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This paper is concerned with optimal trajectory generation for robotic multi-body systems. The focus is on discrete optimal control methods which operate intrinsically in the state space system manifold and do not require coordinate charts or projections. This is accomplished by defining both the dynamics and the optimal control solution as sequences of vector fields mapping to curves on the Lie group through retraction maps, and defining variations and differentiation with respect to suchdoi:10.1109/icra.2014.6907671 dblp:conf/icra/Kobilarov14 fatcat:wcov7dvai5hnjmrz2q2limbxqu