A b s t r a c t : In t h i s paper, t h e dynamics and c o n t r o l of slewing maneuvers of a l a r g e f l e x i b l e s p a c e c r a f t namely. NASA-S p a c e c r a f t Control Laboratory Experiment (SCOLE) t e s t a r t i c l e a r e s t u d i e d . The dynamical equations obtained f o r slewing maneuvers a r e highly n o n l i n e a r and coupled. The maneuver i s expressed in terms of f o u r Euler parameters and i s s p e c i f i e d a s t h e a n g u l a r displacement about an a r b i t r a r y a x i s . The slew maneuver c o n t r o l problem i s developed i n terms of rigid-body slewing and suppression of two e l a s t i c modes i s analyzed using t h e method of n o n l i n e a r decoupling.Nomenclature: P o s i t i o n v e c t o r of mass element on t h e beam from t h e p o i n t of attachment P o s i t i o n v e c t o r from t h e p o i n t of attachment t o t h e mass c e n t e r Displacement v e c t o r of mass element in t h e body-f i x e d frame Force a p p l i e d a t t h e o r b i t e r mass c e n t e r Force a p p l i e d a t t h e r e f l e c t o r mass c e n t e r Moment a p p l i e d about t h e o r b i t e r mass c e n t e r Hass moment of i n e r t i a matrix of t h e s h u t t l e Mass moment of i n e r t i a matrix of t h e r e f l e c t o r The length of t h e beam T o t a l mass of t h e f l e x i b l e beam I a s s of t h e o r b i t e r Mass of t h e r e f l e c t o r P o s i t i o n v e c t o r of t h e mass c e n t e r of t h e o r b i t e r in t h e i n e r t i a l frame P o s i t i o n v e c t o r from t h e o r b i t e r mass c e n t e r t o t h e p o i n t of attachment The beam d e f l e c t i o n in x d i r e c t i o n r e f e r r e d t o t h e body-fixed frame The beam d e f l e c t i o n in y d i r e c t i o n r e f e r r e d t o t h e body-fixed frame The t o r s i o n a l d e f l e c t i o n about z a x i s in t h e body-fi xed frame Velocity v e c t o r of t h e mass c e n t e r of t h e o r b i t e r in t h e body-fixed frame Velocity v e c t o r of t h e p o i n t of attachment in t h e body-fi xed frame Mass per u n i t length Vector r e p r e s e n t i n g t h e a x i s of r o t a t i o n The a n g u l a r v e l o c i t y of t h e o r b i t e r in t h e body-fixed frame Anale of r o t a t i o n I n t r o d u c t i o n : Many f u t u r e NASA missions would u t i l i z e s i g n i f i c a n t l y l a r g e and f l e x i b l e s p a c e c r a f t s and would r e q u i r e very s t r i n g e n t p o i n t i n g and v i b r a t i o n suppression requirements. The a c t i v e c o n t r o l l e r t h a t can achieve t h e s e o b j e c t i v e s w i l l have t o be designed with very a c c u r a t e knowledge of t h e dynamic behavior of -t h e s p a c e c r a f t t o e n s u r e performance r o b u s t n e s s t o a v a r i e t y of d i s t u r b a n c e s and u n c e r t a i n t i e s . In t h e p a s t few y e a r s , s e v e r a l design approaches were proposed f o r v i b r a t i o n c o n t r o l during and a f t e r slewing maneuvers. NASA Langley Research Ce...
This paper examines the technique of partial feedback linearization for the positional control of the joints of a humanoid robot. The unique dynamical model of the humanoid robot is first presented. The dynamics have an Euler-Lagrange form but also contain mixedcontinuous/discrete forces that arise due to contact constraints. The mixed-continuous/discrete contact forces are modeled by using linear restoring and damping elements on the bottom of the feet of the humanoid upon contact with the ground. Also, the robot has six degrees-of-freedom that are not directly actuated. The collocated partial feedback linearization scheme is utilized to provide joint-level position control. Implementation of this control law relies upon contact force measurements.It is suggested that partial feedback linearization is a viable option for joint level control even in the presence of significant noise arising from the contact force measurements.
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