Aerial robots typically avoid vegetation, but traversing compliant obstacles like branches could open access to new areas for applications such as environmental monitoring, precision agriculture, and search and rescue. Existing aerial physical interaction (APhI) approaches, using impedance or admittance controllers, are mainly suited for rigid surfaces. While model-based or robust controllers can handle different interaction modes (pushing, sliding), they often require complex switching policies and accurate environmental models, which are challenging to obtain for the complex and stochastic nature of vegetation. Current drones also typically rely on sensorized end-effectors, limiting interaction versatility. In contrast, animals exhibit remarkable locomotion strategies, seamlessly transitioning between modes by synergistically integrating body morphology, sensing, and feedback control. This research takes inspiration from nature to develop an embodied APhI strategy for traversing single compliant obstacles with a wide, unknown range of stiffness values.

Existing methods for aerial physical interaction primarily focus on rigid or predictable environments. Impedance and admittance controllers, while simple to implement, struggle with compliant surfaces. Model-based and robust controllers offer improved adaptability, demonstrated in tasks like pushing doors or sliding along surfaces, but these usually require high-level switching policies based on empirically-tuned thresholds. These thresholds are particularly difficult to define for unpredictable environments like vegetation. Existing research on APhI with elastic obstacles is limited. Furthermore, current approaches mainly focus on sensorized end-effectors, while vegetation traversal necessitates distributed sensing along the entire robot body. In contrast, animals cleverly integrate morphology, sensing, and control to navigate complex terrains, offering a valuable source of inspiration for robotic design.

This study uses an underactuated aerial robot equipped with a sensorized discoid shell. The disc shape enables contact and sensing across the entire shell, promoting sliding and simplifying control. A six-axis load cell provides distributed haptic sensing. A Nonlinear Model Predictive Control (NMPC) framework is employed. The NMPC considers the full drone dynamics and the external wrench from the obstacle. The controller includes cost terms for path following and physical interaction (impedance behavior), and safety constraints to prevent oscillations and ensure smooth transitions between interaction modes. The NMPC does not require a contact model or knowledge of the obstacle's stiffness, making it adaptable to various compliance levels. The mathematical formulation and implementation details are provided in the Methods section of the original paper and supplementary materials.

Experiments were conducted using a hinged compliant plate with three stiffness values (18, 77.8, and 155.5 N mm rad⁻¹), representing low, mid, and high stiffness. The drone successfully traversed the obstacle in most experiments across all stiffness levels. Analysis of the interaction phases (pushing, sliding, push-and-slide) showed seamless transitions. Quantitative metrics (lateral position error, longitudinal velocity error, maximum force, attitude oscillations) showed consistent performance across stiffness levels, with minor increases in force and pitch oscillations for higher stiffness. An ablation study demonstrated the synergistic importance of both the task-oriented morphology (streamlined, low-friction shell) and the haptic feedback control. Using a squared cage or a high-friction surface resulted in failure. Disabling haptic feedback also caused failure, particularly with higher stiffness obstacles. Experiments with real branches (with and without leaves) further validated the approach, exhibiting similar successful traversal but with shorter interaction times and lower forces and oscillations compared to the hinged plate experiments.

The results show that the synergistic interplay between a task-oriented morphology and a haptic feedback controller is crucial for successful compliant obstacle traversal. The streamlined, low-friction shell enables smooth transitions between interaction modes, reducing the need for complex switching logic. The NMPC controller effectively dampens oscillations without requiring a model of the obstacle's elastic response. The approach generalizes well across a range of stiffness values. These findings highlight the importance of embodied intelligence for tackling complex tasks in unstructured environments.

This study presents a novel embodied aerial physical interaction strategy for traversing single compliant obstacles with unknown stiffness. The synergy between a streamlined, sensorized shell and a haptic-based NMPC controller allows for successful traversal across a wide range of compliance levels. Future research should focus on extending the approach to multiple obstacles, improving haptic sensing resolution for better contact localization and compliance estimation, and integrating high-level path planning for navigation in complex, real-world scenarios.

The current prototype's discoid shell leaves the propellers vulnerable to collisions. A spherical or energy-absorbing cage could improve robustness. The current haptic sensing measures net wrench, limiting the ability to discern individual contacts and accurately assess local interaction forces, posing a challenge for environments with multiple obstacles. Higher-resolution haptic sensing and advanced path planning are needed for improved performance in complex vegetation.