FIREFLY: Fair, Safe Multi-UAV Planning

• FIREFLY Software is a distributed fairness-aware motion planning framework that equitably allocates energy among UAV teams while ensuring mission safety.
• It employs a two-stage receding horizon architecture that combines decentralized fair planning with real-time safety control via CBF-CLF quadratic programs.
• The framework achieves scalable performance with validated fairness improvements and adaptable runtime trade-offs for multi-agent missions.

FiReFly Software refers to a distributed, fairness-aware motion planning framework for multi-UAV (unmanned aerial vehicle) teams, designed to optimize the equitable distribution of energy expenditure among agents while guaranteeing safety and real-time performance (Fronda et al., 20 Aug 2025). The architecture integrates a distributed fairness-centric planner with online safety controllers operating in a receding horizon framework. FiReFly is applicable to reach-avoid and multi-agent resource-sharing missions, emphasizing both mission success and the fair allocation of control effort.

1. Two-Stage Distributed Receding Horizon Architecture

FiReFly operates in discrete time and iteratively solves a two-stage problem at each step:

1. Distributed Fair Planning:
   • Each UAV computes a finite-horizon state and input sequence.
   • A fairness metric—commonly the variance in normalized energy across agents or in energy surges—is minimized with respect to agent-specific dynamics, actuation bounds, and terminal goal constraints.
   • The solution is computed in a distributed, decentralized manner using a modified block coordinate descent procedure. Each agent updates its input according to its local copy of the global state and the gradient of the fairness objective.
2. Online Safety Control:
   • After initial planning, each UAV’s control is passed through a real-time quadratic program enforcing safety via Control Barrier Functions (CBFs) and progress via Control Lyapunov Functions (CLFs).
   • This safety layer minimally perturbs the fair plan, ensuring collision avoidance (inter-agent and with obstacles), input constraints, and steady progress to the specified goal regions.

This division between fairness-centric planning and safety-centric execution provides a modular approach suitable for scaling to larger robotic teams.

2. Fairness Principles and Mathematical Formulation

FiReFly introduces several fairness notions, each formalized as a function of the control sequences:

• Normalized Energy: For UAV $k$, normalized energy $e_k$ is defined as:

$e_k = \frac{1}{\underline{e}_k} \sum_t (u_k[t])^2,$

where $\underline{e}_k$ is the minimum energy needed by agent $k$ to reach the goal in isolation.

• Variance-Based Fairness:

$$f_1(u) = \text{Var}(\mathbf{e}) = \frac{1}{N} \sum_k (e_k - \bar{e})^2$$

with $\bar{e} = \frac{1}{N}\sum_k e_k$.

• Effort-Penalized Fairness:

$f_2(u) = f_1(u) + \beta u^\top Q u$

with $Q$ positive definite, $\beta > 0$.

• Surge-Based Fairness: Considering control surges above a threshold $M$, for UAV $k$,

$z_k = \sum_t (|e_k[t] - e_k[t-1]| - M)$

and,

$$f_3(u) = \text{Var}(\mathbf{z}) = \frac{1}{N} \sum_k (z_k - \bar{z})^2$$

where $\bar{z} = \frac{1}{N} \sum_k z_k$.

These fairness objectives encourage balanced resource consumption even when underlying tasks differ in intrinsic difficulty.

3. Distributed Fair Motion Planning Algorithm

The central distributed planning algorithm operates as follows:

1. Each UAV $k$ holds a copy of the planning variables and fairness gradient.
2. At outer iteration $r$, agent $k$ solves for a descent direction $\epsilon_k^{(r)}$ to minimize:

$$-(\epsilon_k^{(r)})^\top \nabla_{u_k} f(u^{(r-1)}) + \kappa \|\epsilon_k^{(r)}\|^2$$

subject to local dynamics, actuation, and terminal goal constraints.

1. The step is applied via $$u_k^{(r)} = u_k^{(r-1)} + \gamma^{(r)}\epsilon_k^{(r)}$$ with an update scale $\gamma^{(r)}$.
2. Iterations proceed until convergence (change in fairness objective below some threshold).

This procedure eliminates the bottleneck of a centralized update and fits real-time, scaling requirements.

4. Safety Controller via CBF-CLF Quadratic Program

Safety and progress toward goal regions are enforced during execution by solving, at each time step $t$, a QP:

• Variables: updated control $u[t]$ and slack $\delta$
• Objective: $\|u[t]-u^{fair}[t]\|^2 + \delta^2$
• Constraints:
  • CBF: $$\nabla h(s[t])^\top (A s[t] + B u[t]) + \alpha h(s[t]) \geq 0$$ (forward invariance of safe set)
  • CLF: $$\nabla V(s[t])^\top (A s[t] + B u[t]) + \lambda V(s[t]) \leq \delta$$ (goal progress)
  • Input box constraints

Where $h$ encodes minimum distances for inter-UAV and obstacle avoidance, $V$ encodes distance to goal, and $\delta$ allows for feasible relaxation when strict satisfaction is impossible.

5. Performance Metrics, Trade-offs, and Scalability

Performance and scalability are quantified by:

• Mission Success Rate: The fraction of UAVs achieving their goal within planning horizons, consistently near 100% for up to 15 UAVs.
• Fairness Metrics: Reduction in variance-based or surge-based fairness objectives versus a non-fair baseline. For teams up to 50 UAVs, the framework yields improved fairness, though absolute improvement may decrease with scale.
• Runtime: Real-time computation is achievable for up to 15 UAVs. With increased team size, tighter convergence criteria in distributed planning incur higher runtimes (up to $10^3$-fold increases with strict thresholds), necessitating trade-offs between fairness and responsiveness.
• Adaptivity: FiReFly allows user-specified tuning: reducing the frequency or strictness of the fair planner can yield faster, less fair solutions, while more frequent or stricter re-planning improves fairness at computational cost.

6. Distinctive Features and Innovations

• Explicit Fairness: FiReFly’s key innovation is the explicit integration of fairness principles (energy and surge variance minimization) into the receding horizon control loop, in contrast to classical approaches prioritizing only mission success or safety.
• Distributed Implementation: The decentralized, block coordinate descent structure avoids central coordination, facilitating deployment in airspaces with many UAVs.
• Safety via CBF-CLF QP: Combining minimally invasive safety adjustments with fairness-aware planning ensures both theoretical safety guarantees and practical resource balancing.

7. Implications and Outlook

FiReFly advances state-of-the-art multi-agent planning by demonstrating that fairness and safety can be co-optimized within a distributed, real-time receding horizon control paradigm. Key implications include:

• Scalable Fair Resource Allocation: The distributed formulation supports deployment in teams of up to 50 UAVs, conditional on fairness-runtime trade-offs.
• Broader Applicability: The generic formulation of fairness objectives and the modular two-stage architecture can be adapted to other multi-robot domains with heterogeneous resource constraints.
• Future Directions: Further research may focus on improving convergence for very large teams, exploring alternate definitions of fairness, and extending to scenarios with stricter or time-varying safety requirements.

FiReFly establishes a rigorous framework for fairness-oriented, safe, and computationally efficient multi-UAV motion planning, providing an effective design template for multi-agent systems where both mission performance and equitable resource usage are critical (Fronda et al., 20 Aug 2025).