lunar lunar structural

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TECHNOLOGY OF LUNAR EXPLORATION

R E N D E Z V O U S A N D D O C K I N G T E C H N I Q U E S J. H e i l f r o n and F . H . Kaufman 1 2 Space T e c h n o l o g y L a b o r a t o r i e s , I n c .

R e d o n d o B e a c h , C a l i f o r n i a A B S T R A C T

E n g i n e e r i n g techniques a p p l i c a b l e to the r e n d e z v o u s and docking of two c o o p e r a t i v e s p a c e c r a f t a r e t r e a t e d , starting f r o m a set of i n i t i a l conditions at a c q u i s i t i o n and f o l l o w e d by a m i d c o u r s e guidance p h a s e , a b r a k i n g phase, a t e r m i n a l guidance phase, and the act of final m e c h a n i c a l i n t e r c o n n e c - t i o n . A s p e c i f i c Earth o r b i t a l m i s s i o n p r o f i l e e n c o m p a s s i n g the e s s e n t i a l e l e m e n t s of any g e n e r a l r e n d e z v o u s m i s s i o n i s used as the f r a m e w o r k f o r d i s c u s s i n g the p r o b l e m s i n v o l v e d and p r e s e n t i n g techniques f o r t h e i r s o l u t i o n . T h e s e t e c h - niques, t h e r e f o r e , have g e n e r a l a p p l i c a t i o n although the n u m e r i c a l v a l u e s quoted a p p l y o n l y to the s e l e c t e d e x a m p l e . Both manual c o n t r o l and automatic m o d e s a r e p r e s e n t e d t o - g e t h e r w i t h s i m u l a t i o n r e s u l t s . F u e l e c o n o m y , e q u i p m e n t c o m p l e x i t y , and p r a c t i c a l c o n s t r a i n t s i m p o s e d by p r e s e n t d a y h a r d w a r e c a p a b i l i t i e s a r e c o n s i d e r e d . F i n a l l y , the d y n a m i c a s p e c t s of docking during the p e r i o d b e t w e e n i n i t i a l contact and final mating a r e d i s c u s s e d , including s t r u c t u r a l r e q u i r e - m e n t s i m p o s e d on the m e c h a n i s m s .

I N T R O D U C T I O N

T o i m p l e m e n t the p r i m a r y space m i s s i o n of this decade — manned lunar e x p l o r a t i o n — the o p e r a t i o n a l a s s i s t a n c e o f r e n d e z v o u s and docking i s being c o n s i d e r e d as an a l t e r n a t i v e to p o s s i b l e p r o b l e m s in obtaining a b o o s t v e h i c l e c a p a b l e of d i r e c t f l i g h t . T h i s paper c o n c e n t r a t e s on the m e c h a n i z a t i o n of the r e n d e z v o u s and docking phase of such a lunar m i s s i o n .

P r e s e n t e d at the A R S Lunar M i s s i o n s M e e t i n g , C l e v e l a n d , Ohio, July 17-19, 1962· T h i s w o r k w a s s p o n s o r e d in p a r t under N A S A C o n t r a c t N o . N A S 8-2635.

1 A s s o c i a t e D i r e c t o r , Guidance L a b o r a t o r y .

^ A s s o c i a t e M a n a g e r , S y s t e m s D e s i g n D e p a r t m e n t .

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J . HEILFRON AND F. H. KAUFMAN

A s indicated in p r e v i o u s p a p e r s , r e n d e z v o u s can take p l a c e in e i t h e r an Earth o r lunar o r b i t ( o r on the lunar s u r f a c e ) ; it can i n v o l v e the mating of s t a g e s , t r a n s f e r of fuel, o r the r e t u r n of a shuttle to a " m o t h e r " ship; d i r e c t a s c e n t o r parking o r b i t s can be used; the o r b i t s can be c i r c u l a r o r m o r e g e n e r a l e l l i p s e s ; f i n a l l y , e i t h e r or both of the s p a c e c r a f t can p a r t i c i p a t e in the r e n d e z v o u s m a n e u v e r s . Since t h e r e i s no intent h e r e to d i s c u s s the p r o s and cons of e a c h a p p r o a c h o r to c o v e r a l l p o s s i b l e m i s s i o n p r o f i l e s , guidance s c h e m e s , and h a r d w a r e c o n f i g u r a - t i o n s , one p a r t i c u l a r p r o f i l e has b e e n s e l e c t e d to d i s p l a y the

significant f e a t u r e s of m o s t r e n d e z v o u s m i s s i o n s .

In m a n y r e s p e c t s , r e n d e z v o u s is l e s s difficult than a i r c r a f t i n t e r c e p t i o n since the t a r g e t is f r i e n d l y and t h e r e is no s e v e r e t i m e c o n s t r a i n t . T h e l a t t e r feature a l l o w s c o n s i d e r a b l e f r e e - d o m of d e s i g n , e s p e c i a l l y w i t h the g r e a t v e r s a t i l i t y of a human in the l o o p . T h i s r e m a i n s true e v e n f o r a p u r e l y automatic m o d e . P e r h a p s the l a r g e s t d e s i g n p r o b l e m c o n c e r n s the

s e l e c t i o n of the m i s s i o n to be i m p l e m e n t e d f o l l o w e d by the o p t i m i z a t i o n o r s y s t e m s e n g i n e e r i n g of a m e c h a n i z a t i o n f r o m the multitude of p o s s i b l e s c h e m e s and t e c h n i q u e s . A m o s t i m p o r t a n t f a c t o r in the o p t i m i z a t i o n is that of r e l i a b i l i t y and the redundancy, a l t e r n a t e or backup m o d e s , e t c . , a s s o c i a t e d w i t h the a p p r o a c h . Although a p r i m a r y s y s t e m can be r a t h e r e a s i l y m e c h a n i z e d with m o d e s t e q u i p m e n t r e q u i r e m e n t s , r e l i a b i l i t y c o n s i d e r a t i o n s w i l l r e s u l t in a d d i t i o n a l h a r d w a r e , t i g h t e r s p e c i f i c a t i o n s , and m o r e s a f e t y f a c t o r s ( e . g . , p r o p e l - lant m a r g i n ) . T h i s is a v e r y c o m p l e x a r e a and w i l l be m e n - tioned only b r i e f l y in the f o l l o w i n g d i s c u s s i o n .

M I S S I O N S E Q U E N C E

In m i s s i o n s i n v o l v i n g d i r e c t a s c e n t t r a j e c t o r i e s , the r e n - d e z v o u s and a s c e n t phases can be quite i n t e g r a t e d , e s p e c i a l l y for lunar o r b i t r e n d e z v o u s . The same i s true f o r r e n d e z v o u s w i t h a lunar surface base e x c e p t h e r e the d e s c e n t phase i s i n t e r t w i n e d . T h e r e f o r e , to d e s c r i b e m o r e c l e a r l y the f e a t u r e s b a s i c to r e n d e z v o u s only, a parking o r b i t m i s s i o n has b e e n s e l e c t e d to p r o v i d e the f r a m e w o r k f o r the f o l l o w i n g d i s c u s s i o n . The use of a parking o r b i t a l l o w s the range of t i m e a c c e p t a b l e f o r the launch of the second v e h i c l e to be extended f r o m s e v e r a l minutes to s e v e r a l hours p e r d a y .

The s e l e c t e d p r o f i l e , shown in F i g . 1, i n v o l v e s the r e n - d e z v o u s of two s p a c e c r a f t , one t e r m e d the " t a r g e t " and the other the " i n t e r c e p t o r , " both of w h i c h a r e i n i t i a l l y in c o - p l a n a r c i r c u l a r o r b i t s — 225 and 125 naut m i l e s , r e s p e c t i v e l y , above the Earth¹ s surface ( f o r n u m e r i c a l c a l c u l a t i o n s ) . Questions as to the m a k e - u p of e a c h s p a c e c r a f t , how they w e r e p l a c e d in o r b i t , w h i c h w a s launched f i r s t , how long they have b e e n in

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o r b i t , how the o r b i t s b e c a m e c o - p l a n a r , e t c . , c o m e under the j u r i s d i c t i o n of the o v e r a l l lunar m i s s i o n d e s i g n or the a s c e n t guidance phase and a r e not a n s w e r e d h e r e . The p a r t i c u l a r o r b i t s c h o s e n a r e r e a s o n a b l e f o r Earth o r b i t a l o p e r a t i o n s c o n s i d e r i n g the c o n s t r a i n t s i m p o s e d b y the Van A l l e n b e l t and a t m o s p h e r i c d r a g . C i r c u l a r o r b i t s have b e e n chosen f o r computational s i m p l i c i t y .

The r e n d e z v o u s i s a c c o m p l i s h e d by injecting the i n t e r c e p t o r into a Hohmann t r a n s f e r e l l i p s e at the t i m e of p r o p e r r e l a t i v e o r b i t a l phasing of the t w o v e h i c l e s . T h i s o c c u r s once e v e r y 36 hours (24 r e v o l u t i o n s ) f o r the 100 nant m i l e o r b i t s e p a r a - tion s e l e c t e d . F o l l o w i n g i n j e c t i o n , a m i d c o u r s e guidance phase e n s u e s to c o r r e c t i n j e c t i o n e r r o r s and p l a c e the i n t e r - c e p t o r on a c o l l i s i o n c o u r s e w i t h the t a r g e t . When the r e l a t i v e r a n g e has d e c r e a s e d to a suitable v a l u e , the r e l a t i v e v e l o c i t y i s r e d u c e d to e s s e n t i a l l y z e r o . T h i s phase i s t e r m e d " b r a k - i n g .^{4 1} A v e r n i e r phase is u t i l i z e d to p r o v i d e s m a l l t e r m i n a l c o r r e c t i o n s ( p r i m a r i l y l a t e r a l ) and, f i n a l l y , p h y s i c a l contact and m e c h a n i c a l i n t e r c o n n e c t i o n r e s u i t »

In m a n y situations t h e r e is no c l e a r d i v i d i n g line b e t w e e n p h a s e s . H o w e v e r , they have b e e n s e p a r a t e d h e r e to c o r r e - spond to t h r e e m a j o r functional r e q u i r e m e n t s of a r e n d e z v o u s s y s t e m . The f i r s t is to a c c o m p l i s h the m i s s i o n without undue fuel e x p e n d i t u r e . T h i s i s a c c o m p l i s h e d during the m i d c o u r s e phase w h e r e e r r o r s a r e d e t e c t e d e a r l y and c o r r e c t e d at the a p p r o p r i a t e t i m e . Second, r e n d e z v o u s should be a c c o m p l i s h e d as quick as i s r e a s o n a b l y p o s s i b l e . T h i s g i v e s r i s e to the b r a k i n g phase w h e r e i n the s p a c e c r a f t a r e a l l o w e d to c l o s e at a high rate until the end when the r e l a t i v e v e l o c i t y must be r e d u c e d to a v o i d c o l l i s i o n at t o o g r e a t a s p e e d . The third r e q u i r e m e n t is that a c c e p t a b l e t e r m i n a l conditions at i m p a c t m u s t r e s u l t . T h i s i s the task of the t e r m i n a l p h a s e .

A C Q U I S I T I O N A N D T R A N S F E R I N J E C T I O N

The r e l a t i v e g e o m e t r y at the t i m e f o r p r o p e r i n j e c t i o n i s shown in F i g . 1. The i n j e c t i o n can e i t h e r be based on ground c o m m a n d s o r c o n t r o l l e d e n t i r e l y f r o m the s p a c e c r a f t (with g e n e r a l e p h e m e r i s data p r e c o m p u t e d p r i o r to launch o r t r a n s m i t t e d f r o m the ground p r i o r to i n j e c t i o n ) . It w i l l be a s s u m e d h e r e that the t r a n s f e r i s i n i t i a t e d f r o m s p a c e c r a f t m e a s u r e m e n t s . In an actual m i s s i o n this m i g h t be e i t h e r the p r i m a r y o r a backup m o d e of o p e r a t i o n . T o obtain the n e c - e s s a r y data, a c q u i s i t i o n of one v e h i c l e by the other i s r e q u i r e d . A s indicated in F i g . 2, the a c q u i s i t i o n g e o m e t r y is c h a r a c t e r - i z e d by a r a t h e r long r a n g e (250 naut m i l e s ) but, as shall be shown b e l o w , quite s m a l l angular u n c e r t a i n t i e s . N a r r o w b e a m s e n s o r s and s m a l l s e a r c h c o n e s ( i f s e a r c h is used at a l l )

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t h e r e f o r e can be e m p l o y e d . If i n j e c t i o n w e r e p a r t of the ascent phase and r e n d e z v o u s s e n s o r a c q u i s i t i o n d e l a y e d until l a t e r , the a c q u i s i t i o n range would d e c r e a s e and the angular u n c e r t a i n t y would c o r r e s p o n d i n g l y i n c r e a s e . Thus t h e r e a r e c e r t a i n t r a d e o f f s b e t w e e n the a s c e n t and r e n d e z v o u s phases aad r e l a t e d equipment r e q u i r e m e n t s .

A c q u i s i t i o n m a y be a c c o m p l i s h e d b y pointing the s e n s o r s ( r a d a r or o p t i c a l ) at the p r o p e r angle ( a p p r o x i m a t e l y 6 7 ° f r o m the l o c a l v e r t i c a l ) in the plane of the o r b i t and w a i t i n g until the two v e h i c l e s phase around to the d e s i r e d p o s i t i o n . Out-of- plane e r r o r s can a r i s e f r o m s e v e r a l s o u r c e s . F i r s t , t h e r e i s the u n c e r t a i n t y of the o r b i t a l plane of the f i r s t s p a c e c r a f t p r i o r to launch of the second ( l e s s than 1 naut m i l e with e x i s t i n g t r a c k i n g s y s t e m s ) . Second, there a r e a s c e n t guidance e r r o r s f o r the second v e h i c l e w h i c h m i g h t a l s o be e q u i v a l e n t to 1 naut m i l e . F i n a l l y , if, at initiation of a s c e n t of the s e c o n d v e h i c l e , no further t r a c k i n g data w e r e used and the p r e d i c t e d t i m e of p r o p e r phasing f o r a c q u i s i t i o n w a s u n c e r t a i n to one r e v o l u t i o n ^ (out of the p o s s i b l e 24 r e v o l u t i o n m a x i m u m parking o r b i t d u r a - tion) the d i f f e r e n t i a l nodal r e g r e s s i o n ( a s s u m i n g 3 0 ° o r b i t a l i n c l i n a t i o n ) would contribute another 1 naut m i l e . If these e r r o r s a r e independent, the total o u t - o f - p l a n e e r r o r would be r o u g h l y 2 naut m i l e s . A t a range of 250 naut m i l e s this amounts to a r a t h e r s m a l l angle — 0 . 5 ° . E v e n if a r e l a t i v e l y crude g y r o c o m p a s s i n g m o d e w e r e used f o r e s t a b l i s h i n g an in-plane d i r e c t i o n r e f e r e n c e and a f a i r l y inaccurate attitude c o n t r o l s y s t e m e m p l o y e d , it is a l m o s t i n c o n c e i v a b l e that m o r e than a 5 ° b e a m width s e n s o r would be r e q u i r e d .

The e f f e c t of i n - p l a n e e r r o r s depends on how i n j e c t i o n i s i n i t i a t e d . If a r a d a r is used f o r a c q u i s i t i o n , i n j e c t i o n can be c o n v e n i e n t l y initiated when the m e a s u r e d r a n g e c o r r e s p o n d s to a value p r e d e t e r m i n e d f r o m the n o m i n a l o r b i t a l r a d i i — 250 naut m i l e s in the s e l e c t e d c a s e . If a 2 - n a u t - m i l e u n c e r - tainty in r e l a t i v e altitude is a s s u m e d , r e s u l t i n g both f r o m t r a c k i n g and a s c e n t guidance e r r o r s , the angle at which the r e l a t i v e range i s the n o m i n a l v a l u e w i l l be u n c e r t a i n to 0. 5 ° . A g a i n , e v e n if only m o d e s t s p e c i f i c a t i o n s on the h o r i z o n scanner and c o n t r o l s y s t e m a r e set, a 5 ° b e a m width s e n s o r i s adequate. If a 0. 1% range e r r o r e x i s t s , i n j e c t i o n w i l l be started at the w r o n g t i m e and w i l l r e s u l t in a p p r o x i m a t e l y 0. 25 naut m i l e m i s s ( o n e - h a l f an o r b i t l a t e r ) w h i c h can be c o r r e c t e d e a s i l y during the c l o s e d l o o p guidance p h a s e .

Although this u n c e r t a i n t y in p r e d i c t i o n is quite l a r g e , the r e s u l t i n g e r r o r is s m a l l .

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If o p t i c a l s e n s o r s a r e e m p l o y e d , angle m e a s u r e m e n t s o f f e r a m o r e c o n v e n i e n t s o u r c e of data f o r s t a r t i n g i n j e c t i o n . T h i s is a l s o true if an angle t r a c k i n g ( r a t h e r than r a n g e ) r a d a r i s used. H o w e v e r , the a c c u r a c y of the angle m e a s u r e m e n t

depends on the k n o w l e d g e of the l o c a l v e r t i c a l . E r r o r s ranging f r o m a v e r y s m a l l v a l u e to as much as 1 ° m a y r e s u l t depending on the d e t a i l e d m e c h a n i z a t i o n . F o r e x a m p l e , if a h o r i z o n scanner i s used, its e r r o r ( a p p r o x i m a t e l y 0. 5 ) c o m b i n e d with the e r r o r s of the b a s i c a c q u i s i t i o n s e n s o r , its g i m b a l angle t r a n s - d u c e r s , and s t r u c t u r a l m i s a l i g n m e n t s caused in p a r t by t h e r m a l e n v i r o n m e n t m a y l e a d to a 1 ° t o t a l . On the other hand, a

m e c h a n i z a t i o n u t i l i z i n g a star t r a c k e r ( s ) for p r e c i s e attitude r e f e r e n c e (in i n e r t i a l s p a c e ) and ground t r a c k i n g data f o r o r b i t a l p o s i t i o n r e l a t i v e to the e a r t h can l e a d to a v e r y s m a l l e r r o r e s p e c i a l l y if a c c u r a t e angle t r a n s d u c e r s a r e e m p l o y e d and the star t r a c k e r and a c q u i s i t i o n s e n s o r a r e mounted c l o s e t o g e t h e r to r e d u c e s t r u c t u r a l m i s a l i g n m e n t s . The w o r s t c a s e e r r o r of 1 ° i s e q u i v a l e n t to 12 naut m i l e m i s s w h i c h , w h i l e s i z a b l e , can be c o r r e c t e d during the c l o s e d l o o p p o r t i o n of the m i s s i o n with no g r e a t d i f f i c u l t y .

F o l l o w i n g a c q u i s i t i o n and d e t e r m i n a t i o n of the t i m e f o r Hohmann t r a n s f e r i n j e c t i o n , the i n t e r c e p t o r i s o r i e n t e d

h o r i z o n t a l l y and a x i a l thrust a p p l i e d until the r e q u i r e d 180 fps v e l o c i t y i n c r e m e n t has b e e n a c c u m u l a t e d . The r e n d e z v o u s guidance phase m a y then c o m m e n c e at any d e s i r e d t i m e .

The a p p r o p r i a t e i n i t i a l condition e r r o r s f o r the r e n d e z v o u s phase depend on a d e t a i l e d e r r o r a n a l y s i s of the m i s s i o n up to and including i n j e c t i o n . Although the a n a l y s i s is beyond the scope of this p a p e r , r e a s o n a b l e v a l u e s can be s e l e c t e d . A s a l r e a d y m e n t i o n e d , o u t - o f - p l a n e e r r o r s of 2 naut m i l e s a r e not u n r e a s o n a b l e . T h i s p o s i t i o n e r r o r is e q u i v a l e n t to a 14 fps o u t - o f - p l a n e v e l o c i t y e r r o r . In-plane v e r t i c a l p o s i t i o n and v e l o c i t y e r r o r s of these same amounts a r e a l s o quite r e a s o n - a b l e . P o s i t i o n e r r o r along the t r a j e c t o r y depends on the method of initiating t r a n s f e r and can v a r y f r o m 0. 25 naut m i l e to 12 naut m i l e s as d i s c u s s e d a b o v e . T h e v e l o c i t y

e r r o r along the t r a j e c t o r y depends p r i m a r i l y on the k n o w l e d g e of the d i f f e r e n t i a l altitude b e t w e e n o r b i t s and, f o r a 2-naut- m i l e uncertainty, is a p p r o x i m a t e l y 4 f p s .

N o t e : The m a x i m u m v e l o c i t y e r r o r o c c u r s at the line of nodes w h i c h is 9 0 ° r e m o v e d f r o m the point of m a x i m u m p o s i t i o n e r r o r . T h e r e f o r e , both e r r o r s cannot be a m a x - i m u m at the same t i m e , although at 4 5 ° they a r e both s i z a b l e .

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J . HEILFRON A N D F. H. KAUFMAN

M I D C O U R S E G U I D A N C E

A s indicated e a r l i e r , the m i d c o u r s e phase s t a r t s s o m e t i m e after t r a n s f e r i n j e c t i o n and b r i n g s the two v e h i c l e s

t o g e t h e r on a c o l l i s i o n c o u r s e to a s m a l l r a n g e w h e r e b r a k i n g i s i n i t i a t e d . The m i d c o u r s e s c h e m e m u s t , t h e r e f o r e , c o r - r e c t the i n i t i a l t r a n s f e r e r r o r s . Many m i d c o u r s e guidance s c h e m e s have b e e n i n v e s t i g a t e d ranging f r o m o p t i m u m fuel u t i l i z a t i o n types to those e a s i e s t to m e c h a n i z e c o m p u t a t i o n a l l y . T h e y a r e b r i e f l y d i s c u s s e d b e l o w . In a p r a c t i c a l situation, one must e x a m i n e the t r a d e o f f s b e t w e e n fuel e c o n o m y and equipment c o m p l e x i t y and c o n s i d e r not o n l y the e x p e c t e d s o u r c e s and magnitudes of e r r o r s , but a l s o the f l e x i b i l i t y r e q u i r e d to a c c o m p l i s h the m i s s i o n in spite of unexpected trouble s.

O p t i m u m F u e l U t i l i z a t i o n

One of the m o r e i n t e r e s t i n g (and c o m p l e x ) guidance s c h e m e s ( 1 ) p a r t i a l l y m i n i m i z e s the total fuel r e q u i r e d (in the absence of m e a s u r e m e n t e r r o r s ) . F o r any p a r t i c u l a r type of i n i t i a l e r r o r , i . e . , i n - p l a n e o r o u t - o f - p l a n e p o s i t i o n o r v e l o c i t y e r r o r , the o p t i m u m m a n e u v e r i n v o l v e s the a p p l i c a t i o n of a step v e l o c i t y change ( i m p u l s i v e a c c e l e r a t i o n ) at a p a r t i c u l a r point along the o r b i t to e l i m i n a t e p o s i t i o n m i s s at the end, f o l l o w e d b y a second step v e l o c i t y change to a r r i v e f i n a l l y at z e r o r e l a t i v e v e l o c i t y . Both the t i m e of a p p l i c a t i o n of the f i r s t c o r r e c t i o n and the o p t i m u m r e n d e z v o u s point a r e d i f f e r - ent f o r e a c h type and s i z e of i n i t i a l e r r o r . F o r g e n e r a l c o m - binations of i n i t i a l e r r o r s , this t w o - i m p u l s e a p p r o a c h does not r e s u l t in a fuel m i n i m u m , but f r o m a p r a c t i c a l point of v i e w it i s about the m o s t c o m p l e x s c h e m e one would c a r e to m e c h a n i z e .

Using the c o o r d i n a t e s y s t e m shown in F i g . 3, the l i n e a r i z e d equations of thrust f r e e m o t i o n f o r e s s e n t i a l l y c i r c u l a r o r b i t s a r e

χ = Ζωγ

y = -Ζακ + 3co²y £lj

Ζ ζ = - α ) ζ

Solving these equations f o r the i n t e r c e p t o r v e l o c i t y V , r e q u i r e d at the p r e s e n t p o s i t i o n R^ to r e n d e z v o u s an angle Çf later y i e l d s

Numbers in parentheses indicate R e f e r e n c e s at end of paper.

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T E C H N O L O G Y O F LUNAR EXPLORATION

χ^χ χ^χ sinpf + 2 γ^χ 7(1 - cos^f) - 3 ψ sinj/J

"ω 8(1 - cos0) - 3 p( sin0f

- 2 x ^ ( 1 - cospf) + y^ (4 sinßf - 3 ^ cos0

"ω 8(1 - c o s p ) - 3 (7 sinpf

ζ 1 _ cospf

Zl s i n ^

The d i f f e r e n c e b e t w e e n the p r e s e n t v e l o c i t y V and the

r e q u i r e d v e l o c i t y V j r e p r e s e n t s the v e l o c i t y c o r r e c t i o n needed if it is a p p l i e d at point 1. A s s u m i n g this is done, the v e l o c i t y change r e q u i r e d at i n t e r c e p t to m a t c h o r b i t s , i . e . , the braking v e l o c i t y , is g i v e n by

x^ x^ sinpf - 2 y ^ (1 - cosj/)

"05 8 ( 1 - c o s p ) - 3 ÇI sinpf

y² 2 χ^χ (1 - cospf) + y^x (4 sinpi - 3 $

~ω 8(1 - cosj?) - 3 φ sinpi

z2 ^Zl

ω s inj?

The total v e l o c i t y change i s t h e r e f o r e

v^T= | V j- v | + l v²|

W

T h e r e a r e two o p t i m i z a t i o n p o s s i b i l i t i e s . If the f i r s t c o r r e c t i o n is made i m m e d i a t e l y , the o p t i m u m r e n d e z v o u s point is d e t e r m i n e d by m i n i m i z i n g E q . 4 w i t h r e s p e c t to Çl and then computing the r e q u i r e d c o r r e c t i o n - V . How- e v e r , the f i r s t c o r r e c t i o n can be d e l a y e d . Eq. 1 m a y be integrated to predict the position and v e l o c i t y conditions which w i l l apply at some time in the future if no action is presently taken. Using the predicted data, Eq. 4 m a y be again m i n i m i z e d with r e s p e c t to Çf, B y examining a l l future t i m e s , the optimum point for f i r s t c o r r e c t i o n can be d e t e r - mined. This dual optimization r e q u i r e s considerable c o m - putation so a m o r e reasonable technique is to dispense with the prediction aspect and compute the optimum Vrp in r e a l t i m e . The f i r s t c o r r e c t i o n is made as soon as V,p starts to i n c r e a s e . A l s o , as a practical__matter, no c o r r e c t i o n would n o r m a l l y be made unless V·. - V e x c e e d e d its associated uncertainty ( e . g . , the 3cr value) due to m e a s u r e m e n t e r r o r s .

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J. HEILFRON AND F. H. KAUFMAN

Since l i n e a r i z e d a p p r o x i m a t i o n s have b e e n used in the f o r e - g o i n g , it is of i n t e r e s t to e x a m i n e their range of v a l i d i t y . F i g . 4 shows the magnitude of the f i r s t , second, and total v e l o c i t y i n c r e m e n t s d e t e r m i n e d f r o m E q s^e 1-4 for p e r f e c t i n j e c t i o n . F o r the s e l e c t e d m i s s i o n , the equations a r e quite a c c u r a t e f o r r e n d e z v o u s a n g l e s l e s s than 1 2 0 ° . This p o s e s no g r e a t r e s t r i c t i o n since it is r e a s o n a b l e to a s s u m e that t r a n s f e r i n j e c t i o n ( $ = 180°) e r r o r s w i l l not be capable of d e t e c t i o n until s o m e t i m e l a t e r o r they would not have been m a d e in the f i r s t p l a c e ( e x c e p t f o r o u t - o f - p l a n e p o s i t i o n which cannot be c o r r e c t e d t h e n ) .

F i g . 5 shows the magnitude of the v a r i o u s v e l o c i t y i n c r e - ments f o r a 10,000-ft o u t - o f - p l a n e p o s i t i o n e r r o r at i n j e c t i o n as a function of when the f i r s t c o r r e c t i o n is a p p l i e d . The o p t i m u m t i m e is 3 0 ° f r o m n o m i n a l i n t e r c e p t and r e s u l t s in i n t e r c e p t 10° past the n o m i n a l point. A l t h o u g h the Vrp c u r v e shown is quite f l a t , l a r g e r i n i t i a l e r r o r s w i l l r e s u l t in a m o r e pronounced m i n i m u m .

Some of the p e c u l i a r i t i e s in both F i g s . 4 and 5 near $ = 0 a r e due to the fact that the equations a c t u a l l y s o l v e d to produce the c u r v e s accounted f o r n o n i m p u l s i v e and only a x i a l a c c e l e r a - t i o n . A n a c c e l e r a t i o n l e v e l of 1 f t / s e c ^ w a s used as w e l l as a turning r a t e l i m i t of 6 ° / s e c when r e o r i e n t i n g f r o m the d i r e c - tion r e q u i r e d f o r the f i r s t c o r r e c t i o n to that r e q u i r e d for the s e c o n d . T h i s has not a f f e c t e d the m a i n a s p e c t of the r e s u l t s since the V,p of F i g . 4 d o e s not i n c r e a s e near (jl equal z e r o . A i r b o r n e I n t e r c e p t S c h e m e s

T h e r e is an e x t e n s i v e body of k n o w l e d g e , d e v e l o p e d o v e r the past 15 y e a r s , r e l a t i n g to a i r c r a f t i n t e r c e p t i o n which can be a p p l i e d to space r e n d e z v o u s . T h e s e s c h e m e s , e . g . , p r o p o r t i o n a l and b i a s e d p r o p o r t i o n a l n a v i g a t i o n , r e l y only on r e l a t i v e p o s i t i o n and v e l o c i t y m e a s u r e m e n t s b e t w e e n v e h i c l e s and attempt to null the r a t e of r o t a t i o n of the l i n e - o f - s i g h t

( L O S ) . If the L O S r a t e i s z e r o , then, n e g l e c t i n g the d i f f e r e n t i a l g r a v i t y e f f e c t s , c o l l i s i o n w i l l o c c u r since the v e l o c i t y v e c t o r i s a l i g n e d along the L O S . In o r b i t a l r e n d e z v o u s , g r a v i t y d i f f e r e n c e s m a y not be n e g l i g i b l e depending on the o r b i t a l a n g l e s i n v o l v e d . F i g . 6 shows the L O S r a t e f o r the s e l e c t e d m i s s i o n v e r s u s angle f r o m i n t e r c e p t f o r p e r f e c t i n j e c t i o n . A l s o shown is the total v e l o c i t y c o r r e c t i o n r e q u i r e d to null the L O S rate v e r s u s when such a s c h e m e i s i n i t i a t e d . A s i n d i c a t e d , an a p p r e c i a b l e p e n a l t y i s paid f o r u t i l i z i n g such a technique when the o r b i t a l angle is g r e a t e r than 2 0 ° . T h e r e f o r e , t h e r e i s a t r a d e o f f b e t w e e n p e r f o r m a n c e l o s s on one hand and c o m - putational s i m p l i c i t y and independence of the k n o w l e d g e o f the o r b i t c h a r a c t e r i s t i c s on the other hand.

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The p e r f o r m a n c e l o s s can be r e d u c e d g r e a t l y i f no a c t i o n i s taken until the L O S r a t e e x c e e d s a s p e c i f i e d t h r e s h o l d . If this t h r e s h o l d is set at 0 . 5 m r a d / s e c o r h i g h e r , then, at l e a s t for the n o m i n a l p e r f e c t i n j e c t i o n c a s e , no p e r f o r m a n c e l o s s is i n c u r r e d since F i g . 6 i n d i c a t e s that the L O S rate i s l e s s than this value (out to 1 2 0 ° ) .

A t the e x p e n s e of r e q u i r i n g k n o w l e d g e of the o r b i t a l plane d i r e c t i o n , the L O S rate e r r o r to be nulled m a y be d e t e r m i n e d by subtracting the n o m i n a l L O S r a t e (at, for e x a m p l e , the m e a s u r e d r a n g e ) for p e r f e c t i n j e c t i o n f r o m the i n - p l a n e c o m - ponent of the m e a s u r e d r a t e . In p r a c t i c e the r e s u l t i n g e r r o r would be c o m p a r e d to its u n c e r t a i n t y ( e . g . , 3σ v a l u e ) due to m e a s u r e m e n t e r r o r s and no a c t i o n taken unless this u n c e r t a i n t y was e x c e e d e d .

The standard a i r c r a f t i n t e r c e p t i o n p r o b l e m i n v o l v e d o n l y c o l l i s i o n and not z e r o t e r m i n a l v e l o c i t y . S c h e m e s have b e e n c o n s i d e r e d w h i c h produce both ( 2 ) . In this paper w e have a s s i g n e d a s e p a r a t e phase, " b r a k i n g ,¹¹ to the z e r o t e r m i n a l v e l o c i t y a s p e c t although, as m e n t i o n e d e a r l i e r , t h e r e is often no c l e a r d i v i d i n g line b e t w e e n p h a s e s .

B R A K I N G

The m i d c o u r s e guidance s c h e m e s that have b e e n d e s c r i b e d a r e intended to p l a c e the i n t e r c e p t o r on e s s e n t i a l l y a c o l l i s i o n path with the t a r g e t . F o r the p e r f e c t i n j e c t i o n c a s e , an i n t e r - c e p t o r v e l o c i t y change of a p p r o x i m a t e l y 180 fps must be made p r i o r to c o n t a c t . Although this change a p p e a r s as a v e l o c i t y i n c r e a s e in Earth f i x e d o r s i m i l a r c o o r d i n a t e s y s t e m s , it a p p e a r s as a c l o s i n g v e l o c i t y d e c r e a s e in r e l a t i v e c o o r d i n a t e s ; thus, the t e r m " b r a k i n g . " If the t w o v e h i c l e s a r e on a c o l l i s i o n c o u r s e , the o p t i m u m b r a k i n g m a n e u v e r i n v o l v e s an i m p u l s e d e c e l e r a t i o n along the v e l o c i t y v e c t o r and the c o r r e s p o n d i n g step d e c r e a s e in v e l o c i t y . F o r those situations w h e r e l i m i t e d thrust is a v a i l a b l e , the o p t i m u m m a n e u v e r i s m o r e c o m p l e x . H o w e v e r , b r a k i n g n o r m a l l y o c c u r s when the s p a c e c r a f t a r e r e l a t i v e l y c l o s e t o g e t h e r and the t i m e for r e n d e z v o u s c o m p l e - tion s u f f i c i e n t l y s m a l l so that d i f f e r e n t i a l g r a v i t a t i o n a l e f f e c t s g e n e r a l l y can be s a f e l y i g n o r e d . In this e v e n t , w h e t h e r on a c o l l i s i o n c o u r s e o r not, the o p t i m u m a c t i o n i n v o l v e s thrusting at any d e s i r e d a c c e l e r a t i o n l e v e l along the v e l o c i t y v e c t o r to reduce it to z e r o e x c e p t f o r an a r b i t r a r i l y s m a l l value along the final L O S w h i c h w i l l cause the range to go to z e r o after an a p p r o p r i a t e t i m e has e l a p s e d .

If on a c o l l i s i o n c o u r s e ( V along the L O S ) , the a c t i o n must be initiated so as to r e d u c e V to e s s e n t i a l l y z e r o p r i o r to contact. If not on a c o l l i s i o n c o u r s e , the a c t i o n can s t a r t and end at any t i m e as long as the n e g l e c t of g r a v i t y is s t i l l v a l i d .

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J . HEILFRON A N D F. H. KAUFMAN

In p r a c t i c e , t h e r e is a l w a y s a d e s i r e to r e n d e z v o u s as soon as is r e a s o n a b l y p o s s i b l e . T h e r e f o r e , m i n i m u m fuel u t i l i z a t i o n is not a l w a y s o p t i m u m . B e f o r e e x a m i n i n g the g e n e r a l situation at the s t a r t of b r a k i n g , c o n s i d e r the c o l l i s i o n c o u r s e c a s e . If R.£ and V£ a r e the final v a l u e s of range and c l o s i n g v e l o c i t y , r e s p e c t i v e l y , that a r e d e s i r e d after b r a k i n g , then the range R^q at which b r a k i n g should s t a r t is g i v e n by

R = R . + ° ,^f 5

o f 2a L J

w h e r e a = thrust a c c e l e r a t i o n . N o m i n a l l y no a c t i o n would be taken until the range e q u a l e d R ^q and then b r a k i n g i n i t i a t e d until the v e l o c i t y w a s r e d u c e d to V*£. H o w e v e r , unless thrust magnitude c o n t r o l is u t i l i z e d , t h e r e is no g u a r a n t e e , e i t h e r due to thrust o r m a s s u n c e r t a i n t y , that the a c c e l e r a t i o n w i l l be the c o r r e c t v a l u e . If the a c c e l e r a t i o n i s too l o w , c o l l i s i o n can o c c u r at an unacceptable v e l o c i t y ; i f it i s t o o high, the final range can be too g r e a t . T h e r e f o r e , one m u s t p r o v i d e a braking schedule w h i c h a l l o w s f o r the m a x i m u m and m i n i m u m a c c e l e r a t i o n p o s s i b l e and w h i c h s t i l l r e a c h e s the d e s i r e d final conditions in a r e a s o n a b l e t i m e . This can be done v i a t w o switching l i n e s as shown in F i g . 7. The " s t a r t b r a k i n g " c u r v e c o r r e s p o n d s to R^Q ( V^Q) g i v e n b y E q . 5 using the m i n i m u m a c c e l e r a t i o n . The " s t o p b r a k i n g " line can be s e l e c t e d in m a n y w a y s . The one shown c o r r e s p o n d s to a constant t i m e to g o , i . e . , b r a k i n g i s stopped when the t i m e to g o b e c o m e s e x c e s s i v e . Note that the r e g i o n to the left of the s t a r t line is f o r b i d d e n ; o t h e r w i s e c o l l i s i o n w i l l o c c u r (at l e a s t for m i n i m u m a c c e l e r a - tion) p r i o r to b r a k i n g c o m p l e t i o n .

In the g e n e r a l c a s e , the i n t e r c e p t o r w i l l not be on a c o l l i - sion c o u r s e p r i o r to the s t a r t of b r a k i n g . T h e r e f o r e , in a d d i - tion to a b r a k i n g schedule, one m u s t a l s o e m p l o y a guidance s c h e m e which nulls the l a t e r a l m i s s . A s a l r e a d y i n d i c a t e d , braking usually o c c u r s when both the r a n g e and t i m e to r e n d e z - vous a r e s m a l l so that g r a v i t y can be n e g l e c t e d . A n y of the v a r i o u s i n t e r c e p t i o n s c h e m e s can be used e f f i c i e n t l y to null the L O S r a t e , i . e . , the d e s i r e d c o n d i t i o n f o r z e r o l a t e r a l m i s s . T E R M I N A L P H A S E

The t e r m i n a l or v e r n i e r phase b r i n g s the v e h i c l e s t o g e t h e r f r o m the end of braking to final p h y s i c a l c o n t a c t . In m o s t

s y s t e m d e s i g n s , midcourse and b r a k i n g m a n e u v e r s a r e m a d e w i t h an a x i a l engine (with an a c c e l e r a t i o n c a p a b i l i t y b e t w e e n

1 and 3 f t / s e c f o r the s e l e c t e d m i s s i o n ) . During the t e r m i n a l phase it is usually u n d e s i r a b l e to rotate the i n t e r c e p t o r to m a k e v e c t o r c o r r e c t i o n s w i t h this a x i a l e n g i n e . T h e r e f o r e ,

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s m a l l l a t e r a l v e r n i e r engines are added. Longitudinal control can still e m p l o y the main engine, so this dimension is r e a l l y an extension of the braking phase using a schedule as d e s c r i b e d in the f o r e g o i n g , plus c o n t r o l of the v e l o c i t y at impact to keep it within the bounds set by the docking structure. The l a t e r a l scheme must null the L O S r a t e . In c e r t a i n instances w h e r e the target is not attitude stabilized along the L O S , the L O S must be made to match one of the t a r g e t a x e s , e . g . , the r o l l axis or center l i n e . Acceptable values of l a t e r a l m i s s as w e l l as r e l a t i v e angular m i s a l i g n m e n t s must result.

One of the m o r e important aspects of the t e r m i n a l phase i n v o l v e s the "transfer function" of the human o p e r a t o r . S i m - ulation is usually n e c e s s a r y and c e r t a i n results a r e presented in a following section. F o r automatic operation, which might be a backup mode, g e n e r a l guidance r e q u i r e m e n t s can be obtained a n a l y t i c a l l y . In these automatic m o d e s , there is a l o w e r l i m i t of range after which the sensor data b e c o m e s invalid. F o r r a d a r s this is due to the near field of the antenna and, if pulse r a d a r s are used, the pulse width and transponder time d e l a y . F o r optical s e n s o r s , the source to be tracked can b e c o m e l a r g e with r e s p e c t to the field of v i e w . A s indicated in F i g . 8, which depicts the situation after the last c o r r e c t i o n at the m i n i m u m r a n g e , detailed attention must be g i v e n to the v a r i o u s dimensions of the v e h i c l e s , w h e r e the sensors a r e located and hence p r e c i s e l y what they m e a s u r e , the strong interaction of the attitude control s y s t e m , e t c . To simplify m a t t e r s , w e shall consider the degenerate case of point m a s s e s . H e r e the actual m i s s b e c o m e s equal to the distance labeled "d" in F i g . 8 and is given by

d = I T 9 / R a j a ^ a 1

w h e r e the subscript "a" r e f e r s to the actual value of the p a r a m e t e r as opposed to a subscript " m " used later to denote the m e a s u r e d v a l u e . A l s o , the subscript " 1 " r e f e r s to conditions after the last c o r r e c t i o n . Subscript " 2 " w i l l r e f e r to

conditions b e f o r e this c o r r e c t i o n . If the last c o r r e c t i o n i s made by measuring the l a t e r a l v e l o c i t y R^m2 ^ m 2 3^{u s t} P ^{r i o r} ^{t o} the t i m e the m i n i m u m m e a s u r e d r a n g e i s r e a c h e d and thrust applied to null this m e a s u r e d v e l o c i t y , an e r r o r w i l l result as given by

R Ô = R 9 - R 9 = l a t e r a l v e l o c i t y e r r o r 7

al âlâ2â2 ^m2 ^m2^L^J To obtain a quantitative value for the m i s s , assume that the m e a s u r e m e n t e r r o r s in R, R , and Ô a r e j " 5 ft, j " 0.5 fps,

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J. HEILFRON AND F. H. KAUFMAN

and t 0 . 5 m r a d / s e c , r e s p e c t i v e l y . F u r t h e r , a s s u m e that the m i n i m u m s e n s o r range is 10 ft so the l a s t c o r r e c t i o n i s m a d e at a m e a s u r e d value of 15 ft, the m e a s u r e d c l o s i n g v e l o c i t y is

1 fps, and the L O S r a t e nulling s c h e m e d e s i g n e d so that no a c t i o n is taken unless the m e a s u r e d value e x c e e d s a t h r e s h o l d of 1 m r a d / s e c . F o r this e x a m p l e , the w o r s t c a s e m i s s equals 0. 6 ft. In an actual situation other e r r o r s w h i c h have been n e g l e c t e d , such as attitude m i s a l i g n m e n t , w i l l cause a m i s s of s i m i l a r magnitude so that total capture d i s t a n c e s of a foot or so a r e r e a s o n a b l e . Specific attention m u s t be g i v e n to the d e s i g n of the attitude c o n t r o l s y s t e m to insure not only that its a s s o c i a t e d m i s s is s m a l l , but a l s o that its angular m i s a l i g n - m e n t is within the a c c e p t a b l e l i m i t s of the docking m e c h a n i s m . R E N D E Z V O U S SENSOR R E Q U I R E M E N T S

In a l l guidance s c h e m e s , m e a s u r e m e n t s of at l e a s t r e l a t i v e range and v e l o c i t y is r e q u i r e d . C e r t a i n of the s c h e m e s r e q u i r e additional i n f o r m a t i o n , usually the d i r e c t i o n of the l o c a l v e r - t i c a l and o r b i t a l plane n o r m a l , upon w h i c h to base a c o o r d i n a t e s y s t e m . T h e r e a r e a c c u r a c y c o n s t r a i n t s r e l a t i n g to e a c h of the v a r i o u s p i e c e s of data. T h e i n f o r m a t i o n must be g a t h e r e d o v e r a c o n s i d e r a b l e v a r i a t i o n in r e l a t i v e r a n g e , e . g . , f r o m Ζ50 naut m i l e s to 10 ft in the s e l e c t e d c a s e , and p o s s i b l y w h i l e the s p a c e c r a f t u n d e r g o l a r g e attitude e x c u r s i o n s w i t h r e s p e c t to the L O S . A l l of these c o n s i d e r a t i o n s a f f e c t the d e s i g n of the s e n s o r ( s ) . Note that the b a s i c s e n s o r s m a y be l o c a t e d e i t h e r in the i n t e r c e p t o r or in the t a r g e t . In the l a t t e r c a s e , the i n t e r c e p t o r must be capable of r e c e i v i n g and p r o p e r l y i n t e r - p r e t i n g the c o m m a n d s o r data t r a n s m i t t e d f r o m the t a r g e t . T o reduce e q u i p m e n t w e i g h t , s i z e , and p o w e r and to enhance a c c u r a c y , c o o p e r a t i v e t r a n s p o n d e r s , b e a c o n s , l i g h t s o u r c e s , e t c . , a r e p l a c e d in the v e h i c l e not containing the b a s i c s e n s o r s .

R a d a r o f f e r s the m o s t c o n v e n i e n t method of obtaining range i n f o r m a t i o n although o p t i c a l m e t h o d s ( e . g . , t r i a n g u l a t i o n m a y be e m p l o y e d at short r a n g e s . E i t h e r pulse o r C W techniques a r e u s a b l e . C W a p p e a r s to o f f e r r e l i a b i l i t y a d v a n t a g e s in that only s o l i d state d e v i c e s need be used ( 3 ) , C W a l s o can p r o v i d e h i g h e r a c c u r a c y at l e a s t at short r a n g e s v i a phase l o c k t e c h - niques and i s not b o t h e r e d by uncompensated t i m e d e l a y s i n h e r e n t in pulse a p p r o a c h e s . R a n g e r a t e can be obtained b y d i f f e r e n t i a t i n g range or by d i r e c t m e a s u r e m e n t of D o p p l e r shift. T h e r e a r e no p r o b l e m s in obtaining adequate r a n g e and range rate a c c u r a c i e s f o r v a l u e s + 0. 1% ± 5 ft ( b i a s ) and t 0. 5 fps can be a c h i e v e d .

The other t w o l a t e r a l v e l o c i t y c o m p o n e n t s depend on the d e t e r m i n a t i o n of the L O S r a t e s in i n e r t i a l space since the product of L O S rate with r a n g e g i v e s the d e s i r e d l a t e r a l

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v e l o c i t i e s . A n a c c u r a c y of 0 . 5 m r a d / s e c is a c c e p t a b l e at short r a n g e s ; h o w e v e r , much l e s s e r r o r i s d e s i r e d at long r a n g e s . If guidance w e r e i n i t i a t e d at a range of 100 naut m i l e s (0 = 1 2 0 ° ) , then 0 . 0 1 m r a d / s e c i s d e s i r a b l e . T h i s a c c u r a c y can be r e l a x e d by initiating guidance l a t e r . H o w - e v e r , as a g e n e r a l r u l e , such a d e l a y i m p l i e s i n c r e a s e d fuel expenditure depending on the type and s i z e s of i n i t i a l e r r o r s . T h e r e a r e n u m e r o u s a p p r o a c h e s f o r d e t e r m i n i n g the L O S r a t e s u t i l i z i n g a g a i n e i t h e r o p t i c a l o r v a r i o u s r a d a r ( l o b i n g , m o n o p u l s e , or i n t e r f e r o m e t e r ) t e c h n i q u e s . T h e m o s t s t r a i g h t - f o r w a r d and usually l e a s t a c c u r a t e method i s to p r o v i d e a g i m b a l e d s e e k e r with g y r o s mounted on the g i m b a l e d m e m b e r to g i v e the d e s i r e d r a t e s d i r e c t l y . The a c c u r a c y is l i m i t e d by the fixed g y r o d r i f t s r e g a r d l e s s o f the smoothing t i m e used, and the e l e c t r i c a l p o w e r r e q u i r e m e n t s can be p r o h i b i t i v e . A v a r i a t i o n of the s e e k e r a p p r o a c h i n v o l v e s s t a b i l i z i n g the. v e h i - cle in s o m e known d i r e c t i o n and m e a s u r i n g the s e e k e r angle via g i m b a l angle t r a n s d u c e r s . A n g u l a r change d i v i d e d b y the o b s e r v a t i o n t i m e g i v e s the a v e r a g e r a t e although m o r e s o p h i s - t i c a t e d f i l t e r i n g can be d e v i s e d . The a c c u r a c y of the d e v i c e ( s ) which p r o v i d e the c o n t r o l s y s t e m r e f e r e n c e now b e c o m e s i m p o r t a n t .

The L O S s e n s o r can be f i x e d to the s p a c e c r a f t and p r o v i d e suitable e r r o r s i g n a l s ( a n g l e s b e t w e e n L O S and b o r e sight a x i s ) to the attitude c o n t r o l s y s t e m f o r use in a l i g n i n g the v e h i c l e along the L O S . H e r e the w h o l e v e h i c l e a c t s as a s e e k e r , and the s c h e m e i s no m o r e a c c u r a t e than the g i m b a l e d a p p r o a c h if the same type g y r o s a r e u s e d . If the f i x e d s e n s o r has a l a r g e enough f i e l d of v i e w o v e r w h i c h angle i n f o r m a t i o n i s a c c u r a t e , these data can r e p l a c e the s e e k e r g i m b a l angle i n f o r m a t i o n when the v e h i c l e i s not c o n t r o l l e d along the L O S .

An i n e r t i a l p l a t f o r m o f f e r s the m e a n s of p r o v i d i n g e i t h e r a p r e c i s e r e f e r e n c e if the v e h i c l e i s s t a b i l i z e d in i n e r t i a l space or can be used to d e t e r m i n e a c c u r a t e l y the angular change in the L O S if the v e h i c l e i s s e r v o e d to i t . A p l a t f o r m m i g h t be l e f t o v e r f r o m the a s c e n t phase o r d e s t i n e d to be used in a l a t e r p o r t i o n of the m i s s i o n . C o n s e q u e n t l y , it m a y not be d i r e c t l y c h a r g e a b l e as s p e c i a l r e n d e z v o u s e q u i p m e n t . The p l a t f o r m can be a s s u m e d to be suitably a l i g n e d p r i o r to i n j e c - tion, and its d r i f t up to the t i m e of docking i s n o r m a l l y n e g l i - g i b l e . It a l s o can be used to p r o v i d e any c o o r d i n a t e s y s t e m r e f e r e n c e that m a y be r e q u i r e d . If a p l a t f o r m is not u t i l i z e d and c o o r d i n a t e d i r e c t i o n s s t i l l d e s i r e d , the v e h i c l e m a y be aligned along the l o c a l v e r t i c a l b y h o r i z o n s c a n n e r s and a g y r o c o m p a s s m o d e used to d e t e c t o r b i t a l r a t e and the d i r e c - tion of the o r b i t . If this s c h e m e is s e l e c t e d , s e n s o r s a l w a y s r e q u i r i n g v e h i c l e a l i g n m e n t along the L O S cannot be e m p l o y e d .

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The p r o p u l s i o n c o n f i g u r a t i o n a l s o i n t e r a c t s h e a v i l y w i t h the r e n d e z v o u s s e n s o r s . A s m e n t i o n e d e a r l i e r , n o r m a l l y a s i n g l e a x i a l engine (with two thrust c h a m b e r s canted f r o m the c e n t e r line so as not to i m p i n g e on the t a r g e t during the final docking p e r i o d ) is used for a l l v e l o c i t y c o r r e c t i o n s during the m i d - c o u r s e and b r a k i n g p e r i o d s . In g e n e r a l the s p a c e c r a f t m u s t be o r i e n t e d in the p r o p e r d i r e c t i o n to m a k e v e c t o r c o r r e c t i o n s . If data a r e d e s i r e d during these m a n e u v e r s , the s e n s o r s must have a suitable f i e l d of v i e w . I n e r t i a l c o o r d i n a t e s y s t e m i n f o r m a t i o n can be l o s t i f the h o r i z o n s c a n n e r - g y r o c o m p a s s a p p r o a c h is u s e d . H o w e v e r , it i s often f e a s i b l e to make m e a s - u r e m e n t s b e f o r e and after t h r u s t i n g s and to "dead r e c k o n " d u r - ing the actual m a n e u v e r s . T h i s e l i m i n a t e s c e r t a i n p r o b l e m s .

T h e r e a r e a multitude of s i m i l a r c o n s i d e r a t i o n s w h i c h affect the s e l e c t i o n of the r e n d e z v o u s s c h e m e including the s e n s o r a p p r o a c h . S c h e m e s can be d e v i s e d w h i c h r e q u i r e s e n s o r c h a r - a c t e r i s t i c s c o m p l e t e l y within the state of the t e c h n i c a l a r t . H o w e v e r , such equipment i s not " o f f - t h e - s h e l f . " The d e t a i l e d d e s i g n ( s ) m u s t be t a i l o r e d to the s p e c i f i c m i s s i o n and m e c h a n i - z a t i o n and, t h e r e f o r e , m u s t a w a i t c e r t a i n m a j o r d e c i s i o n s as to the w a y manned lunar e x p l o r a t i o n w i l l be a c c o m p l i s h e d . M A N N E D R E N D E Z V O U S A N D D O C K I N G S I M U L A T I O N S

A number of manned r e n d e z v o u s and docking simulations have b e e n r e p o r t e d t e s t i f y i n g to m a n ' s potential c a p a b i l i t y f o r

s k i l l f u l l y and r e l i a b l y p e r f o r m i n g these m a n e u v e r s . L e v i n and W a r d (4) f i r s t r e p o r t e d studies on m a n ' s c a p a b i l i t y f o r c o - p l a n a r o r b i t a l r e n d e z v o u s . Since then, e x t e n s i v e s i m u l a - tions of manned r e n d e z v o u s have b e e n conducted b y N A S A — f i r s t , c o - p l a n a r studies d e s c r i b e d in R e f . 5, and then six d e g r e e - o f - f r e e d o m s i m u l a t i o n s r e p o r t e d in R e f . 6. A d d i t i o n a l simulations (7) d e m o n s t r a t e that the data fundamental for conducting automatic r e n d e z v o u s a r e c o m p a t i b l e w i t h manned r e n d e z v o u s . A n y of the techniques d e s c r i b e d in these s i m u l a - tions a r e adequate f o r basing the a c c o m p l i s h m e n t of p r o j e c t e d lunar m i s s i o n s by manned r e n d e z v o u s .

A l l of these studies r e q u i r e an e x t e n s i o n in the r e g i o n of final t e r m i n a l c o n t r o l just p r i o r to docking contact, that i s , the l a s t f e w hundred f e e t . R e f . 8 r e p o r t s a s i m u l a t i o n which w a s conducted to d e t e r m i n e m a n¹ s a b i l i t y to match v i s u a l l y his s p a c e c r a f t ' s p o s i t i o n , v e l o c i t y , and angular a l i g n m e n t with that of a t a r g e t s p a c e c r a f t . A m e a s u r e m e n t of the a c c u r a c y of man c o n t r o l l e d docking guidance s y s t e m is v i t a l in defining m a n ' s c a p a b i l i t i e s and f o r e s t a b l i s h i n g r e a l i s t i c r e q u i r e m e n t s on the docking structure and i t s m e c h a n i s m s . S p e c i f i c a l l y , this s i m u l a t i o n d e t e r m i n e d the 1) f e a s i b i l i t y of docking, 2) t e r m i n a l v a l u e s of range r a t e , L O S a n g l e , L O S

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r a t e , l a t e r a l m i s s , r e l a t i v e r o l l angle e r r o r , and fuel u t i l i z a - tion, 3) t y p i c a l p i l o t p r o c e d u r e s and c a p a b i l i t i e s , and 4) m i n i - m u m d i s p l a y r e q u i r e m e n t s .

The t a r g e t v e h i c l e w a s a s s u m e d to be a t t i t u d e - s t a b i l i z e d in a c i r c u l a r o r b i t w i t h its longitudinal a x i s c o i n c i d e n t w i t h the i n e r t i a l v e l o c i t y v e c t o r , i . e . , not a l i g n e d along the t a r g e t - t o - i n t e r c e p t o r L O S . Using a s i m u l a t e d p e r i s c o p e v i e w of the t a r g e t plus r a d a r - d e r i v e d r a n g e and range r a t e i n f o r m a t i o n , the p i l o t w a s r e q u i r e d to m a n e u v e r his v e h i c l e (the i n t e r c e p t o r ) into the o r b i t plane, t o a l i g n his r o l l a x i s , to e s t a b l i s h a

s p e c i f i e d r e l a t i v e r o l l attitude ( a l l w i t h r e s p e c t to the t a r g e t ) , and in this o r i e n t a t i o n to dock the v e h i c l e s w i t h a d e s i r e d c l o s i n g r a t e of a p p r o a c h .

T w o c o n t r o l sticks w e r e p r o v i d e d in the c o c k p i t s i m u l a t o r so that the p i l o t could c o m m a n d t r a n s l a t i o n a l a c c e l e r a t i o n along e a c h b o d y a x i s and attitude c o n t r o l about e a c h b o d y a x i s . The i n t e r c e p t o r v e h i c l e w a s i n i t i a l l y 3000 ft a w a y f r o m the t a r g e t v e h i c l e w i t h a c l o s i n g r a n g e r a t e of 30 fps and w i t h n e g l i g i b l e L O S r a t e s (2 m r a d / s e c o r l e s s ) . V a r i o u s c o m b i n a - tions of i n t e r c e p t o r attitude e r r o r s w e r e a l s o included as i n i t i a l c o n d i t i o n s . T e r m i n a t i o n of e a c h f l i g h t o c c u r r e d when the docking f a c e s of the t w o v e h i c l e s r e a c h e d an 8-ft s e p a r a - t i o n .

A n o p t i c a l s e n s o r , such as a p e r i s c o p e or T V c a m e r a , w a s a s s u m e d mounted on and b o d y - f i x e d to the i n t e r c e p t o r docking face w i t h the o p t i c a l L O S c o l l i n e a r w i t h the r o l l a x i s . R e f e r - r i n g to F i g . 9, t h r e e docking f a c e m a r k e r s (such as l a m p s ) w e r e a s s u m e d to be mounted on the docking f a c e of the t a r g e t .

The m a r k e r s w e r e spaced 9 0 ° a p a r t so that a r e l a t i v e r o l l e r r o r b e t w e e n the i n t e r c e p t o r and the t a r g e t could be d e t e r - m i n e d f r o m the p i l o t ' s d i s p l a y .

In the f i x e d - b a s e s i m u l a t o r c o c k p i t , the p i l o t w a s p r e s e n t e d w i t h an o s c i l l o s c o p e d i s p l a y of the docking and r e a r f a c e s of the t a r g e t . In addition, l o g r a n g e and r a n g e r a t e m a r k e r s w e r e s u p e r i m p o s e d on the s a m e d i s p l a y surface d i r e c t l y b e l o w the p e r i s c o p e v i e w as shown in F i g . 9. The c i r c u l a r t a r g e t f a c e s w e r e e s s e n t i a l l y the s a m e s i z e . The t a r g e t docking f a c e was i d e n t i f i e d b y the r o l l a x i s m a r k e r s (not p r e s e n t on the r e a r f a c e ) . The d i s p l a y d i m e n s i o n s c o r r e s p o n d e d e x a c t l y to a t a r - get v i e w as seen through an a p e r t u r e on the i n t e r c e p t o r docking f a c e .

Attitude e r r o r s w e r e i n d i c a t e d in the d i s p l a y by the distance that the c e n t r o i d of the t w o t a r g e t c i r c l e s w a s d i s p l a c e d f r o m the c e n t e r of the s i m u l a t e d v i e w i n g s c r e e n . Guidance e r r o r s w e r e i n d i c a t e d by the r e l a t i v e d i s p l a c e m e n t of the f r o n t and r e a r c i r c l e s . T h i s d i s p l a c e m e n t w a s p r o p o r t i o n a l to the L O S

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J . HEILFRON A N D F. H. K A U F M A N

angle in the c a s e of p e r f e c t attitude c o n t r o l ( i . e . , when the c e n t r o i d of the t a r g e t c o i n c i d e d w i t h the v i e w i n g p o r t c e n t e r ) .

F i v e p i l o t s ( r e f e r r e d to h e r e as p i l o t s A through E ) w e r e s e l e c t e d f o r s i m u l a t o r t r a i n i n g . S e l e c t i o n s w e r e m a d e on the b a s i s of n o n f a m i l i a r i t y with the o r b i t a l docking s y s t e m . H o w - e v e r , p i l o t s D and Ε w e r e s e l e c t e d b e c a u s e of t h e i r p r e v i o u s a i r c r a f t f l i g h t t r a i n i n g and e x p e r i e n c e . Each p i l o t made 12

s i m u l a t e d f l i g h t s after a t r a i n i n g p e r i o d of a p p r o x i m a t e l y 2 h r s . F r o m these 60 f l i g h t s , 52 w e r e used to p r o v i d e the individual p i l o t a v e r a g e s p r e s e n t e d in F i g . 10. E i g h t flights r e s u l t e d in data e x t r e m e s w h i c h w e r e not included in the a v e r a g e s . The o v e r a l l a v e r a g e i s indicated w i t h a dashed l i n e .

R e f e r r i n g to F i g s . 10-a and 10-b, the v a r i a t i o n of the individual a v e r a g e of the p i l o t s f r o m the o v e r a l l a v e r a g e is a p p r o x i m a t e l y 50% of the o v e r a l l a v e r a g e value f o r both L O S angle and L O S r a t e . Note that e x c l u d i n g p i l o t Ε data would l o w e r the o v e r a l l a v e r a g e v a l u e s s i g n i f i c a n t l y . The o v e r a l l a v e r a g e value of range r a t e ( 0 . 4 f t / s e c ) and the v a r i a t i o n of individual a v e r a g e s f r o m this value a r e s m a l l , a s shown in F i g . 1 0 - c . A l a r g e v a r i a t i o n b e t w e e n p i l o t s in l a t e r a l m i s s w a s r e c o r d e d ( F i g . 1 0 - d ) . It i s f e l t that these v a r i a t i o n s would be r e d u c e d w i t h i n c r e a s e d p i l o t t r a i n i n g .

A v e r a g e r o l l e r r o r s a r e shown in F i g . 1 0 - e . During the e a r l i e r f l i g h t s , s o m e of the p i l o t s c o n c e n t r a t e d on L O S c o r r e c - tions and n e g l e c t e d to c o r r e c t the r o l l e r r o r until a l m o s t the l a s t p o s s i b l e m o m e n t . A f t e r being i n s t r u c t e d to d e v o t e m o r e attention to r o l l angle e r r o r , the c o r r e c t i o n s w e r e made quite e a s i l y . A s shown in F i g . 10-f, four of the p i l o t s had s i m i l a r a v e r a g e f l i g h t t i m e s , w h i l e p i l o t B ' s a v e r a g e is s o m e w h a t l o w e r . P i l o t B^!s data p e r h a p s g i v e an i n d i c a t i o n of the m i n i - m u m f l i g h t t i m e to be e x p e c t e d f o r the g i v e n set of i n i t i a l c o n d i t i o n s .

A s indicated by F i g . 10-g, the individual d e v i a t i o n s f r o m the o v e r a l l a v e r a g e of guidance fuel r e q u i r e d w a s s m a l l , indicating that a l l the p i l o t s e n c o u n t e r e d a p p r o x i m a t e l y the s a m e d e g r e e of d i f f i c u l t y in m a k i n g e f f i c i e n t guidance c o r r e c - t i o n s . The d e v i a t i o n s f r o m the o v e r a l l a v e r a g e of attitude c o n t r o l fuel in F i g . 10-h a p p e a r to be r e l a t i v e l y l a r g e . H o w - e v e r , if t y p i c a l v a l u e s of i n e r t i a s , m o m e n t a r m s , and s p e c i f i c i m p u l s e a r e a s s u m e d f o r the v e h i c l e , the individual a v e r a g e s of n o r m a l i z e d attitude c o n t r o l s y s t e m ( A C S ) fuel as w e l l as the o v e r a l l a v e r a g e can be shown to be s m a l l in t e r m s of w e i g h t .

The c o n c l u s i o n r e a c h e d that both the o v e r - a l l a v e r a g e t e r - m i n a l v a l u e s and the individual p e r c e n t d e v i a t i o n s f r o m the a v e r a g e v a l u e s could be l o w e r e d by a higher p i l o t t r a i n i n g l e v e l is j u s t i f i e d by the s i g n i f i c a n t i m p r o v e m e n t in the r e l a t i v e

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s u c c e s s of the l a t e r s i m u l a t e d f l i g h t s . If the p i l o t s w e r e t r a i n e d f o r a l o n g e r p e r i o d , it i s r e a s o n a b l e to p r o j e c t that the L O S a n g l e , L O S r a t e , r e l a t i v e r o l l e r r o r , and l a t e r a l m i s s t e r m i n a l v a l u e s could be r e d u c e d by a f a c t o r of t w o .

S e v e r a l f l i g h t s w e r e m a d e w i t h no r a n g e and range r a t e i n f o r m a t i o n e x p l i c i t l y d i s p l a y e d to the p i l o t , i . e . , he m a n e u - v e r e d using the o p t i c a l d i s p l a y a l o n e . The f e w f l i g h t s made in this m a n n e r w e r e r e l a t i v e l y s u c c e s s f u l , c o m p a r e d to f l i g h t s m a d e w i t h r a d a r data. T h i s s u g g e s t s that, w i t h a s u f f i c i e n t l y high d e g r e e of p i l o t t r a i n i n g , the r a d a r - d e r i v e d i n f o r m a t i o n can be r e m o v e d without i m p a i r i n g the s u c c e s s of the m i s s i o n . One s u c c e s s f u l flight w a s m a d e w i t h the o p t i c a l d i s p l a y ,

e x c l u d i n g r a n g e and r a n g e r a t e i n f o r m a t i o n , but p r o v i d i n g a m e t e r e d L O S angle i n s t e a d . T i m e w a s not a v a i l a b l e to i n v e s - tigate a l l of the s i g n i f i c a n t a s p e c t s of m i n i m u m d i s p l a y r e q u i r e - m e n t s . The i n v e r s e r e l a t i o n b e t w e e n d i s p l a y r e q u i r e m e n t s and p i l o t t r a i n i n g l e v e l w a s c l e a r l y i n d i c a t e d although not s t a t i s - t i c a l l y d e t e r m i n e d .

D O C K I N G S T R U C T U R E A N D M E C H A N I S M S

B e c a u s e of u n c e r t a i n t i e s w h i c h o c c u r in the t e r m i n a l guidance, p r o p u l s i o n , and attitude c o n t r o l s y s t e m s f o r both manned and automatic c o n t r o l l e d d o c k i n g , a l l o w a n c e m u s t be m a d e in docking s t r u c t u r e and m e c h a n i s m d e s i g n s to a c c o m - m o d a t e the l a t e r a l docking m i s s , attitude m i s a l i g n m e n t be~

t w e e n the s p a c e c r a f t at d o c k i n g , and the n o m i n a l i m p a c t v e l o c i t y and its d i s p e r s i o n s . T y p i c a l d e s i g n g o a l s which e f f e c t a c c e p t a b l e c o m p r o m i s e s b e t w e e n docking a c c u r a c y i m p l i c a t i o n s and s t r u c t u r e s i z e and w e i g h t a r e

C l o s i n g r a t e 0 . 1 - 2 . 5 f t / s e c L a t e r a l m i s s (capture d i s t a n c e ) + 1.5 ft

Attitude m i s a l i g n m e n t (any a x i s ) ί 5 deg

C o m p a r i n g t h e s e d e s i g n c r i t e r i a w i t h the e x p e c t e d docking a c c u r a c i e s d i s c u s s e d e a r l i e r i n d i c a t e s that r e a s o n a b l e p r o v i - sion has b e e n m a d e f o r a b n o r m a l e v e n t s .

The i m p l i c a t i o n s of t h e s e i n i t i a l conditions a r e that the d e s i g n of the docking s t r u c t u r e and m e c h a n i s m s must p r o v i d e t h r e e m a j o r c a p a b i l i t i e s : a ) a capture and g e n e r a l a l i g n m e n t of the t w o s p a c e c r a f t ; b) a c o n t r o l l e d a b s o r p t i o n of the i m p a c t e n e r g y without d a m a g e ; c ) a latching of the d o c k e d s p a c e c r a f t to produce the r e q u i r e d s t r u c t u r a l i n t e g r i t y and fine a l i g n m e n t of the two v e h i c l e s .

Although p a r a l l e l o r s i d e - b y - s i d e docking techniques c e r t a i n l y can be e n g i n e e r e d , it i s b e l i e v e d that tandem d o c k - ing methods w i l l be the f i r s t used on e a r l y lunar m i s s i o n s .

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T h e s e methods a r e at l e a s t as e a s i l y i m p l e m e n t e d as the p a r a l l e l d e s i g n a p p r o a c h e s , and docking i m p a c t loads a r e a b s o r b e d along the s p a c e c r a f t a x i s n o r m a l l y d e s i g n e d by l o a d s during the b o o s t p h a s e . F o r these r e a s o n s , the c o n f i g u - r a t i o n s shown a r e l i m i t e d to c o n c e p t s r e l a t e d to tandem d o c k - ing.

C o n s i d e r a t i o n s of connecting t o g e t h e r a t w o - s t a g e d i n j e c - tion r o c k e t in o r b i t f o r lunar m i s s i o n s as w e l l as p r o v i d i n g for p e r s o n n e l and p r o p e l l a n t t r a n s f e r l e a d s to the chosing of techniques that a l l o w c l o s e mating of the s p a c e c r a f t . T o a c c o m p l i s h capture and g e n e r a l a l i g n m e n t , t h e r e a r e at l e a s t t h r e e g e n e r a l c o n f i g u r a t i o n s ; matched c o n e s , unmatched

c o n e s , and s e l f - a l i g n i n g p r o b e s , which can a l l o w c l o s e m a t i n g . The m a t c h e d cone c o n f i g u r a t i o n , d i a g r a m m e d in F i g . 11-a, u t i l i z e s i d e n t i c a l " c o n i c a l " s u r f a c e s ; one r e c e s s e d , the other p r o t r u d i n g , to p r o v i d e capture and a l i g n i n g c a p a b i l i t y . The cone a n g l e s of both p o r t i o n s of the docking s t r u c t u r e a r e i d e n t i c a l . The c h o i c e of capture distance is p r i m a r i l y d e p e n d - ent upon the t e r m i n a l guidance s y s t e m a c c u r a c y including a judgment f a c t o r f o r s o m e a b n o r m a l c o n d i t i o n s . Capture d i s t a n c e s of 1.5 ft g e n e r a l l y a r e s u i t a b l e . The upper l i m i t on cone angle δ is a function of a c c e p t a b l e d e s i g n l o a d s and the r e l a t i v e m o t i o n f o l l o w i n g docking i m p a c t s . A r e a s o n a b l e upper l i m i t f o r δ is 3 0 ° . O v e r a l l v e h i c l e length as w e l l as docking s t r u c t u r e w e i g h t tend to a l l o w δ to be no l o w e r than 2 0 ° .

Matched c o n e s , when the v e h i c l e s have c o m p l e t e d docking, w i l l i n h e r e n t l y p r o v i d e the g e n e r a l a l i g n m e n t r e q u i r e d . H o w - e v e r , high s t r e s s l e v e l s can be e x p e c t e d to o c c u r along e i t h e r c o n i c a l surface at points A and Β shown in F i g . 11-a. Contact s t r e s s e s o c c u r f o r n o m i n a l o f f s e t conditions at point A and can o c c u r f o r n o m i n a l conditions of o f f s e t and angular m i s a l i g n - m e n t at point B . The angular m i s a l i g n m e n t conditions shown in F i g . 11-a a r e e x a g g e r a t e d f o r p i c t o r i a l p u r p o s e s . Simula- tions of m a t c h e d cone docking r e p o r t e d in R e f . 9 show that, e v e n f o r high c l o s i n g v e l o c i t i e s , f r i c t i o n and m e c h a n i s m d y n a m i c s can s t i l l p r e v e n t capture and a l i g n m e n t . This p r o b l e m is a g g r a v a t e d by l o w e r c l o s i n g v e l o c i t i e s . In f a c t , the m a t c h e d cone c o n f i g u r a t i o n r e q u i r e s a c a r e f u l c o n t r o l on both the l o w e r and upper l i m i t of c l o s i n g rate f o r successful d o c k i n g . Matched c o n e s n e v e r t h e l e s s can be made to w o r k .

The unmatched cone c o n f i g u r a t i o n shown in F i g . 11-b p r o v i d e s c o n s i d e r a b l e i m p r o v e m e n t in capture c a p a b i l i t y f o r a g i v e n r e c e s s e d cone depth, and the contact s t r e s s e s along the r e c e s s e d cone w a l l a r e no w o r s e than the m a t c h e d cone c o n f i g u r a t i o n . H o w e v e r , since the r e c e s s e d cone angle of about 3 0 ° i s l a r g e r than the p r o t r u d i n g cone angle of about 1 2 . 5 ° , contact s t r e s s p r o b l e m s due to i m p a c t s on the shoul-

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d e r s of the r e c e s s e d cone ( s e e point B, F i g . 1 1 - a ) a r e virtually- e l i m i n a t e d . H o w e v e r , since the unmatched cone d o e s not have the a l i g n m e n t c a p a b i l i t y of the m a t c h e d c o n e , an a x i a l r o c k e t should be added to one ( o r both of the v e h i c l e s ) to a s s i s t final a l i g n m e n t .

The s e l f - a l i g n i n g p r o b e c o n f i g u r a t i o n u s e s the capture and g e n e r a l a l i g n i n g q u a l i t i e s of m a t c h e d c o n e s at i n i t i a l contact but a v o i d s the u n d e s i r a b l e contact s t r e s s e s and potential f r i c - tion p r o b l e m s b y capturing the t w o v e h i c l e s b e f o r e the s i g n i f i - cant docking l o a d s a r e a b s o r b e d . F i g . 12 shows the p r o b e , which i s capable of a b s o r b i n g i m p a c t l o a d s along the p r o b e a x i s , e n t e r i n g a s m a l l r e c e s s e d cone w h o s e capture c a p a b i l i t y can be m a d e equal to that of the other c o n f i g u r a t i o n s but f o r much s m a l l e r cone d i m e n s i o n s .

The s e l f - a l i g n i n g probe i s doubly a r t i c u l a t e d and as such v e r y l i t t l e f o r c e i s e x e r t e d b e t w e e n the two v e h i c l e s until the probe is seated and latched in the r e c e s s e d c o n e . F o r this r e a s o n , successful docking can o c c u r w i t h the s e l f - a l i g n i n g p r o b e f o r e v e n v e r y l o w c l o s i n g r a t e s . T h i s is p a r t i c u l a r l y valuable f o r m a n - c o n t r o l l e d docking since m a n i n h e r e n t l y tends to c l o s e s l o w l y as d i s c u s s e d in R e f . 8.

The m o m e n t s applied to e i t h e r v e h i c l e can be taken out by c o n t r o l l e d - c o n t a c t b u m p e r s on the outer s h e l l s t r u c t u r e of the v e h i c l e s . The s e l f - a l i g n i n g p r o b e c o n f i g u r a t i o n i s i d e a l l y suited to p r o p e l l a n t t r a n s f e r . H o w e v e r , v a r i a t i o n s on the b a s i c p r i n c i p l e can be a p p l i e d f o r connecting s t a g e s f o r m u l - t i p l e stage o p e r a t i o n or p e r s o n n e l t r a n s f e r . E n e r g y a b s o r p t i o n for the s e l f - a l i g n i n g p r o b e can be i m p l e m e n t e d b y a r a t c h e t e d

spring along the b o o m a x i s , b y b u m p e r s on the outer s h e l l s h o u l d e r s , and by the attitude c o n t r o l s y s t e m of the v e h i c l e s . The p r o b e can be d r a w n up f o r final stage latching w h e r e d e s i r e d .

A t y p i c a l s t r u c t u r a l d e s i g n f o r the e n e r g y a b s o r p t i o n and latching the unmatched (and m a t c h e d ) cone c o n f i g u r a t i o n is shown in F i g . 11. Supporting the r e c e s s e d cone by s p r i n g - d a m p e r s and w i t h latching d e v i c e s on the p e r i p h e r y of the v e h i c l e g i v e s a c o n f i g u r a t i o n w h i c h i s at l e a s t as c o m p l e x as the s e l f - a l i g n i n g p r o b e if the contact s t r e s s e s a r e e q u i v a l e n t l y l i m i t e d .

In a l l c a s e s c o a r s e r o l l a l i g n m e n t is a c c o m p l i s h e d by attitude c o n t r o l and guidance s e n s o r s . Fine r o l l a l i g n m e n t w h e r e n e c e s s a r y g e n e r a l l y can be e f f i c i e n t l y i m p l e m e n t e d by aligning s m a l l d e v i c e s r a t h e r than e n t i r e s t a g e s , although the s e l f - a l i g n i n g p r o b e can be r e a d i l y adapted to stage r o l l a l i g n - m e n t . A l l of these techniques r e t a i n a c a p a b i l i t y f o r m u l t i p l e docking and hence a f l e x i b i l i t y in o p e r a t i o n s planning.