Results

Anthropomorphic hand with distributed touch

Designing an anthropomorphic tactile hand for aerial robots begins with understanding how human fingers achieve reliable grasping through synergistic morphology and tactile perception. Translating this biological inspiration to drone applications, moreover, requires reconciling the design with the strict payload and mass limitations of micro aerial vehicles (MAVs). Drones, in fact, rely on small batteries to power both onboard electronics and propulsion, where propulsion alone consumes nearly all the available energy. As a result, even small increases in payload can substantially reduce flight time and negatively impact maneuverability. This makes simplicity, low mass, and minimal power consumption essential design requirements for any tactile hand intended for aerial manipulation. Furthermore, such an anthropomorphic hand should reliably sustain the MAV’s weight while requiring minimal actuation or power, and adding minimal mass to the system. With these constraints in mind, we arrive at the design depicted in Fig. 1. Each finger in our system is composed of three rounded phalanges connected by revolute joints that mimic the human finger’s kinematics. Torsional springs at each joint provide passive stiffness and set the hand’s nominal posture to a naturally closed state without requiring continuous actuation. The phalanges incorporate a soft silicone interior that supplies friction and compliance for interacting with objects of varying shape, geometry, and texture, mimicking the morphologies of biological finger pads. The phalanges follow the human anatomical pattern in which the proximal segment is longest, followed by the middle and then the distal. This configuration evolved in primates to optimize grasping across diverse objects41, in particular for suspensory and climbing behaviors. By replicating this morphology, we aim to leverage these evolutionary advantages to improve the hand’s adaptability to various perching targets. To convey the sense of touch in a distributed manner, tactile sensors based on capacitance are mounted on the surface of each phalanx and provide binary contact information spread across a soft, compliant surface. A single artificial tendon running along the back of each finger connects the phalanges to a lightweight actuation spool: tightening the tendon opens the finger, while releasing it allows the springs to close the finger passively. This combination of compliant morphology, passive mechanics, and minimal actuation results in a tactile hand that is both energetically suitable for aerial perching applications and adaptable to diverse target geometries.

Fig. 1: Biological inspiration, design, and implementation of the tactile flying gripper.a The human hand leverages fingers in an antagonistic configuration relative to the thumb (left), which enables grasping objects of varying geometries and sizes while providing tactile feedback along multiple planes and directions. b Our proposed anthropomorphic hand adopts a similar configuration with distributed touch sensing. Nine tactile sensors (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{C}}}{1}$$\end{document}C1 to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{C}}}{9}$$\end{document}C9) are positioned at the center of each phalange, providing a binary contact signal whenever a sensor \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{C}}}{i}$$\end{document}Ci contacts the environment. The drone body frame of reference, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{B}}$$\end{document}B, is located at the CoM. c The mechanical implementation of the tactile hand is mounted on top of a 4-inch quad frame. We highlight the individual components. Capacitive touch sensor: copper foil connected to a capacitive sensing board provides binary information about touch events. Note that the capacitive sensor on the last phalanx is connected to copper foil on the front and the back of the phalanx, allowing for two-sided contact detection. Motor and tendon tension spool: by tensioning the tendon, the finger opens while the torsional springs in the joints ensure passive closing. All components are operated by a RaspberryPi 5 companion computer and powered by a 4S battery._

Tactile perching control

As observed in nature, touch is a critical sensing modality to align the airborne agents with their perching target. By reacting to tactile cues, the MAV can adjust its position and alignment to ensure a safe grasp, robust to position and alignment offsets. This work uses a Finite State Machine (FSM), as depicted in Fig. 2, that progresses through various states to bring the MAV from a (potentially incorrect) initial target pose estimate to a safely perched state. Hereby, the FSM relies on the following assumptions about the environment and the perching target:

Fig. 2: State machine, resulting procedure, and signal processing for the tactile perching approach.a A block diagram of the state machine used to implement the tactile perching approach. b The resulting behavior of the physical prototype when commanded by the state machine. The system transitions between TAKEOFF, SEARCHING, TOUCHED, APPROACH, POSITION, ROTATION, FINALIZE, PERCH, and ABORT, driven by contact events and pose convergence. c Processing of the raw capacitive values from the touch sensors to binary contact signals. An example trial (Trial XVII in Fig. 4) showcases the functionality of the capacitive touch sensors. By thresholding the difference from the nominal value, we obtain a robust binary signal.

A.1 The initial target pose estimate is in the vicinity of the true target pose.

A.2 The target object has a characteristic diameter that fits within the gripper.

A.3 The area surrounding the initial target estimate is free of obstacles, other than the target itself.

The following section will introduce the FSM states {TAKEOFF, SEARCH, TOUCHED, APPROACH, POSITION, ROTATE, FINALIZE, PERCHED, ABORT} and their transitions.

In TAKEOFF, the MAV executes a takeoff from the ground. It will approach a pre-defined takeoff location above the origin. Once the position error satisfies ∥epos∥ < _ϵ_pos, the FSM transitions to SEARCH.

In SEARCH, the MAV follows a search pattern defined by a vector field \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bf{g}}({{\bf{p}}}{{\mathcal{B}}},{{\bf{p}}}{{\mathcal{T}},0},t)$$\end{document}g(pB,pT,0,t), following the implementation in ref. 37. Additionally, the search pattern commands a hand opening vector \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bf{s}}({{\bf{p}}}{{\mathcal{B}}},{{\bf{p}}}{{\mathcal{T}},0},t)$$\end{document}s(pB,pT,0,t), with one value in [0, 1] per finger, denoting the degree of opening of the finger. Hereby \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\bf{p}}}{{\mathcal{B}}}$$\end{document}pB is the current position of the MAV in the world frame, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\bf{p}}}{{\mathcal{T}},0}$$\end{document}pT,0 is the initial pose estimate in the world frame, and t is the current time. Hereby, the vector field specifies the target velocity of the MAV at a certain location and time, and s is the hand opening state. We choose to implement the vector field as a height-stepping sinusoidal figure-eight pattern as depicted in Fig. 2. The search pattern is planar; after each completed cycle of the search pattern, we increase its altitude. At the same time, we also command the MAV to slowly open and close the hand such that it reaches its opening apex at the apexes of the figure-eight. This increases the reach of the search pattern and therefore the chance of a touch event occurring. A touch event triggers a transition to TOUCHED.

In TOUCHED, the MAV exploits the first contact to obtain an initial target estimate and moves to a reference position offset below and away from the contact point (toward the direction of the body frame at the center-of-mass (CoM) of the MAV \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{B}}$$\end{document}B) by Δ__z and Δ__γ, with the hand fully opened. When ∥epos∥ < _ϵ_pos, the FSM enters APPROACH.

In APPROACH, the MAV moves to a reference position offset below the contact-based target position estimate and switches to POSITION once the position error again falls below _ϵ_pos.

In POSITION, the MAV moves to the target position estimate without any offset, after having positioned itself below during the previous state; satisfaction of ∥epos∥ < _ϵ_pos then leads to ROTATE.

In ROTATE, the MAV incrementally closes its fingers to provoke contact, using the pattern of contact to infer the target orientation: fingers that detect contact stop closing, and the MAV yaws away from them until the contact is no longer present. Since the closing values for all fingers increase monotonically, i.e., the fingers do not reopen during this state, the process is guaranteed to converge to a fully closed grasp. Furthermore, small lateral position corrections are applied if contact is unilateral. This process continues until all arms report at least one pad with consistent contact, at which point the FSM transitions to FINALIZE.

In FINALIZE, all fingers are driven to a fully closed configuration and the grasp is validated by checking that all bottom pads are active and tendon tensions have equalized. A valid grasp leads to the terminal PERCHED state, in which the MAV is supported by the target and its motors are turned off.

From any state, if the tracking error exceeds the safety threshold _ϵ_abort, the FSM transitions to ABORT. In ABORT, the MAV returns to a safe hover above the origin and re-enters SEARCH, thereby re-initializing the perching attempt.

Robustness to target offsets

In order to quantitatively evaluate the performance of the proposed tactile-based perching strategy, we perform a Monte-Carlo simulation study. We conduct 100 simulated trials for various offsets in initial target position and orientation offsets as well as different target cylinder radii. We employ the Genesis World simulator42 in which a 6-degree-of-freedom (DoF) model of the MAV and a tendon-actuated gripper with linear joint stiffness is simulated. The low-level position, orientation, and rate controllers of the MAV are fed noisy state measurements to increase representativeness of real-world conditions. Figure 3 shows a set of still images of one of the experiments as well as the resulting success rates and mean time to perch for the proposed method and a baseline feed-forward perching strategy without tactile feedback. The baseline feed-forward perching strategy is implemented by commanding the MAV to approach the target at its initial pose estimate from below, and fully closing the hand after reaching the target position estimate, without considering any feedback. Supplementary Movie 1 shows animations of representative trials for rotational, inclinational, and positional misalignments, as well as a single experiment from the Monte-Carlo study. Except for the inclinational sweep, the tactile-based perching strategy outperforms the feed-forward baseline in all experiments, showing a larger bandwidth with success rates above 99% for positional offsets, for orientation offsets and for target cylinder radii. The inclinational sweep shows that the underactuated gripper alone is capable of adapting to the target orientation, enabling a robust perching strategy.

Fig. 3: Robustness of the proposed approach to target pose estimation offsets, and target sizes.a Still images of 100 trials of a single experiment. b The success rate and the mean time to perch with its standard deviation. We compare a baseline feed-forward perching strategy (orange) with our tactile-based perching strategy (blue). (From left to right) 100 trials for various positional offsets, 100 trials for various rotational offsets, 100 trials for various inclinational offsets, and 100 trials for various target sizes. c The anthropomorphic, compliant hand supporting the full MAVs weight while hanging from various structures of different diameters and shapes. Thanks to its parallel revolute joints, the gripper exhibits passive compliance, allowing it to adapt to a wide range of targets. Even objects with non-uniform diameters and low-friction plastic or metallic surfaces, such as a traffic cone or a structural T-Beam, can be grasped and support the MAVs weight, as the arms close passively and compress until the contact force balances the spring torsion.

To showcase the ability of versatile grasping, we perform a series of static perching experiments with targets of different shapes and sizes and surfaces. Each finger of the gripper contains three parallel revolute joints, making it compliant to different structures, and thus enabling the MAV to attach itself to differently shaped targets. Figure 3 shows the gripper successfully hanging from various structures, including a human arm, multiple tree branches of different diameters, rectangular wooden beams, and a traffic cone with a varying diameter and a very s low-friction plastic surface. In each case, different phalanges take on the role of the main contact point, and consequently a different revolute spring carries the main portion of the load. This demonstrates the gripper’s adaptability solely through its mechanically compliant design.

Using the physical prototype introduced before, we perform a series of flight experiments to validate the proposed tactile-based perching strategy. We conduct 26 trials with different target geometries and initial target pose estimate offsets as detailed in Fig. 4. Supplementary Movie 2 shows a close-up of the tactile perching procedure as well as a top-down view of all trials. All data collected during these experiments are provided via our repository (https://github.com/BioMorphic-Intelligence-Lab/feely_drone). Figure 5 shows still images of one of the trials as well as the time series data of the x coordinate and yaw angle for all 26 trials. It shows that in all trials the MAV is able to converge to the correct target position and orientation. Naturally, some trials take longer, as the duration of the searching phase is dependent on the drone starting position, the initial target position offset, and the initial target orientation offset, which lead to different contact times.

Fig. 4: Experimental setup (offsets) and result (success & time-to-perch) of each trial with the physical prototype.a, b Table of initial target pose estimation offsets (x and y position and angle θ for yaw and inclination) for all trials with the cylindrical and T-Bar perching target, respectively. The trials highlighted in bold are further visualized in Fig. 5. c Time series data of the MAV's x position and yaw angle, showcasing all trials aligning with and converging to the target pose. The data are normalized to have the target pose at the origin. Note that the data is normalized such that the approach happens entirely along the x axis. The black dots indicate when a trial has successfully reached the perching state.

Fig. 5: Visualizations of experiments with the physical prototype.a Three-dimensional trajectory plots of selected trials. For different initial takeoff positions and initial offsets, contact occurs at different times. However, in all cases the proposed approach is able to align with and successfully perch on the target. b Snapshots of Trial XIII from Fig. 4 showcasing the different phases of the tactile perching maneuver. See Fig. 4 for the initial offsets.

This is further illustrated in Fig. 5, which shows the 3D trajectory of selected trials. E.g., in trial III the MAV makes contact immediately during the initial approach and therefore aligns quickly with the target, while in trial XI the MAV performs multiple passes of the search pattern until contact occurs and therefore aligns later. Additionally, Fig. 6 shows the x, y, and z position, arm opening states, contact data, and state-machine states over the full duration of Trial III. After takeoff, the MAV executes the search pattern while opening and closing its fingers. A single contact occurs at t = 15 s, which triggers the MAV to safely approach the target from below and perform alignment. Finally, all fingers close, sufficient contact is detected at around t = 35 s, and a stable grasp is confirmed, triggering the perch state.

Fig. 6: Highlights of the proposed system's capabilities.a Full trial overview plot for trial III (c.f. Fig. 5) showcasing the position, arm opening states, and contact signals over the different phases of the tactile perching procedure. Initially, the MAV takes off, then it proceeds to search for the target; contact occurs, and it approaches the target, then it positions underneath the target and starts aligning rotationally. During finalization, it then closes all fingers until it can confirm a stable grasp and enters the perch state. b, c Still images (videos in supplementary material) of the tactile perching procedure for a steeply inclined cylindrical (Trial XV) and T-Bar target (Trial XX), respectively.