INTRODUCTION

Micro propulsion has been massively studied since it is a critical component of maneuverable microrobots for in vivo applications, such as drug delivery, biosensing, and microsurgery [1]. To navigate a microrobot inside human body, the propulsion mechanism should be microscale, controllable in magnitude and direction, and wireless in power supply. The existing methods include external electromagnetic field driving magnetic helical swimmers [2], catalytic reaction by chemical fuel [3], etc.

Among many methods, microstreaming is a competitive candidate which generates a significant and directional flow in microscale. The directional microstreaming using a one-end-sealed glass capillary tube has been first reported for 1-D propulsion [4]. Later, the similar concept has been proved using MEMS (Microelectromechanical Systems) fabricated devices [5,6]. An air bubble was automatically trapped inside the oneend-open microtube as soon as the hydrophobic microtube was immersed into water. Directional microstreaming was generated by exciting the gaseous bubble trapped in the microtube using an external acoustic wave: the interface of the bubble near the opening of the tube oscillates back and forth at the frequency of the external acoustic field, and thus generates a non-zero time-averaged outgoing microstreaming flow from the opening of the tube. Consequently, the flow exerts a reaction force in the opposite direction as propulsion on the tube. Such microstreaming propulsion provides the advantages of easy actuation, light and simple peripheral devices, wireless transmission, and minimal harm and interference of the actuation signal to living organisms and other medical equipment.

Here, the resonance frequency of the bubble is critically determined by the length of the bubble that is similar to the length of the tube. This implies selective actuation: only frequency-matched bubbles are activated among a group of multiple bubbles of various lengths. Using this characteristic, 2-D steered propulsion was reported where two groups of microtubes with two different lengths were oriented orthogonally [7,8]. Each group had its own resonance frequency. One group was used to propel the swimmer while the other was used to steer the direction. By switching the frequency of the acoustic input, a variety of 2-D propelling motion was demonstrated. However, the implementation of the above concept into maneuverable 3-D propulsion has not been reported and brings many challenges. The upmost challenge is 3-D microfabrication with orthogonal alignments of microtubes. Another challenging problem is that maintaining the orientation of the drone suspended in a 3-D space is extremely difficult.

This article presents how we tackle the above challenges to achieve the maneuverable 3-D swimming. Maneuverable 3-D propulsion needs at least three independent propulsions in different directions. For example, one is for the vertical motion to change the elevation while two others is to generate a clockwise/counterclockwise yaw (Fig. 1). Accordingly, three groups of microtubes are incorporated to the 3-D micro drone body. One group is responsible for the upward motion; the downward motion is driven by gravity. The other two groups produce the forward motion when actuated simultaneously as well as clockwise/counterclockwise yaw when actuated individually. The complex structure of 3-D micro swimming drone (smaller than 1 mm 3 in volume) was fabricated by a two-photon polymerization 3-D printer, which accurately builds hollow microtubes lying on three non-parallel planes inside the drone body.

The second challenge is related to stability in 3-D swimming. As opposed to 2-D swimming where the bottom solid surface serves as a confinement, the bottom surface does not always exist in 3-D swimming. This increased degree of freedom puts the drone in a random orientation after actuations or under disturbances, which makes subsequent actuations difficult. As a result, it is critically important to restore the micro drone in pre-determined posture before each actuation. Hence, a restoring mechanism is incorporated into the drone by carefully redistributing the drone mass: create a mismatch between the center of gravity (CG) and the center of buoyancy (CB). The mismatch always generates a restoring torque to bring Fig. 1. The schematics for 3-D micro swimming drone with three types of microtubes at different lengths, which enable propulsion in three directions.

t h e d r o n e t o t h e u p r i g h t p o s t u r e . T h e n , s u b s e q u e n t a c t u a t i o n s c a n b e e a s i l y d e t e rm i n e d a n d p r o g r am e d t o a c h i e v e d e s i r e d m o t i o n s . A s a r e s u l t, s u c h a u t om a t i c r e s t o r a t i o n f a c i l i t a t e s a s t a b l e 3 -D sw imm i n g p e r f o rm a n c e , w h i c h b r i n g s t h e p r e s e n t m i c r o d r o n e c l o s e r t o p r a c t i c a l a p p l i c a t i o n s . W i t h t h e s e tw o f e a t u r e s , t h e p r e s e n t m i c

) . T h e m i c r o t u b e s i n t h e d r o n e a u t om a t i c a l l y t r a p p e d a i r i n s i d e a s s o o n a s t h e d r o n e w a s imm e r s e d i n t h e s o l u t i o n . T h e m i c r o d r o n e w a s f i r s t s u s p e n d e d i n i t s u p r i g h t p o s t u r e ( e q u i l i b r i um s t a t e ) . T h e n , t h e m i c r o d r o n e w a s h e l d b y tw e e z e r s i n a r a n d om o r i e n t a t i o n a n d t h e n r e l e a s e d . T h e r e s t o r a t i o n t im e f r om t h e i n i t i a l l y d i s t u r b e d o r i e n t a t i o n t o t h e u p r i g h t p o s t u r e w a s m e a s u r e d b y a n a l y z i n g t h e im a g e s r e c o r d e d b y a c am e r a (K P -D 2 0AU , H i t a c h i , J a p a n ) . 3 -D Sw imm i n g w i t h M a n e u v e r a b i l i t y

T h e m i c r o sw imm i n g d r o n e w a s t e s t e d i n a n a c r y l i c t a n k ( 1 0 × 1 0 × 5 cm 3

) f i l l e d w i t h t h e s am e s o l u t i o n a b o v e . Tw o p i e z o e l e c t r i c d i a p h r a gm s ( 7 B B -2 7 -4 L 0 , M u r a t a E l e c t r o n i c s , U SA ) w e r e g l u e d t o t h e s i d ew a l l s o f t h e t a n k a n d c o n n e c t e d t o a f u n c t i o n g e n e r a t o r w i t h a n am p l i f i e r . T h e r e s o n a n c e f r e q u e n c y o f e a c h t y p e o f t h e m i

R E SU L T S D e s i g n o f t h e 3D M i c r o Sw imm i n g D r o n e T o n a v i g a t e i n 3 -D s p a c e , t h r e e t y p e s o f m i c r o t u b e s a r e p l a c e d i n d i f f e r e n t o r i e n t a t i o n s a n d p o s i t i o n s i n s i d e t h e d r o n e b o d y ( F i g . 2 ) . T h e l e n g t h a n d t h e n um b e r o f t u b e s f o r

e a c h t y p e a r e a s f o l l ow s : " L a t e r a l 1 " ( 8 9 0 μm l o n g × 2 ) , " L a t e r a l 2 " ( 5 9 0 μm l o n g × 3 ) , a n d "V e r t i c a l " ( 4 7 0 μm l o n g ×

) . A d e c r e a s e i n d i am e t e r n e a r t h e t u b e o p e n i n g i n t r o d u c e s a p h y s i c a l b a r r i e r t o f i x t h e i n t e r f a c e o f t h e b u b b l e a n d t h u s m a i n t a i ns i t s l e n g t h d u r i n g b u b b l e t r a p p i n g a n d o p e r a t i o n [ 9 ]

. T h e i n d i v i d u a l r e s o n a n c e f r e q u e n c i e s o f L a t e r a l 1 , L a t e r a l 2 , a n d V e r t i c a l w e r e 5 . 9 kH z , 7 . 9 kH z , a n d 1 1 . 7

kH z . A s t h e p r o p u l s i o n d i r e c t i o n i s o p p o s i t e t o t h e o u t g o i n g d i r e c t i o n o f t h e o p e n i n g o f

) . I n t h i s c o n f i g u r a t i o n , t h e -D m i c r o d r o n e i s i n e q u i l i b r i um w i t h i t s u p r i g h t p o s t u r e w h e n t h e CG i s l o c a t e d b e l ow C B i n g r a v i t a t i o n a l d i r e c t i o n ( F i g . , m i d d l e ) . W h e n e v e r a n y d i s t u r b a n c e o r p r o p u l s i o n f o r c e d e v i a t e s t h e d r o n e f r om t h i s p o s t u r e , t h e CG a n d C B g e n e r a t e s a t o r q u e t o r e s t o r e t h e d r o n e t o t h e u p r i g h t p o s t u r e b y e i t h e r r o l l i n g ( F i g . , l e f t a n d r i g h t ) o r p i t c h i n g ( F i g . 4 ( a ) ) . T h e d y n am i c s o f r e s t o r a t i o n c a n b e f o rm u l a t e d b y t h e b a l a n c e o f t o r q u e a b o u t CG :

! " # $ " % # +' ( ) * " $ " % ++ , -. / 0 1 2=0

w he r e I i s t h e m om e n t o f i n e r t i a o f r o l l i n g ( 4 . 2 5 × 1 0 -1 7 k g • m 2 ) o r o f p i t c h i n g ( 6 . 5 8 × 1 0 -1 7 k g • m 2 ) , θ t h e a n g u l a r d i s p l a c em e n t , A t h e r o t a t i n g d r a g c o e f f i c i e n t o b t a i n e d e x p e r im e n t a l l y , μ t h e f l u i d v i s c o s i t y ( 0 . 0 0 1 5 N • s /m 2 ) , ρ i s t h e f l u i d d e n s i t y ( 1 0 4 5 k g /m 3 ) , R t h e e q u i v a l e n t d r o n e s i z e ( 4 5 6 μm ) , V t h e d r o n e v o l um e ( 4 . 9 × 1 0 -1 0 m 3 ) , g t h e g r a v i t y

O r i e n t a t i o n r e s t o r i n g m e c h a n i sm : n o n -u n i f o rm m a s s d i st r i b u t i o n r e s t o r e s t h e d r o n e t o t h e u p r i g h t p o s t u r e (m i d d l e ) . T h e l o c a t i o n m i sm a t c h b e t w e e n C B a n d C G g e n e r a t e s a r e s t o r i n g t o r q u e ( T ) f r om d i s t u r b e d o r i e n t a t i o n s ( l e f t a n d r i g h t f i g u r e s )

F r om E q . ( 1 ) , t h e t im e c o n s t a n t i s d e r i v e d a s :

F o r t h e d e s i g n i n F i g . 2 , E q . ( 2 ) y i e l d s τ ≈ 0 . 1 s e c .

T h e e x p e r im e n t a l d em o n s t r a t i o n a b o u t r e s t o r a t i o n o f t h e 3 -D m i c r o d r o n e i s s h ow n i n F i g . 4 ( a ) a n d ( b ) w h e r e t h e d r o n e i s i n i t i a l l y h e l d b y a tw e e z e r i n a d e v i a t e d p o s t u r e

a n d t h e n r e s t o r e s i t s e l f a f t e r b e i n g r e l e a s e d . T h e a v e r a g e d ( o u t o f 2 1 t r i a l s ) t im e t r a c e o f r e s t o r a t i o n i n r o l l i n g w a s m e a s u r e d ( n o rm a l i z e d a n g u l a r d i s p l a c em e n t 2 2 E F v s . d im e n s i o n l e s s t im e G 5 F) , a s d i s p l a y e d i n F i g . 4 ( c ) , a n d s h ow s a n e x c e l l e n t g r e em e n t w i t h E q . ( 1 ). A l l r e s t o r a t i o n s a r e c om p l e t e d w i t h i n 0 . 4 s e c , m e a n i n g t h a t a p a u s e l o n g e r t h a n 0 .

s e c b e tw e e n tw o a c t u a t i o n s a s s u r e s r e t u r n i n g o f t h e d r o n e a lw a y s t o t h e u p r i g h t p o s t u r e b e f o r e n e x t a c t u a t i o n s t a r t s . B a s e d o n t h i s , a n i n t e r v a l i s a d d e d i n t h e a c t u a t i o n s i g n a l . M a n e u v e r a b i l i t y T h e i n d i v i d u a l p r o p u l s i o n s f r om e a c h t y p e o f m i c r o t u b e s a r e v e r i f i e d b y a c t u a t i n g a t t h e i r ow n r e s o n a n c e f r e q u e n c i e s . T h e a c t u a t i o n f r e q u e n c y a n d v o l t a g e f o r t h e t h r e e t y p e s o f m i c r o t u b e s o n t h e p r e s e n t d r o n e a r e a s f o l l ow e d :

( 1 ) V e r t i c a l : 1 1 . 7 kH z , 5 8 V , ( 2 ) L a t e r a l 1 : 5 . 9 kH z , 2 2 V , a n d ( 3 ) L a t e r a l 2 : 7 . 9 kH z , 2 T h e e f f i c a c y o f t h e r e s t o r a t i o n i s c l e a r l y c a p t u r e d i n F i g . 5 ( a ) w h e r e t h e m i c r o d r o n e l e a n s f o rw a r d w h i l e p r o p e l l i n g u p : p i t c h e s a t 1 . 5 s e c d u r i n g t h e a c t u a t i o n s , a n d t h e n r e t u r n s t o i t s u p r i g h t p o s t u r e d u r i n g t h e p a u s e i n t e r v a l a t 3 . 0 s e c .

V . F i g u r e 5 s h ow s t h e s n a p s h o t s . V e r t i c a l i s a b l e t o p r o p e l t h e 3 -D m i c r o d r o n e u pw a r d b y e i t h e r t a k i n g o f f f r om t h e b o t t om o f t h e t a n k ( F i g . 5 ( a ) ) o r m o v i n g u p f r om a n y s u s p e n d e d p o s i t i o n i n a 3 -D s p a c e . N o t e t h a t t h e v o l t a g e r e q u i r e d f o r t a ke o f f i s u s u a l l y h i g h e r t h a n t h e o n e f o r l i f t i n g t h e d r o n e i n a s u s p e n d e d p o s i t i o n f a r aw a y f r om t h e b o t t om s u r f a c e . B o t h L a t e r a l 1 a n d 2 w e r e i n d i v i d u a l l y t e s t e d o n t h e s u s p e n d i n g 3 -D m i c r o d r o n e i n t h e s o l u t i o n , w h e r e f r i c t i o n e f f e c t s o n t h e b o t t om s o l i d s u r f a c e a r e a b s e n t . T h e m i c r o t u b e s o f L a t e r a l 1 y aw s t h e m i c r o d r o n e c o u n t e r c l o c kw i s e ( F i g . 5 ( c ) ) , w h i l e t h e m i c r o t u b e s o f L a t e r a l 2 y aw s t h e m i c r o d r o n e c l o c kw i s e ( F i g . 5 ( b ) ) . T h i s p r o v e s t h a t e a c h t y p e o f t h e p r o p u l s i o n c a n b e i n d i v i d u a l l y a n d s e l e c t i v e l y a c t u a t e d b y a p p l y i n g t h e r e s o n a n c e f r e q u e n c y o f t h e c o r r e s p o n d i n g m i c r o tu b e s . A s m e n t i o n e d i n t h e p r e v i o u s s e c t i o n , t h e a c t u a t i o n s i g n a l h a s a d u t y c y c l e ( sw i t c h

C o n s e c u t i v e a n d j o i n t a c t i v a t i o n s o f m u l t i p l e m i c r o t u b e s c a n g e n e r a t e v a r i o u s p a t h s , n a v i g a t e t h e d r o n e

i n 3 -D s p a c e , a n d dem o n s t r a t e s u c c e s s f u l m a n e u v e r a b i l i t y . H e r e t h r e e d i f f e r e n t p a t h s a r e d em o n s t r a t e d . P a t h 1 c o n s i s t s o f 2 a c t u a t i o n s t e p s : a c t i v a t i n g V e r t i c a l f o l l ow e d b y t h e j o i n t a c t u a t i o n o f L a t e r a l 1 a n d 2 , a s s h ow n i n F i g . 6 ( a ) . A t f i r s t , t h e m i c r o d r o n e i s s i t t i n g o n t h e b o t t om a t r e s t . O n c e V e r t i c a l i s a c t i v a t e d , i t t a k e s o f f f r om t h e b o t t om a n d e l e v a t e s t o a c e r t a i n p o s i t i o n . T h e n , t h e a c t i v a t i o n i s sw i t c h e d t o b o t h L a t e r a l 1 a n d 2 r e s u l t i n g i n a f o rw a r d m o v em e n t ( t o t h e l e f t o f t h e f i g u r e ) . N o t e t h a t t h e d r o n e s l i g h t l y s i n k s d ow n b y g r a v i t y d u r i n g t h e f o rw a r d m o t i o n . A s l i g h t f o rw a r d d i s p l a c em e n t d u r i n g t h e t a ke o f f i s d u e t o t h e c r o s s -t a l k , a n o n -n e g l i g i b l e p r o p u l s i o n f r om n o nd om i n a n t m i c r o t u b e s . A l t h o u g h e a c h t y p e o f t h e m i c r o t u b e h a s s t r o n g e s t o s c i l l a t i o n a t i t s ow n r e s o n a n c e f r e q u e n c y , i t s t i l l o s c i l l a t e s a t t h e o f f -r e s o n a n c e f r e q u e n c i e s a n d g e n e r a t e s a m i n o r p r o p e l l i n g f o r c e a s w e l l . T h i s c r o s s -t a l k i s u s u a l l y o b s e r v e d w h e n t h e a c t u a t i o n v o l t a g e i s l a r g e r t h a n

CONCLUSION

This article describes a micro swimming drone navigating pre-designed paths in a 3-D space. The drone is propelled by the microstreaming flow generated from the acoustically oscillating cylindrical bubbles. Three groups of microtubes at different lengths are placing on different planes within the drone and responsible for propulsion in upward and forward and clockwise/counterclockwise yaw. The drone moves downward without any propulsion due to the gravity. By switching the acoustic frequency, only selected bubbles are activated when the acoustic frequency matches their resonance frequency. Therefore, the drone can propel in multiple directions in a controlled manner by sole or joint actuation of microbubbles and reaches any position in a 3-D space. An additional unique feature is the restoring mechanism of the drone posture by re-distributing the drone mass to have a mismatch between the center of gravity and the center of buoyancy. This configuration always generates a torques restoring the drone back to the upright posture regardless of external disturbances and previous actuations. This design significantly increases the stability of the drone. Otherwise, the orientation of the drone would be easily disturbed to random positions thus making the following actuations very difficult. A mathematical model was formulated to analyze the restoring dynamics and time showing an excellent agreement with experimental results. This model facilitates to design the actuation signal that has a proper on/off duty cycle. Utilizing these features, a variety of programmed swimming paths are experimentally achieved, demonstrating the maneuverability of the micro swimming drone.