💻 computer science

STL-Based Motion Planning and Uncertainty-Aware Risk Analysis for Human-Robot Collaboration with a Multi-Rotor Aerial Vehicle

This paper presents an uncertainty-aware motion planning and risk analysis framework that utilizes Signal Temporal Logic and smooth robustness approximations to generate safe, dynamically feasible trajectories for multi-rotor aerial vehicles collaborating with humans in uncertain environments, validated through simulations of power line maintenance tasks.

Original authors: Giuseppe Silano, Amr Afifi, Martin Saska, Antonio Franchi

Published 2026-07-29

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CC BY 4.0

Original authors: Giuseppe Silano, Amr Afifi, Martin Saska, Antonio Franchi

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a world where robots aren't just clunky metal boxes that follow simple commands, but nimble partners capable of working right alongside humans in tricky, dangerous places. This is the frontier of "Human-Robot Collaboration," a field where engineers try to teach machines to understand not just where to go, but how to move so they don't scare, hurt, or annoy the people they are helping. To do this, scientists use a special kind of "robot language" called Signal Temporal Logic (STL). Think of STL not as code, but as a very strict, very detailed recipe. Instead of just saying "go to the kitchen," it says, "stay inside the kitchen walls, avoid the stove, approach the human from the front (never the back!), move slowly so you don't blow their hair back, and wait for exactly five seconds before handing over the cookie." This paper tackles the hard problem of making a flying robot (a drone) follow these complex, human-friendly recipes while dealing with real-world physics, wind, and the fact that humans might wiggle or move unexpectedly.

The authors of this paper, Giuseppe Silano and his team, have built a new "brain" for a multi-rotor drone designed to help humans, specifically in high-stakes jobs like fixing power lines high in the air. Their goal was to create a system where the drone doesn't just fly from point A to point B, but flies in a way that is safe, comfortable, and respectful of the human worker's space. They used their "STL recipe" to encode rules like "don't approach from behind," "keep the propeller noise low," and "wait until you are directly in front of the worker before handing over a tool."

The team discovered that making a drone follow these strict, human-centric rules is incredibly difficult because the math involved is messy, bumpy, and full of twists and turns (what mathematicians call "non-convex and non-smooth"). To solve this, they invented a clever trick: they smoothed out the bumpy math, allowing the computer to use powerful gradient-based tools to find the best path. They also added a "comfort mode" to the drone's brain, which minimizes energy use and keeps the propellers from spinning too fast near the human, reducing noise and wind.

But here is the really cool part: the team realized that humans aren't perfect statues; they wiggle, shift, and might not stand exactly where the drone expects. To handle this, they created a "risk radar." This system doesn't just guess if the plan will work; it runs thousands of simulations in the computer's head, imagining the human moving in slightly different ways. It then calculates a "safety score" (using something called Value-at-Risk) to tell the operators: "If the human moves this much, there is an 80% chance the drone will still be safe, but if they move that much, we need a new plan."

Finally, they gave the drone a "panic button" strategy. If the drone gets blown off course by a sudden gust of wind or a battery hiccup, it doesn't just crash or give up. Instead, it triggers an instant, on-the-fly replanning mode. This mode is a "safety-first" version of the main brain; it temporarily ignores the fancy comfort rules to focus entirely on getting the drone back to a safe path as fast as possible, ensuring it never hits the human or the obstacles.

The team tested all of this in a virtual world using a simulator called Gazebo, which mimics real physics, and in a computer program called MATLAB. In these simulations, the drone successfully delivered tools to a human worker in a power-line maintenance scenario. It avoided obstacles, approached from the preferred direction, kept its speed low and quiet, and even recovered when they "pushed" it off course with simulated wind. The results suggest that this method works well to create a safe, efficient, and polite flying robot, though the authors note these are simulations and real-world field tests are the next step. They didn't just prove the drone could fly; they proved it could fly nicely and safely even when things get a little uncertain.

Technical Summary: STL-Based Motion Planning and Uncertainty-Aware Risk Analysis for Human-Robot Collaboration with a Multi-Rotor Aerial Vehicle

Problem Statement
The paper addresses the challenge of enabling safe, ergonomic, and comfortable collaboration between Multi-Rotor Aerial Vehicles (MRAVs) and human operators in high-risk, close-proximity environments, specifically motivated by power line maintenance scenarios. Existing aerial human-robot interaction (HRI) approaches often fail to jointly address nonlinear vehicle dynamics, actuation limits, ergonomic constraints, temporal mission requirements, and human pose uncertainty within a unified framework. While some methods handle safety or perception, few incorporate formal temporal logic to encode complex mission objectives (such as approach direction, visibility, and timing) while explicitly modeling the full nonlinear dynamics of the aerial platform. The core problem is to compute dynamically feasible trajectories that satisfy these multifaceted specifications while quantifying the risk of specification violations under uncertainty.

Methodology
The proposed framework integrates Signal Temporal Logic (STL) with nonlinear optimization and risk analysis.

System Modeling: The MRAV is modeled as a Generically-Tilted Multi-Rotor (GTMR) system using full nonlinear Newton-Euler dynamics, accounting for both underactuated and fully-actuated configurations. The state includes position, orientation, linear and angular velocities, and motor forces.
Mission Specification via STL: Mission objectives are encoded into a single STL formula ( $\pi$ $π$ ). This formula combines:
- Safety: Workspace containment, obstacle avoidance, and prohibiting approaches from behind the operator.
- Visibility: Reaching a designated location in front of the operator and maintaining heading alignment for visual contact.
- Ergonomics: Approaching from operator-preferred directions (e.g., front, side, top).
- Comfort: Limiting approach velocity and propeller speeds to reduce noise and wind.
- Temporal Logic: Enforcing specific sequences (e.g., visibility phase before handover) and time windows.
Optimization-Based Planning: The trajectory generation is formulated as a nonlinear, non-smooth, and non-convex optimization problem. The objective minimizes an energy term (to extend endurance) while maximizing the robustness of the STL formula.
- Smooth Approximation: To handle the non-differentiable min/max operators inherent in STL robustness calculation, the authors employ a smooth approximation (based on Log-Sum-Exponential and smooth min/max functions). This enables the use of gradient-based optimization techniques (specifically IPOPT via CasADi).
- Constraints: The optimization explicitly enforces the GTMR dynamics, actuator force limits, and a minimum robustness threshold ( $\kappa$ ) to ensure safety margins.
Uncertainty-Aware Risk Analysis: To address human pose uncertainty, the framework treats the human state as a stochastic process. It computes the robustness score for thousands of realizations of human pose variations. Risk metrics, specifically Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR), are calculated to quantify the probability of STL specification violations. This allows operators to determine if a planned trajectory remains safe under specific levels of human uncertainty.
Event-Driven Replanning: An online recovery mechanism is introduced to handle disturbances (e.g., wind, hardware faults). Instead of re-optimizing the full mission, the system triggers a short-horizon replanner when geometric deviation or predicted safety-critical robustness falls below thresholds. This replanner enforces only the safety-critical subset of STL predicates (workspace, obstacles, no-approach-from-behind) to rapidly restore feasibility, temporarily relaxing comfort and ergonomic constraints to prioritize collision avoidance.

Key Contributions
The paper claims the following contributions:

Unified Framework: The first formulation of object handover planning for MRAVs that simultaneously integrates full nonlinear dynamics, actuator constraints, ergonomic/comfort preferences, and formal STL specifications.
Risk-Aware Analysis: A systematic method to quantify the risk of mission failure under human pose uncertainty using VaR and CVaR metrics, providing a statistical basis for mission acceptance.
Robustness-Aware Replanning: An event-triggered online strategy that prioritizes safety-critical recovery over full specification adherence during disturbances, ensuring computational efficiency and rapid reconnection to the nominal plan.
Energy-Aware Optimization: The inclusion of an energy minimization term that reshapes trajectories to reduce actuator usage and extend endurance without violating mission specifications.
Validation: Extensive validation through MATLAB numerical simulations and Gazebo physics-based simulations (Software-In-The-Loop) on an object handover task.

Results
The framework was evaluated in two stages:

MATLAB Simulations: Demonstrated that the smooth approximation enables the solution of the complex optimization problem. Results showed that including the energy term resulted in smoother trajectories with lower peak propeller speeds and reduced energy consumption compared to energy-agnostic planning, while still satisfying all STL constraints. The risk analysis successfully quantified how increasing human pose covariance degraded robustness margins, with VaR and CVaR providing clear thresholds for acceptable uncertainty levels.
Gazebo Simulations: Validated the closed-loop feasibility of the planned trajectories under full vehicle dynamics and onboard control. The system successfully executed handover tasks with different approach preferences (e.g., left-handed, top-to-bottom), adhering to velocity and propeller limits. The event-driven replanner successfully recovered from simulated disturbances within sub-second to few-second timescales, maintaining safety-critical constraints while relaxing non-critical ones.

Significance and Claims
The authors position this work as a significant advancement over prior conference versions and existing literature by moving beyond simplified vehicle models and geometric planners. The paper claims that their approach provides a rigorous, formal method for encoding complex HRI requirements (safety, ergonomics, timing) into a single optimization problem. By introducing uncertainty-aware risk metrics, the framework offers a quantitative tool to assess mission viability before execution, rather than relying on conservative margins alone. The separation of offline planning (full specification) and online recovery (safety-critical subset) is highlighted as a practical strategy for real-time deployment in dynamic, uncertain environments. The authors explicitly state that the work does not claim real-time guarantees for arbitrary unstructured environments but is tailored for repetitive, structured missions like power line maintenance. Future work is identified as field experiments and the integration of human fatigue models.

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