RoboFly: An insect-sized robot with simplified fabrication that is capable of flight, ground, and water surface locomotion

The RoboFly has a set of four passive legs in vertical plane as shown in Fig. 1. This wide stance provides fabrication simplicity and facilitates landing.

The piezo actuators were driven by a desktop computer equipped with a digital-to-analog conversion board (NI 6259) running Simulink Real-Time (MathWorks, Natick, MA, USA) and amplified using three high voltage amplifiers (Trek 2205, Lockport, New York). One amplifier supplies the DC ‘bias’ signal to both actuators; the other two amplifiers each supply the separate sinusoidal drive signals to the two wings.

Ground locomotion is performed by flapping the wings at a lower frequency than is needed for takeoff. We chose the stroke amplitude for ground locomotion to be same as that for flight. Stroke amplitude is determined by the amplitude of the drive signal voltage (Figs. 3, 4).

The wing flapping frequency is varied depending on the mode of the locomotion that we want to carry out. However, it is kept constant for a particular mode which can be one of the following set of actions at any time instance– ground locomotion, water locomotion, and flight. Maneuvers while performing these actions were carried out by varying the voltages at which the actuators are driven. All actions besides flight are performed at non-resonant frequency to avoid accidental lift-off. Each actuator is driven at a voltage signal, $V(t)=V_{0}+A_{0}\sin(\omega t)+A_{1}\sin(2\omega t)$, where $V_{0}$ is the offset voltage, $A_{0}$ the amplitude, $A_{1}=\mu A_{0}$ the amplitude for the second harmonic term; a typical value $\mu$ ranges from $-$0.3 to 0.3. By adding a second harmonic at double the frequency, so that either the downstroke or upstroke is faster (Fig. 4), the robot is driven forward or backward as result of aerodynamic drag on the wings. For example, forward motion occurs when the signal to the wings drives them rapidly backwards. A similar mechanism was proposed to induce torques about a vertical or yaw axis in [3] and [29].

In case of aerial locomotion, the wings are flapped at resonant frequency to generate maximum lift. One way to determine the resonant frequency that maximizes the lift for flapping-wing micro aerial vehicles (FWMAV) is presented in [30], in which the authors performed the system identification of an FWMAV to fit a linearized second order model.

We hypothesized that forward motion on the ground is due to the robot momentarily exceeding coulomb friction during the fast period of the wing stroke. To determine whether this motion was primarily driven by inertial or by aerodynamic forces, we performed an experiment in which the wings were replaced by carbon rods with identical mass and moment of inertia. When supplied with driving signals that moved the robot when it was equipped with wings, it was observed that the robot with carbon rods did not move significantly from its initial position. This indicates that the forces causing the ground locomotion are mainly due to the aerodynamic drag acting on the wings. To understand why this should be so, we note that the Reynolds’ number of the wing is approximately 3000 [27], that is, dominated by inertial forces. This indicates that drag is proportional to the square of the wing velocity according to $f_{d}=\frac{1}{2}C_{D}\rho Av^{2}$, where $C_{D}$ is the aerodynamic drag coefficient, $\rho$ is the air density, $A$ is the frontal area of the wing, and $v$ is the velocity of the wing. Therefore, a faster wingstroke with a higher $v$ will produce higher drag than a slow stroke.

Fig. 5 and the supplementary video [31] show the robot performing ground locomotion along a straight line. In these trials, the wings were flapped at 60 Hz with an amplitude 210 V. Fig. 8 and the video [31] show that ground ambulation allows the robot to navigate under a closed door.

To determine how the driving signal affects locomotion, the RoboFly was driven in the forward direction with a range of different voltages and frequencies. Displacements were measured with a ruler, and the speed was calculated by dividing by the time taken. The results show that robot velocity increases with increasing flapping frequency and amplitude (Fig. 6). We conjecture that the large velocity increases that occur at different amplitudes are the result of the robot overcoming coulomb friction at a critical phase of wing flapping. The small increase from 225 V to 250 V is likely attributable to the small resulting additional stroke amplitude.

Steering is performed by varying the signals given to each flapping wing independently. To steer the body to the left, the left wing is flapped at a reduced drive signal amplitude relative to the right wing (Fig. 7). The rate of rotation is determined by the relative drive signal amplitude difference in the two wings. A sharp turn can be achieved by keeping one wing stationary while the other wing flaps. The extreme continuation of this would be rotation about a vertical axis passing through the center of the body, for which the wings are flapped 180°out of phase. A continuous range of turn angles can be achieved by modulating the difference between left and right wing drive signals.

Fig. 9 and the supplementary video [31] show that the robot is able to steer in addition to moving forward. Here, the wings were flapped at 70 Hz as above, but the left wing was flapped with larger drive signal amplitude (250 V) whereas the right wing was flapped at a lower value (200 V). Similarly, the robot was observed to steer in the other direction when these amplitudes were reversed. Moving backwards was also achieved using the appropriate driving signal.

Hovering at a specified location in space was performed using feedback from a motion capture (MoCap) system (four Prime 13 cameras, OptiTrak, Inc., Salem, OR) which tracks retroreflective markers attached on the robot. This MoCap system sends position and orientation information over Ethernet at 240 Hz to the host desktop computer which runs Simulink Real-Time.

RoboFly is an under-actuated system. However, it can move to any point in space by changing its attitude and tilting the thrust vector in the desired direction of motion. For altitude control the robot uses a proportional-integral-derivative (PID) controller to achieve desired height. The controller used by the robot for position control is shown in the block diagram in Fig. 10. The MoCap system, through the host computer, continuously sends the position and orientation data over the ethernet to the Simulink Target computer which runs the controller. When the controller is fed with the reference point $[x_{d}(t),y_{d}(t),z_{d}(t)]^{T}$, it varies the signal amplitude to react to the error in altitude, as mentioned above. At the same time, the controller varies the wing signal according to two control loops— inner attitude loop and outer lateral position loop, as shown in the block diagram.

As for the altitude controller which runs in parallel with the attitude controller, the height of the robot is controlled using a PID controller. The thrust generated by the wings of the robot is approximately linear with the wing amplitude. Vertical acceleration can be written by the control law as follows:

where $e_{z}=z_{d}-z$ is the error between desired height $z_{d}$ and current height $z$; $k_{ph}$, $k_{dh}$ and $k_{ih}$ are proportional, derivative and integral gains, respectively. $z$ values received from the MoCap system are first filtered using a low-pass Butterworth filter before taking derivatives.

As for the cascaded lateral and attitude controllers, the outer loop receives the current and desired lateral positions in the world coordinate system. The error goes through a proportional-derivative (PD) controller, which generates a desired change in attitude vector trajectory $\mathbf{\hat{z}_{d}(t)}$ which is fed into the inner attitude control loop. The outer loop assumes that the inner loop responds to attitude changes almost instantaneously.

In the outer loop, the lateral position of the robot is controlled by determining the desired inclination trajectory $\mathbf{\hat{z}_{d}}=[\hat{z}_{dx}\hskip 3.61371pt\hat{z}_{dy}]^{T}$. This is performed by a PD controller in the world coordinate system:

where $(x,y)$ and $(x_{d},y_{d})$ are the current and desired lateral positions in global coordinate system, respectively; $k_{pl}$ and $k_{dl}$ are the proportional and derivative gains, respectively.

In the inner loop, attitude is controlled by rotating the robot’s thrust vector towards the desired lateral position. In other words, objective of the inner loop is to align the thrust vector $\mathbf{\hat{z}}=[\hat{z}_{x}\hskip 3.61371pt\hat{z}_{y}]^{T}$ along the desired inclination trajectory $\mathbf{\hat{z}_{d}}$. So far we have everything in the world coordinate system; however, desired roll and pitch torques need to be determined in body-attached frame.

The robot’s attitude is parameterized by a rotation matrix $\mathbf{R}$ that relates body and world coordinates according to $\boldsymbol{v}=\mathbf{R}\boldsymbol{v}^{\prime}$, where we define $\boldsymbol{v}$ to be any vector expressed in world coordinates, and $\boldsymbol{v}^{\prime}$ is the same vector expressed in body-attached coordinates. The matrix $\mathbf{R}$ and body angular velocity $\boldsymbol{\omega}^{\prime}$ were computed from the quaternion representation provided by the motion capture system. The error ${e}^{\prime}_{\hat{\mathbf{z}}}$ between desired trajectory and the current thrust vector position, in body-attached frame is determined as follows:

where $\mathbf{R}_{2}$ is the upper-left 2$\times$2 block of the rotation matrix $\mathbf{R}$.

The inner faster loop for determining the roll and pitch torques in body-attached frame works as follows:

where $k_{pa}$, $k_{da}$ and $k_{ia}$ are the proportional, derivative and integral gains, respectively. Note that in this controller, torque about the $x$-axis depends on inclination along the $y$-axis and vice versa. The attitude error is the difference between desired and actual inclination. If the robot is facing in the world x-direction, the y-direction will be towards the left of the robot. In a situation where the lateral reference point in on the right of the robot, the attitude error vector will have a component in –y direction. It will require the robot to perform positive roll about body x axis. This justifies the negative sign with $e^{\prime}_{\hat{z}y}$ in the above expression.

The controller described above produces a thrust $a_{z}$ and torques $\tau_{x}$ and $\tau_{y}$ that are normalized by body mass and moment of inertia, respectively. To map these accelerations into voltage values supplied to the piezoelectric actuators. We assume that the thrust force is linearly proportional to amplitude. To estimate the moment arm for computing torques, we approximately determined the distance between the center of mass and the aerodynamic center of thrust for individual wing, using CAD model of the robot. The yaw motion of the robot is left uncontrolled in these experiments, as it does not affect the lateral and vertical control of the robot.

We demonstrated controlled takeoff in Fig. 12. Frames from a hovering flight are shown in Fig. 13 where the robot was flown for around 2 seconds. The 3-dimensional trajectory plot of this flight is shown in Fig. 14 (a). The robot was commanded to fly at a height of $4$ cm from the starting point. It can be seen in Fig. 14 (b) that the robot successfully maintained the height at approximately $4.5$ cm from the takeoff point. The RMS position errors during the last one second of the flight were 1.8, 1.75, and 0.5 cm for its x, y, and z positions, respectively.

One of the objectives of the re-design reported in this work was to give the robot the capability of landing upright even in the event of loss of control, without the need of long extended-out legs as in [33]. An upright landing allows for an easy transition to the next desired task, such as walking, sensing, or subsequent flights. This is facilitated by our robot’s low center of mass, which makes it harder for the robot to topple.

We demonstrated an uncontrolled takeoff as shown in Fig. 11. In this video, the robot is seen to be flying with unstable attitudes and landing shortly after. Under feedback control, the robot remains approximately level as shown in Fig. 12. Under these conditions, the robot was able to perform a landing by gradually lowering the commanded altitude as shown in Fig. 14 (c) which was plotted for another experiment where the robot was flown for a longer duration.

Additionally, we showed that the robot was able to land even when feedback control was not present, indicating that the lowered center of gravity of our design improves landing robustness (Fig. 11).

Our design is inspired by insects, such as stoneflies and mayflies, that use their flapping wings to push themselves along the air-water interface [20]. Like these animals, our robot moves along the surface by propelling itself with its flapping wings. Compared to an airborne RoboFly [22] which has six spatial degrees of freedom, an interfacially flying RoboFly has only three degrees of freedom because it is constrained to move along a surface. However, the surface tension forces acting on the legs of the RoboFly still makes it difficult to model the locomotion. Mukundarajan et al. [20] present a dynamic model for an interfacial flight for actual biological insects. According to this model, forces acting on an actual biological insect performing interfacial flight are as follows: 1) horizontal air drag acting on the wings, 2) horizontal capillary-gravity wave drag, 3) water drag acting on the legs at the contact with the water surface in the opposite direction to that of the motion, 4) body weight in vertical direction, 5) vertical resultant force due to surface tension, and 6) vertical water drag. The static case of the RoboFly locomotion is presented in this section.

In case of an object not moving or oscillating vertically, it can float on the water surface if its weight is balanced by the sum of two types of forces exerted on it. The first of these forces is buoyancy force. According to Archimedes’ principle, the buoyancy force exerted on an object is equal to the weight of the water displaced. Therefore, objects with density lower than that of water tend to float, and those with density larger than that of water sink. Water-walking arthropods have density larger than water, and therefore they would sink unless supported by the second type of force which is due to the surface tension of water. This phenomenon is explained in detail in the following subsection on legs design.

Legs play an important role in keeping the RoboFly on the water surface without breaking the surface tension film. Rigid and compliant legs were considered in [13]. However, that study was conducted on a robot which used actuating legs for propulsion. Here, we explore the use of wings for propulsion. Therefore, to keep the design simple, a rigid and passive set of three horizontal legs are attached to the RoboFly. These legs lie in the same plane at its bottom so that every part of the legs is in contact with the ground when placed on a flat surface. Cylindrical rods are chosen over square cross-section ones for the legs to avoid complication arising due to a potential case where the robot rests or lands on an edge of a leg. A simple configuration of three parallel legs is considered for this study.

Once we know the configuration and shape of the legs, next design parameters to be considered are 1) material, 2) diameter, 3) length, and 4) distance between the rods.

The diameter of the legs plays an important role in determining the ratio of buoyancy force and curvature force. The capillary length $l_{c}$, as shown in Fig. 15 (a) is independent of the leg diameter and contact angle. To keep the surface unbroken it is important to have the curvature force significantly larger than the buoyancy force. A carbon fiber rod of diameter 0.5 mm was chosen for the legs. This diameter corresponds to a Bond number, $Bo\approx 0.31$, as calculated later in this section. Legs made out of stainless steel were used in [13]. Here, carbon fiber rod was chosen for its strength-to-weight ratio: it weighs about 3.6 mg/cm, whereas a stainless steel rod of the same diameter weighs about 15 mg/cm. Since the goal of this robot is also to perform multi-modal locomotion which includes flying, it is important to minimize mass.

While determining the length of legs, it is important to understand the forces acting on the legs while resting on the water surface. Surface tension causing curvature force is assumed to be the primary source of support to balance the weight. Buoyancy forces are not significant for the floating bodies of sub-gram weight, which is also demonstrated in [15]. Buoyancy force depends on the volume of water displaced because of the floating body, it corresponds to volume $V_{b}$ as can be seen in Fig. 15 (a). Curvature force, on the other hand, corresponds to volume $V_{m}$ displaced outside the contact line. This volume $V_{m}$ depends on the capillary length, $l_{c}$, which is determined as $l_{c}=(\sigma/\rho g)^{0.5}\approx 2.6$ mm for objects floating on water surfaces, where $\sigma$ and $\rho$ are coefficient of surface tension and density of water, respectively. It can be seen from Fig. 15 (a) that $F_{B}/F_{c}\sim V_{b}/V_{m}\sim w/l_{c}=0.25/2.6=(Bo)^{0.5}<<1$. Therefore, we can assume $F_{c}$ to be a significant contributor in supporting the robot at the surface. The above expression also gives us $Bo$, Bond number, equal to $0.31$.

For simplicity, we consider the weight $F_{W}$, as shown in Fig. 15 (b), to act uniformly along the entire length of all the three legs. In other words, we assume uniform weight distribution on these legs. Let’s, for a moment, assume the submerged angle $\phi$, as shown in Fig. 15 (a), is equal to $90^{o}$. In that case, the curvature force in vertical direction $F_{c}$ can be calculated as $F_{c}=2\sigma L\cos(\theta)$, where $L$ is the total length of the legs, and $\theta$ is the contact angle. From this expression, the maximum curvature force can be written as $2\sigma L$, which can be set equal to the weight to determine the minimum length of the legs, that turns out to be $L_{min}$=0.5 cm. However, this length of the legs is sufficient only when the entire supporting force due to surface tension acts in the vertical direction, which is not always the case. Also, the dimple due to a neighbouring leg can interfere with that of the one under study, which can reduce the supporting curvature forces as explained in [13]. Additionally, ripples that are generated due to the ground effect of flapping wings have unknown effect on the legs, and it can also reduce the supporting force at the interface. Because of these unknown effects, we turn to empirical study conducted by Hu et al. in [17]. A study of 342 species of water striders was conducted, and the relation between the maximum curvature force and body weight was found out. The plot of the relation is shown in Fig. 16. The best fit line of the plot of this data was given by $max(F_{c})=48F_{W}^{0.58}$, where the forces are measured in dynes. Considering a $80$ mg robot, $max(F_{c})\approx 600$ dynes, which corresponds to $L\approx 4.2$ cm. This length of legs will add an extra mass of $\sim 15$ mg to the robot, which is compensated by further changing the total length of legs to $5$ cm. So, the set of horizontal legs now consists of three pieces with the center one $2.5$ cm long and other two $1.25$ cm each. RoboFly is also compared with other water striders in Fig. 16.

Special attention is given to the minimum distance between two adjacent legs. If they are too close, the dimple caused by a leg on the water surface will interfere with that by its neighbouring legs. This will reduce the lift force generated by the surface tension at the contact with legs, this is shown in the study by [13] about the deformed water profile reducing the lift force. For a static case, it can be seen in their work that the dimple dies down at about $6$ mm from a floating object, which requires us to have at least $12$ mm of gap between legs. Keeping that in mind, we choose to have them $15$ mm apart to be in safe situation in dynamic case in which the robot will be performing water locomotion.

The signal generated in this case is similar to the one used for ground locomotion. When the wings are flapped, ripples can be seen generating and propagating away from the robot on the water surface. Though the effect of ripples is unknown on the motion of the robot, it is observed that the robot doesn’t move in any direction when the two wings are driven by the same driving signal without any second harmonic component. It can be concluded that the ripples have equal effect in all directions, and thus can be ignored in the dynamic force balance in the horizontal plane.

RoboFly with its horizontal legs is shown in Fig. 17. The design parameters for the legs are summarized in Table II. As mentioned in above section, RoboFly has the capability to move in either direction. Frames captured from a video of RoboFly moving from left to right are shown in Fig. 19. The robot in this video was driven with a second harmonic signal of amplitude 220 V, and the wings were flapped at 35 Hz, far below its resonant frequency. The recorded speed of this interfacial flight was $\approx$0.5 cm/s. In addition to the straight-line motion, the robot can also steer by flapping one wing at a larger amplitude than the other. The robot can be seen taking a sharp turn towards left in Fig. 20 by flapping the right wing at a larger amplitude (220 V) than the left one (180 V). The angular speed is recorded as $\approx$20^o per second. Fig. 21 shows a set of images in which an airborne robot is seen to be landing on the water surface. In this case, the robot simply jumps off the cardboard box in the background. It can be seen that the robot didn’t land in its stable orientation; however, it still manages to recover without breaking the surface tension of the water. This can be attributed to the length of the legs being inspired by the actual biological species which may not have all the legs touching the water surface all the time. We were able to achieve this landing behavior consistently.

When the robot tries to take off, it relies on the wing lift to generate enough thrust to break its contact with the water surface. Immediately preceding the contact breakage, the surface tension which pulls the robot back assumes its maximum value, $2\sigma L$. If we assume, in a failed attempt of take-off, the robot comes to a static position right before the contact breaks, the meniscus assumes the maximum height. For the static analysis at this position, we can set the buoyancy force $F_{B}$ equal to zero as robot legs are at their maximum height on the water surface. This will reduce the equation of motion to as in (5).

Now, substituting $F_{C,max}=2\sigma L$ and values of all the unknowns, we can see that the value of $F_{L}$ corresponds to $800$ mg of force, which is 10 times the weight of the robot. It is impossible for this insect scale robot to lift off with an additional load of 9 times its own weight. That means it has to rely on some external factor to break the contact with the water surface. This phenomenon can be attributed to the behavior that has been observed with its biological counterpart nymphaeae. These insects, as shown in [20], oscillates in the vertical direction as they generate lift only in the downstroke; therefore, the meniscus is observed to be assuming its maximum height during downstroke and maximum depth during upstroke. As nymphaeae are seen to be taking off after some time which varies from a fraction of seconds to a few seconds, once the oscillations assume large amplitudes and the inertia is large enough to break the surface.

In nymphaeae study, the required lift-to-weight ratio is observed to be $q=3.4$, whereas it is observed to be $q\approx 10$ in the case of its robotic counterpart. The transition from iterfacial flight to airborne flight with the help of induced oscillations is considered to be out of scope for this paper.

The locomotion of aquatic and semi-aquatic insects can be characterized using the thrust generating mechanism. The water surface locomotion shown by RoboFly is similar to most semiaquatic insects which utilize their hydrophobic legs for flotation and propulsion. This locomotion is known as water walking. Water walking insects also rely on surface tension for flotation as reviewed in [17, 18, 19].

Another locomotion inspired by Marangoni propulsion of rove beetle and semiaquatic insects like Microvelia and Velia is reviewed in [19]. In this locomotion, the thrust is generated by uneven surface tension because of a chemical released by the insects.

Honeybees, when trapped on the water surface, show a unique type of locomotion referred to as hydrofoiling locomotion by [34]. Honeybees are seen to be using their wings as hydrofoils to generate hydrodynamic thrust. Another interesting locomotion on water surface similar to honeybee’s hydrofoiling locomotion is the rowing locomotion shown by the stonefly as reported in [35]. This locomotion makes use of both hydrodynamic drag as well as aerodynamic lift for propulsion.