Halteres for the Micromechanical Flying Insect ¤ W.C. Wu R.J. Wood R.S. Fearing Department of EECS, University of California, Berkeley, CA 94720 fwcwu, rjwood, [email protected] Abstract MFI. On the other hand, piezoelectric vibrating struc- tures have been developed and have proven to be able The mechanism which real flying insects use to de- to detect Coriolis force with high accuracy [8]. There- tect body rotation has been simulated. The results show fore, based on the gyroscopic sensing of real flies, a that an angular rate sensor can be made based on such novel design using piezoelectric devices is being con- a biological mechanism. Two types of biomimetic gy- sidered. This paper describes the simulations and fab- roscopes have been constructed using foils of stainless rication of this type of biologically inspired angular steel. The ¯rst device is connected directly to a com- rate sensor for use on the MFI. pliant cantilever. The second device is placed on a mechanically amplifying fourbar structure. Both de- 2 Haltere Morphology vices are driven by piezoelectric actuators and detect the Coriolis force using strain gages. The experimental Research on insect flight revealed that in order to results show successful measurements of angular veloc- maintain stable flight, insects use structures, called ities and these devices have the bene¯ts of low power halteres, to detect body rotations via gyroscopic forces and high sensitivity. [5]. The halteres of a fly evolved from hindwings and are hidden in the space between thorax and abdomen 1 Introduction so that air current has negligible e®ect on them (see ¯gure 1). The halteres resemble small balls at the end Micro aerial vehicles (MAVs) have drawn a great of thin sticks. There are about 400 sensilla embedded deal of attention in the past decade due to the quick in the flexible exoskeleton at the haltere base. These advances in microtechnology. Commercial and mili- tary applications for micro-robotic devices have been identi¯ed including operations in hazardous environ- ments, search-and-rescue within collapsed buildings, reconnaissance and surveillance, etc.. Although sev- eral groups have worked on MAVs based on ¯xed and rotary wings [6], flapping flight provides superior maneuverability that would be bene¯cial in obstacle avoidance and for navigation in small spaces [11]. Inspired by the exceptional flight capabilities achieved by real insects, the UC Berkeley Microme- chanical Flying Insect (MFI) project uses biomimetic principles to develop a flapping wing MAV that will be capable of sustained autonomous flight. The over- all structure of the MFI has been designed and some Figure 1: Schematic of enlarged halteres of a fly. components have been built and tested [3],[10],[11]. As with real insects, angular rotation detection by the mechanoreceptors function as strain gages to detect sensory system of the MFI is important for stabilizing the Coriolis force exerted on the halteres [4]. During flight. Although precise MEMS gyroscopes are com- flight the halteres beat up and down in vertical planes mercially available, their designs (package size, power through an average angle of nearly 180o anti-phase to requirements, etc.) are in general not suitable for the the wings at the wingbeat frequency. When a fly’s hal- ¤This work was funded by NSF KDI ECS 9873474, ONR teres are removed or immobilized, it quickly falls to the MURI N00014-98-1-0671, and DARPA. ground. In addition, the two halteres of a fly are non- olis force and has only radial and tangential compo- nents. The gravitational force (mg) is always constant and depending on the haltere position and the insect's body attitude in space, its distribution in the three directions varies. However, the e®ect of this gravita- tional force on the angular velocity sensing is negligible because it is a tonic lateral component which can be considered as DC o®set on the Coriolis force and re- moved easily by the subsequent signal processing step. 3 Simulations To detect angular rotations, the lateral forces on the Figure 2: Haltere force modulation. halteres are measured because the large primary iner- tial force has no contribution in the lateral direction coplanar (each is tilted backward from the transverse and hence it is possible to measure the Coriolis sig- plane by about 30o) so that flies can detect rotations nal among all other interfering force signals appearing about all three turning axes. in this direction. Figure 3 shows the lateral compo- As detailed in [7], a complex force, as a result of nents of the Coriolis force on both halteres for rota- insect motion and haltere kinematics, acts on the hal- tions about the roll, pitch, and yaw axes. Because of teres during flight (see ¯gure 2). Assuming no transla- the dependence of the Coriolis force on the haltere ve- tional motion of the insect, this force can be expressed locity, these force signals are modulated in time with in vector notation by the following: haltere beat frequency. For a roll rotation, the sig- nal is modulated with the haltere beat frequency and F = mg¡ma¡m!_ £r¡m! £(! £r)¡2m! £v (1) the left and right signals are 180o out-of-phase. For a pitch rotation, the signal is also modulated with the where m is the mass of the haltere, r, v, and a are haltere beat frequency, but the left and right signals the position, velocity, and acceleration of the haltere are in-phase. For a yaw rotation, the signal is modu- relative to the insect body, ! and !_ are the angular lated with double the haltere beat frequency and the velocity and angular acceleration of the insect, and g is left and right signals are 180o out-of-phase. the gravitational constant. Further, this force can be decomposed into radial, tangential, and lateral compo- Left Haltere Right Haltere −4 −4 x 10 x 10 nents as depicted by the exploded view of the haltere 1 1 in ¯gure 1. Insect's body rotations produce centrifugal 0.5 0.5 0 0 Roll (¡m! £ (! £ r)) and Coriolis (¡2m! £ v) forces on force (N) −0.5 −0.5 the halteres. The centrifugal force is generally smaller −1 −1 0 −4 0.5 1 0 −4 0.5 1 x 10 x 10 than the Coriolis force and mostly in the radial and 2 2 tangential directions. Moreover, since the centrifugal 1 1 force is proportional to the square of angular velocity 0 0 Pitch force (N) −1 −1 of the insect, it provides no information on the sign −2 −2 0 −5 0.5 1 0 −5 0.5 1 of rotations. The Coriolis force, on the other hand, x 10 x 10 5 5 is proportional to the product of the angular velocity 2.5 2.5 of the insect and the instantaneous haltere velocity. 0 0 Yaw The Coriolis force has components in all three direc- force (N) −2.5 −2.5 −5 −5 tions and contains information on the axis, sign, and 0 0.5 1 0 0.5 1 magnitude of the insect's body rotation. The angular acceleration force (¡m!_ £ r) is proportional to the Figure 3: Coriolis lateral forces for rotations about product of the angular acceleration of the insect and roll, pitch, and yaw axes. Signals during one haltere the instantaneous position of the haltere. The angular cycle are shown. acceleration and the Coriolis force signals are separa- ble because of the 90o phase shift (they are orthogonal Utilizing the characteristics (frequency, modula- functions). The primary inertial force (¡ma) depends tion, and phase) of these force signals on the left and on the haltere acceleration relative to the insect body. right halteres, a demodulation scheme is proposed to This force is orders of magnitude larger than the Cori- distinguish roll, pitch, and yaw rotations. First, a pitch rotation can be separated from roll and yaw ro- tions is given by the following: tations by adding the left and right signals. Because 3 EIt bh 2 the left and right signals are in-phase for pitch while kt 3l3 It 12 b = = = 3 = (2) out-of-phase for roll and yaw, adding the left and right k EIl I hb h2 l 3l3 l signals retains pitch component and eliminates roll and 12 yaw components. Then, roll and yaw rotations can be where It and Il are the tangential and lateral cross sec- separated by multiplying demodulating signals of dif- tional moments of inertia, b is the width of the beam, ferent frequencies. A sinusoidal signal at the haltere and h is the thickness. frequency retrieves the roll signal while a sinusoidal One of the major concerns with the design of the signal of double the haltere frequency retrieves the yaw haltere is actuation. Since the Coriolis force is pro- signal. Figure 4 illustrates the proposed demodulation portional to the haltere velocity, it is desired to have scheme. Ideally, the magnitudes of the ampli¯ers, Ar, a high haltere beat frequency and a large stroke. Two Ay, and Ap, would be proportional to ¡1=2m, where methods of actuation will be discussed here. The sim- m is the mass of the haltere. pler of the two places the haltere on a vibrating struc- ture with a high Q compliant beamin between. The vibrating structure, in this case a piezoelectric actua- tor, drives the haltere into resonance, while its high Q gives large stroke amplitudes. This method has the bene¯ts of not only being simple to construct, but also this structure has the ability to be driven par- asitically from the body vibrations of the MFI.