RENDEZVOUS AND DOCKING TECHNIQUES

TECHNOLOGY OF LUNAR EXPLORATION

RENDEZVOUS AND DOCKING TECHNIQUES J. H e i l f r o n

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and F . H . Kaufman

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Space T e c h n o l o g y L a b o r a t o r i e s , Inc. Redondo B e a c h , C a l i f o r n i a ABSTRACT E n g i n e e r i n g techniques applicable 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 treated, 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 phase, a braking 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 tion. 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 for 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 solution. 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 application although the n u m e r i c a l v a l u e s quoted apply only 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 gether with simulation r e s u l t s . F u e l e c o n o m y , equipment 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 day 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 dynamic a s p e c t s of docking during the p e r i o d b e t w e e n initial contact and final mating a r e d i s c u s s e d , including structural r e q u i r e ments i m p o s e d on the m e c h a n i s m s . INTRODUCTION 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 of 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 capable of d i r e c t flight. This 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 sponsored 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 . ^Associate Manager, Systems Design Department.

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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 place 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, or 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 ascent or parking o r b i t s can be used; the orbits can be c i r c u l a r or m o r e g e n e r a l e l l i p s e s ; finally, either or both of the spacecraft can participate 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 discuss the p r o s and cons of e a c h approach or 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 tions, one p a r t i c u l a r p r o f i l e has been s e l e c t e d to d i s p l a y the significant features of m o s t r e n d e z v o u s m i s s i o n s . In many 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 there is no s e v e r e t i m e constraint. The 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 with 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 . This 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 or 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 important factor 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, alternate or backup m o d e s , e t c . , a s s o c i a t e d with 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 rather e a s i l y m e c h a n i z e d with m o d e s t equipment 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 additional 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 safety 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 . MISSION 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 ascent t r a j e c t o r i e s , the r e n d e z v o u s and ascent 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 for r e n d e z v o u s with 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 features basic 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 been 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 acceptable for 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 per 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 which 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 1 the Earth 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 each 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 , which was launched f i r s t , how long they have been in 238

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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 ascent 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 chosen a r e r e a s o n a b l e f o r Earth o r b i t a l operations 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 by the Van A l l e n belt 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 been 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 two v e h i c l e s . This 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 injection, a m i d c o u r s e guidance phase ensues to c o r r e c t injection e r r o r s and place 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 with the t a r g e t . When the r e l a t i v e range 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 is reduced to e s s e n t i a l l y z e r o . T h i s phase is t e r m e d " b r a k 41 ing. 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, finally, 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 suit» In m a n y situations there is no c l e a r dividing line b e t w e e n p h a s e s . H o w e v e r , they have been separated h e r e to c o r r e spond to three 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 is 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 is r e a s o n a b l y p o s s i b l e . This g i v e s r i s e to the braking 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 reduced to a v o i d c o l l i s i o n at too 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 must r e s u l t . T h i s is the task of the t e r m i n a l p h a s e . ACQUISITION AND TRANSFER INJECTION The r e l a t i v e g e o m e t r y at the t i m e for p r o p e r injection is shown in F i g . 1. The injection can e i t h e r be based on ground c o m m a n d s or 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 initiated f r o m spacecraft measurements. In an actual m i s s i o n this might be either the p r i m a r y or a backup mode 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 range (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 cones ( i f s e a r c h is used at a l l ) 239

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t h e r e f o r e can be e m p l o y e d . If injection w e r e p a r t of the ascent phase and r e n d e z v o u s sensor acquisition d e l a y e d until l a t e r , the acquisition range would d e c r e a s e and the angular uncertainty 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 there a r e c e r t a i n tradeoffs b e t w e e n the ascent 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 by pointing the s e n s o r s ( r a d a r or optical) 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 waiting 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-ofplane 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 , there is the uncertainty of the o r b i t a l plane of the f i r s t spacecraft 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 tracking s y s t e m s ) . Second, there a r e ascent guidance e r r o r s for the second v e h i c l e which might a l s o be equivalent to 1 naut m i l e . F i n a l l y , if, at initiation of ascent of the second v e h i c l e , no further tracking data w e r e used and the p r e d i c t e d time 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 uncertain 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 duration) the d i f f e r e n t i a l nodal r e g r e s s i o n (assuming 30° o r b i t a l inclination) 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 roughly 2 naut m i l e s . A t a range of 250 naut m i l e s this amounts to a rather 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 mode w e r e used for establishing 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 sensor would be r e q u i r e d . The effect of in-plane e r r o r s depends on how injection i s initiated. If a r a d a r is used for a c q u i s i t i o n , injection can be conveniently initiated when the m e a s u r e d range 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 nominal 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 assumed, resulting both f r o m tracking and ascent guidance e r r o r s , the angle at which the r e l a t i v e range is the nominal value w i l l be uncertain 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 sensor is adequate. If a 0. 1% range e r r o r e x i s t s , injection 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 ) which 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 phase.

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

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If optical 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 offer a m o r e convenient source of data for starting injection. T h i s is a l s o true if an angle tracking ( r a t h e r than r a n g e ) radar 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 knowledge 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 value 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 is used, its e r r o r ( a p p r o x i m a t e l y 0. 5 ) combined with the e r r o r s of the basic acquisition 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 structural 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 lead to a 1 ° total. 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 space) and ground tracking data f o r o r b i t a l position r e l a t i v e to the e a r t h can lead 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 accurate 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 acquisition sensor are mounted c l o s e together to reduce structural 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 ° is equivalent to 12 naut m i l e m i s s which, while 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 loop p o r t i o n of the m i s s i o n with no g r e a t difficulty. F o l l o w i n g acquisition 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 injection, the i n t e r c e p t o r i s oriented h o r i z o n t a l l y and a x i a l thrust applied 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 been accumulated. 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 injection. Although the analysis is beyond the scope of this paper, 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 mentioned, out-of-plane e r r o r s of 2 naut m i l e s are not u n r e a s o n a b l e . This p o s i t i o n e r r o r is equivalent to a 14 fps out-of-plane v e l o c i t y e r r o r . In-plane v e r t i c a l position 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 able. 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 . The 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 knowledge of the d i f f e r e n t i a l altitude between o r b i t s and, for a 2-nautm i l e uncertainty, is a p p r o x i m a t e l y 4 fps.

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 which is 9 0 ° r e m o v e d f r o m the point of m a x i m u m position 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 are both s i z a b l e .

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MIDCOURSE GUIDANCE A s indicated e a r l i e r , the m i d c o u r s e phase starts some t i m e after t r a n s f e r injection and b r i n g s the two v e h i c l e s together on a c o l l i s i o n c o u r s e to a s m a l l range w h e r e braking i s initiated. The m i d c o u r s e s c h e m e must, t h e r e f o r e , c o r r e c t the initial 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 been i n v e s t i g a t e d ranging f r o m optimum fuel utilization types to those e a s i e s t to m e c h a n i z e computationally. 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 tradeoffs 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 only 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. Optimum Fuel 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 . , in-plane or o u t - o f - p l a n e position or v e l o c i t y e r r o r , the optimum m a n e u v e r i n v o l v e s the application 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 position m i s s at the end, f o l l o w e d by a second step v e l o c i t y change to a r r i v e finally 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 application of the f i r s t c o r r e c t i o n and the optimum r e n d e z v o u s point a r e d i f f e r ent for each type and s i z e of initial e r r o r . F o r g e n e r a l c o m binations of initial e r r o r s , this t w o - i m p u l s e approach does not result 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 is 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 mechanize. Using the coordinate 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 are χ = Ζωγ 2

y = -Ζακ + 3co y

£lj

Ζ ζ = -α) ζ Solving these equations for 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 position R^ to r e n d e z v o u s an angle Çf l a t e r y i e l d s

N u m b e r s in p a r e n t h e s e s indicate R e f e r e n c e s at end of paper. 242

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

χχ

χ χ sinpf + 2 γ χ

7(1 - cos^f) - 3 ψ sinj/J

8(1 - cos0) - 3 p( sin0f

"ω

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

8(1 - c o s p ) - 3 (7 sinpf

ζ1 _ Z

l

cospf sin^

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 applied 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 match 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 - 2y^ (1 - cosj/)

"05

8 ( 1 - cosp) - 3 ÇI sinpf

y2

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

~ω z

2 ω

8(1 - cosj?) - 3 φ sinpi Z

l s inj?

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

v = | V j - v | + lv | T

2

W

T h e r e are 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 optimum 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 with 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 . Howe 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 . E q . 1 m a y be integrated to p r e d i c t the position and v e l o c i t y conditions which w i l l apply at some t i m e in the future if no action i s p r e s e n t l y taken. Using the p r e d i c t e d 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 m i n e d . This dual o p t i m i z a t i o n r e q u i r e s c o n s i d e r a b l e c o m putation so a m o r e reasonable technique is to dispense with the p r e d i c t i o n aspect and compute the optimum V r p 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 a s s o c i a t e d uncertainty ( e . g . , the 3cr v a l u e ) due to m e a s u r e m e n t e r r o r s . 243

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 been used in the f o r e going, 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 injection. 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 accurate f o r r e n d e z v o u s angles l e s s than 120°. 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 assume that t r a n s f e r injection ( $ = 180°) e r r o r s w i l l not be capable of detection until some t i m e l a t e r o r they would not have been made in the f i r s t place ( e x c e p t f o r out-of-plane position which cannot be c o r r e c t e d then). 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 out-of-plane position e r r o r at injection 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 optimum t i m e is 30° f r o m nominal 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 nominal point. Although the Vrp c u r v e shown is quite flat, l a r g e r initial 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 actually solved to produce the c u r v e s accounted for nonimpulsive and only a x i a l a c c e l e r a tion. 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 ^ was used as w e l l as a turning rate 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 second. T h i s has not affected 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 does not i n c r e a s e near (jl equal z e r o . A i r b o r n e Intercept Schemes 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 applied 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 biased 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 rate of rotation of the l i n e - o f - s i g h t ( L O S ) . If the L O S rate is 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 occur since the v e l o c i t y v e c t o r is aligned 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 angles i n v o l v e d . F i g . 6 shows the L O S rate for 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 LOS rate v e r s u s when such a s c h e m e is initiated. A s indicated, an a p p r e c i a b l e penalty is 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 , there is a t r a d e o f f between 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 knowledge of 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. 244

TECHNOLOGY OF LUNAR EXPLORATION

The p e r f o r m a n c e l o s s can be reduced g r e a t l y i f no action is taken until the L O S rate 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 threshold is set at 0.5 m r a d / s e c or h i g h e r , then, at l e a s t for the nominal p e r f e c t injection 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 indicates that the L O S rate is l e s s than this value (out to 1 2 0 ° ) . At the expense 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 nominal L O S rate (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 injection f r o m the in-plane 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 resulting e r r o r would be c o m p a r e d to its uncertainty ( e . g . , 3σ value) 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 uncertainty 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 only 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 . Schemes have been c o n s i d e r e d which produce both ( 2 ) . In this paper w e have 11 a s s i g n e d a separate phase, "braking, 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 mentioned e a r l i e r , there is often no c l e a r d i v i d i n g line b e t w e e n phases. BRAKING The m i d c o u r s e guidance s c h e m e s that have been d e s c r i b e d a r e intended to place 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 injection 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 contact. Although this change appears as a v e l o c i t y i n c r e a s e in Earth fixed or 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 appears 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 two 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 optimum braking 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 , braking 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 sufficiently 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 effects 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 , whether on a c o l l i s i o n c o u r s e or not, the optimum action 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 which 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 action must be initiated so as to reduce 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 action can start 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 . 245

J. HEILFRON AND F. H. KAUFMAN

In p r a c t i c e , there 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 start of braking, 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 values 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 braking, then the range R q at which braking should start is g i v e n by

R

o

=R.+ °, f

2a

f

5

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 action would be taken until the range equaled R q and then braking initiated until the v e l o c i t y was reduced 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 , there is no guarantee, either due to thrust o r m a s s uncertainty, 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 occur at an unacceptable v e l o c i t y ; if it is too high, the final range can be too g r e a t . T h e r e f o r e , one must p r o v i d e a braking schedule which 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 reasonable t i m e . This can be done via two switching l i n e s as shown in F i g . 7. The " s t a r t braking" 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 "stop braking" line can be s e l e c t e d in many 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 . , braking i s stopped when the t i m e to go 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 forbidden; o t h e r w i s e c o l l i s i o n w i l l occur (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 braking 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 start of braking. T h e r e f o r e , in addition to a braking schedule, one must a l s o e m p l o y a guidance scheme which nulls the l a t e r a l m i s s . A s a l r e a d y indicated, braking usually o c c u r s when both the range 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 condition 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 PHASE 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 contact. In m o s t system designs, midcourse and braking m a n e u v e r s a r e made with 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 for 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 undesirable to rotate the i n t e r c e p t o r to make v e c t o r c o r r e c t i o n s with this a x i a l e n g i n e . T h e r e f o r e , 246

TECHNOLOGY OF LUNAR EXPLORATION

s m a l l l a t e r a l v e r n i e r engines a r e added. Longitudinal c o n t r o l can s t i l l e m p l o y the m a i n e n g i n e , so this d i m e n s i o n is r e a l l y an e x t e n s i o n 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 i m p a c t to keep it within the bounds set by the docking s t r u c t u r e . The l a t e r a l s c h e m e 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 t a r g e t i s not attitude s t a b i l i z e d along the L O S , the L O S must be made to m a t c h one of the t a r g e t a x e s , e . g . , the r o l l a x i s or c e n t e r l i n e . A c c e p t a b l e v a l u e s 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 r e s u l t . One of the m o r e i m p o r t a n t a s p e c t s of the t e r m i n a l phase i n v o l v e s the " t r a n s f e r 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 r e s u l t s a r e p r e s e n t e d in a f o l l o w i n g s e c t i o n . F o r automatic o p e r a t i o n , which m i g h t be a backup m o d e , 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 , t h e r e i s 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 i n v a l i d . 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 a r e used, the pulse width and transponder t i m e d e l a y . F o r o p t i c a l s e n s o r s , the source to be t r a c k e d can b e c o m e l a r g e with r e s p e c t to the f i e l d of v i e w . A s indicated in F i g . 8, w h i c h d e p i c t s 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 , d e t a i l e d attention must be g i v e n to the v a r i o u s d i m e n s i o n s of the v e h i c l e s , w h e r e the s e n s o r s a r e l o c a t e d and hence p r e c i s e l y what they m e a s u r e , the strong i n t e r a c t i o n of the attitude c o n t r o l s y s t e m , e t c . T o s i m p l i f y m a t t e r s , w e shall c o n s i d e r the d e g e n e r a t e 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 l a b e l e d "d" in F i g . 8 and i s g i v e n by d = IT 9 /R a 1 aj a^ 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 l a t e r 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 c o n d i tions after the l a s t 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 u st r i or t o P made by m e a s u r i n g the l a t e r a l v e l o c i t y R m 2 ^ m 2 3 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 r e s u l t as g i v e n by R

a

l

Ô a

l

=R

a

2

9 a 2

- R

m

2

9 2

m

= lateral velocity e r r o r

J

7

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, 247

L

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 , assume that the m i n i m u m sensor range is 10 ft so the l a s t c o r r e c t i o n is made 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 rate nulling scheme d e s i g n e d so that no action is taken unless the m e a s u r e d value e x c e e d s a threshold 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 case 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 distances of a foot or so a r e r e a s o n a b l e . Specific attention must be g i v e n to the design 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 ment is within the acceptable 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 which to base a coordinate s y s t e m . T h e r e a r e a c c u r a c y constraints r e l a t i n g to each of the v a r i o u s p i e c e s of data. The i n f o r m a t i o n must be gathered 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 while the spacecraft undergo l a r g e attitude e x c u r s i o n s with 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 affect the d e s i g n of the s e n s o r ( s ) . Note that the basic 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 latter 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 preting the c o m m a n d s or 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 equipment w e i g h t , s i z e , and p o w e r and to enhance accuracy, cooperative transponders, beacons, light sources, e t c . , a r e p l a c e d in the v e h i c l e not containing the basic s e n s o r s . Radar o f f e r s the m o s t convenient method of obtaining range i n f o r m a t i o n although optical methods ( e . g . , triangulation 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 or C W techniques a r e u s a b l e . C W appears to offer r e l i a b i l i t y advantages in that only solid 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 higher 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 is not bothered by uncompensated t i m e d e l a y s inherent in pulse a p p r o a c h e s . Range r a t e can be obtained b y differentiating 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 range and range rate a c c u r a c i e s f o r values + 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 two l a t e r a l v e l o c i t y components 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 range g i v e s the d e s i r e d l a t e r a l 248

TECHNOLOGY OF LUNAR EXPLORATION

v e l o c i t i e s . An a c c u r a c y of 0.5 m r a d / s e c is acceptable 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 is d e s i r e d at long r a n g e s . If guidance w e r e initiated 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 is 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 numerous approaches for 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 again e i t h e r o p t i c a l or v a r i o u s r a d a r (lobing, monopulse, or i n t e r f e r o m e t e r ) techniques. The 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 drifts r e g a r d l e s s of 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 approach 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 some 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 by 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 rate although m o r e s o p h i s ticated 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 important. The L O S s e n s o r can be fixed 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 signals ( 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 for use in aligning 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 acts as a s e e k e r , and the scheme 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 approach if the same type g y r o s a r e used. If the fixed sensor 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 is 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 left o v e r f r o m the ascent phase or destined 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 . Consequently, 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 equipment. 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 is 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 coordinate 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 coordinate 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 scanners and a g y r o c o m p a s s mode used to d e t e c t o r b i t a l rate 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 . 249

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The propulsion configuration a l s o i n t e r a c t s h e a v i l y with the r e n d e z v o u s s e n s o r s . A s mentioned e a r l i e r , n o r m a l l y a single a x i a l engine (with two thrust c h a m b e r s canted f r o m the center 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 braking 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 must 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 make 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 field 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 if 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 approach is used. H o w e v e r , it is 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 thrustings and to "dead r e c k o n " during the actual m a n e u v e r s . This 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 which 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 sensor approach. Schemes can be d e v i s e d which r e q u i r e sensor 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 technical art. H o w e v e r , such equipment is not " o f f - t h e - s h e l f . " The detailed d e s i g n ( s ) must 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 zation and, t h e r e f o r e , must await 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 RENDEZVOUS AND DOCKING SIMULATIONS A number of manned r e n d e z v o u s and docking simulations have been r e p o r t e d testifying to m a n ' s potential capability for skillfully 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 . Levin 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 been 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 simulations r e p o r t e d in R e f . 6. Additional simulations (7) demonstrate 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 with 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 simulations 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 last f e w hundred f e e t . R e f . 8 r e p o r t s a simulation which 1 was conducted to d e t e r m i n e man 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 position, 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 establishing 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 its m e c h a n i s m s . S p e c i f i c a l l y , this simulation 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 values of range r a t e , L O S a n g l e , L O S 250

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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 pilot 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 mum display requirements. 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 with its longitudinal a x i s coincident with 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 aligned 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 simulated 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 range and range rate i n f o r m a t i o n , the pilot 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, to align 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 with 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 with a d e s i r e d c l o s i n g rate 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 cockpit simulator so that the pilot could c o m m a n d translational a c c e l e r a t i o n along each body a x i s and attitude c o n t r o l about each body 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 with a c l o s i n g range rate of 30 fps and with 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 initial c o n d i t i o n s . T e r m i n a t i o n of each flight o c c u r r e d when the docking f a c e s of the two v e h i c l e s r e a c h e d an 8-ft s e p a r a tion. An 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 assumed 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 with the o p t i c a l L O S c o l l i n e a r with the r o l l a x i s . R e f e r ring to F i g . 9, three docking face 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 face 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 mined 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 cockpit, the p i l o t w a s p r e s e n t e d with 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 range rate 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 same 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 faces w e r e e s s e n t i a l l y the same s i z e . The t a r g e t docking face was identified 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 face. Attitude e r r o r s w e r e indicated in the d i s p l a y by the distance that the c e n t r o i d of the two 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 center of the simulated v i e w i n g s c r e e n . Guidance e r r o r s w e r e indicated by the r e l a t i v e d i s p l a c e m e n t of the front 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 251

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angle in the case 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 with the v i e w i n g port c e n t e r ) . F i v e pilots ( r e f e r r e d to h e r e as pilots A through E ) w e r e s e l e c t e d f o r simulator t r a i n i n g . Selections w e r e made 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 , pilots D and Ε w e r e s e l e c t e d because of t h e i r p r e v i o u s a i r c r a f t flight training and e x p e r i e n c e . Each p i l o t made 12 simulated flights after a training 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 pilot a v e r a g e s p r e s e n t e d in F i g . 10. Eight flights resulted in data e x t r e m e s which 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 with 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 pilots 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 for both L O S angle and L O S r a t e . Note that excluding pilot 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 rate ( 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 pilots 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 is f e l t that these v a r i a t i o n s would be reduced with 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 , some of the p i l o t s concentrated 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 instructed 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 flight t i m e s , while pilot B ' s a v e r a g e is somewhat ! l o w e r . P i l o t B s data perhaps g i v e an indication of the m i n i mum flight 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 initial conditions. 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 pilots encountered a p p r o x i m a t e l y the same d e g r e e of difficulty in making 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 appear 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 impulse 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 conclusion reached 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 training l e v e l is justified by the significant i m p r o v e m e n t in the r e l a t i v e 252

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s u c c e s s of the l a t e r simulated f l i g h t s . If the pilots w e r e trained f o r a l o n g e r p e r i o d , it is reasonable 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 reduced by a factor of t w o . S e v e r a l flights w e r e m a d e with no range and range rate 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 pilot, i . e . , he maneuv e r e d using the optical d i s p l a y a l o n e . The f e w flights made in this manner w e r e r e l a t i v e l y successful, c o m p a r e d to flights made with r a d a r data. T h i s suggests that, with a sufficiently high d e g r e e of p i l o t training, 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 successful flight w a s made with the o p t i c a l d i s p l a y , excluding range and range rate 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 instead. 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 significant 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 pilot training l e v e l w a s c l e a r l y indicated although not s t a t i s tically determined. DOCKING S T R U C T U R E A N D MECHANISMS Because of u n c e r t a i n t i e s which o c c u r in the t e r m i n a l guidance, propulsion, and attitude c o n t r o l s y s t e m s for both manned and automatic c o n t r o l l e d docking, a l l o w a n c e must be made in docking structure and m e c h a n i s m designs to a c c o m modate 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~ tween the s p a c e c r a f t at docking, and the nominal 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 effect acceptable 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 structure s i z e and w e i g h t a r e C l o s i n g rate L a t e r a l m i s s (capture d i s t a n c e ) Attitude m i s a l i g n m e n t (any a x i s )

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C o m p a r i n g these d e s i g n c r i t e r i a with 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 indicates that r e a s o n a b l e p r o v i sion has been made 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 these i n i t i a l conditions a r e that the design of the docking structure and m e c h a n i s m s must p r o v i d e three 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 two 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 docked spacecraft 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 alignment of the two v e h i c l e s . Although p a r a l l e l or 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 . 253

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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 absorbed along the s p a c e c r a f t a x i s n o r m a l l y designed by loads during the boost phase. F o r these r e a s o n s , the configurations shown a r e l i m i t e d to concepts 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 propellant 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 . To 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 three g e n e r a l configurations; 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 mating. The matched cone configuration, d i a g r a m m e d in F i g . 11-a, u t i l i z e s identical " 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 protruding, to p r o v i d e capture and aligning c a p a b i l i t y . The cone angles of both portions of the docking structure a r e i d e n t i c a l . The choice of capture distance is p r i m a r i l y dependent 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 conditions. 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 suitable. The upper l i m i t on cone angle δ is a function of acceptable d e s i g n loads 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 for 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 structure 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 inherently 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 either 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 occur for nominal offset conditions at point A and can occur for nominal conditions of offset and angular m i s a l i g n ment 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 . Simulations of matched cone docking r e p o r t e d in R e f . 9 show that, e v e n for 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 fact, the matched cone configuration r e q u i r e s a careful 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 docking. Matched cones n e v e r t h e l e s s can be made to w o r k . The unmatched cone configuration 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 capability 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 matched cone configuration. 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 protruding 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 shoul254

TECHNOLOGY OF LUNAR EXPLORATION

d e r s of the r e c e s s e d cone ( s e e point B, F i g . 11-a) a r e virtuallye 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 matched cone, 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 alignment. The s e l f - a l i g n i n g probe configuration uses the capture and g e n e r a l aligning qualities of matched cones at i n i t i a l contact but a v o i d s the undesirable 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 loads a r e a b s o r b e d . F i g . 12 shows the p r o b e , which is capable of absorbing i m p a c t loads along the probe a x i s , entering a s m a l l r e c e s s e d cone whose capture c a p a b i l i t y can be made equal to that of the other configurations 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 is doubly articulated 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 with the s e l f - a l i g n i n g probe 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 for m a n - c o n t r o l l e d docking since man inherently 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 shell structure of the v e h i c l e s . The s e l f - a l i g n i n g probe configuration i s i d e a l l y suited to propellant 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 basic p r i n c i p l e can be applied for connecting stages f o r m u l tiple 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 probe can be i m p l e m e n t e d by a ratcheted spring along the b o o m a x i s , b y b u m p e r s on the outer shell shoulders, 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 probe can be drawn up f o r final stage latching w h e r e desired. A t y p i c a l structural d e s i g n f o r the e n e r g y absorption and latching the unmatched (and m a t c h e d ) cone configuration 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 with 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 configuration which is 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 probe 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 limited. 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 alignment 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 ment. A l l of these techniques retain a c a p a b i l i t y f o r multiple 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. 255

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

AC K N O W L E D G M E N T The authors g r a t e f u l l y acknowledge the contributions of W . Sehr o e d e r on t e r m i n a l guidance and J. C . F o x and T . G. Windeknecht on manned o r b i t a l docking simulation as w e l l as other m e m b e r s of the staff of Space T e c h n o l o g y L a b o r a t o r i e s , Inc. who have supported these r e n d e z v o u s and docking studies. REFERENCES 1 Hornby, Η . , " A n a n a l y t i c a l study of o r b i t a l r e n d e z v o u s for l e a s t fuel and l e a s t e n e r g y , « N A S A T N - D - 1 2 0 7 , A m e s R e s e a r c h C e n t e r ( M a r c h 1962). 2 C i c o l a n i , L . S . , " T r a j e c t o r y c o n t r o l in r e n d e z v o u s p r o b l e m s using p r o p o r t i o n a l navigation, " N A S A T N - D - 7 7 2 , A m e s R e s e a r c h C e n t e r ( A p r i l 1961). 3 Jacob, D . Μ , , " S T E L A T R A C r e n d e z v o u s ranging and tracking r a d a r , " P r o c . Eighth Annual Radar Symposium, U n i v e r s i t y of M i c h i g a n Institute of Science and T e c h n o l o g y (1962). 4 L e v i n , E . and W a r d , J. W . , "Manned c o n t r o l of o r b i t a l r e n d e z v o u s , " The Rand C o r p . , R e p t . P - 1 8 3 4 ( O c t o b e r 20, 1959)· 5 W o l o w i c z , C . Η . , D r a k e , Η . Μ . , and V i d e a n , Ε . Η . , "Simulator i n v e s t i g a t i o n of c o n t r o l s and d i s p l a y r e q u i r e d for t e r m i n a l phase of 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 , " N A S A TN-D-511 (October I960). 6 B r i s s e n d e n , R . F . , Burton, Β . Β . , F o u d r i a t , E . C . , and Whitten, J. Β . , " A n a l o g simulation of p i l o t - c o n t r o l l e d r e n d e z v o u s , " N A S A T N - D - 7 4 7 ( A p r i l 1961). 7 W a k a m i y a , Y . and W a r d , J. W « , "Manned r e n d e z v o u s s i m u l a t i o n , " S T L T M - 9 3 1 3 . 8-153 ( N o v e m b e r 8, 1961). 8 F o x , J. C . and Winde knee ht, T . G . , "Six d e g r e e - o f f r e e d o m simulation of a manned o r b i t a l docking s y s t e m , " S T L 9352.8-37 ( A p r i l 1962). 9 W a r d , J. and W i l l i a m s , Η . , " O r b i t a l docking d y n a m i c s , " r e p r i n t 1953-61, A R S Guidance, C o n t r o l , and N a v i g a t i o n C o n f e r e n c e , August 1961.

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1

5

E

J. HEILFRON AND F. H. KAUFMAN

D

263 Fig.

11

H I G H IMPACT

STRESS

^

configurations

^

^^^S^—

/

DOCKING MOTOR /

^^^^^^"^ V UNMATCHED CONE

7

Γ

MATCHED CONE

Docking cone

(b)

j

Ί

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jT ^ ^ A ^ ^ — ^

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EXPLORATION

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NG

(a)

^ ^ ^ ^ ^ D J A M P E R

V^|sPR,

C

L _ _ _ _ _ _ _ _ J - ^ - ^

ALLOWABLE OFFSET DISTANCE ν

TECHNOLOGY OF LUNAR

J. HEILFRON AND F. H. KAUFMAN

FINAL PROBE RATCHETED ADJUSTMENT

Fig.

12

PROBE LATCHED

FIRST CONTACT

Self-aligning probe configuration

264