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Randomized Motion Planning Nancy Amato Fall 04 Univ of Padova Configuration Space 1 Configuration Space Acknowledgement Parts of these course notes are based on notes from courses given by Jean Claude Latombe at Stanford University and Chapters 2 and 3 in his text Robot Motion Planning Kluwer 1991 O Burc han Bayaz t at Washington University in St Louis Seth Hutchinson at the University of Illinois at Urbana Champaign and Leo Joskowicz at Hebrew University Randomized Motion Planning Nancy Amato Fall 04 Univ of Padova Configuration Space 2 C space of Rigid Object Main Idea Represent the robot as a point called a configuration in a parameter space the configuration space or C space Note For now assume robot is a rigid object not constrained by any kinematic or dynamic constraints z F y W A y x F A O W z O A x Workspace W physical workspace represented as N dimensional Euclidean Space IRN where N 2 3 FW fixed Cartesian coordinate system frame of W OW fixed origin of FW Robot A moving rigid object robot represented as compact subset of IRN at reference position and orientation FA frame of A aka local frame of A fixed wrt A i e each point in A has fixed coordinates in FA moving wrt FW OA origin of FA aka the reference point of A Randomized Motion Planning Nancy Amato Fall 04 Univ of Padova Configuration Space 3 C space of Rigid Object cont d Definitions A configuration q of A is a specification of the position and orientation of FA wrt FW The configuration space of A is the space C of all the possible configurations of A The reference configuration of A denoted by 0 is some arbitrary configuration of A Note C is independent of choice of FA and FW but its representation is not Notation A q subset of W occupied by A at configuration q a q position of point a A in W when A at configuration q x q position of feature x A in W when A at configuration q Randomized Motion Planning Nancy Amato Fall 04 Univ of Padova Configuration Space 4 Configurations as transformations Sometimes



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