundamentally shape the resulting algorithmic approach: discrete formulations typically rely on branch-and-bound methods, whereas continuous formulations allow gradient-based methods. Consequently, upstream modeling decisions often determine the difficulty and performance of downstream algorithm development.

Rather than directly addressing challenges in algorithm development — such as the exponential complexity inherent in discrete optimization—this research proposes to integrate downstream algorithm development with upstream model design. By recasting challenging decision-making problems in multiagent robotic systems into novel optimization models, the proposed approach aims to expose problem structures that are more amenable to scalable optimization algorithms and, in turn, enable new directions in algorithm development. Potential research directions include studying how modeling decisions influence algorithmic scalability, convergence behavior, and solution quality, as well as developing principled guidelines for model-algorithm co-design, with a particular emphasis on applications in multi-robot trajectory optimization.

Beyond UAV–UGV systems, this research has broader implications for multi-robot systems operating at scale by advancing a model-algorithm co-design perspective on coordinated autonomy. Rather than improving individual robots in isolation, the proposed approach emphasizes how modeling choices shape the feasibility and efficiency of coordination among heterogeneous robots with complementary capabilities, including mobility, sensing, endurance, payload capacity, and onboard computation. It aims to support real-time multiagent decision-making in dynamic and uncertain environments. The resulting capability in planning and replanning opens possibility to coordinated autonomy in larger and more diverse robotic teams, with potential applications in environmental monitoring, infrastructure inspection, disaster response, precision agriculture, and future air-ground mobility systems.