Dynamics of Vehicle-Manipulator Systems
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This chapter presents the dynamic equations of vehicle-manipulator systems, which is the principal topic of the book. Because the configuration space of the vehicle and the manipulator are different in nature we need to use the well-defined formulation of the state space presented in the previous chapters to obtain a singularity-free set of dynamic equations. The configuration space of the manipulator is Euclidean, so standard formulations of Lagrange’s equations can be used. For the vehicle, however, the configuration space is a manifold, so we need to modify Lagrange’s equations to be valid also on matrix Lie groups, which are in fact manifolds.
This chapter will give the reader a deep understanding of how the underlying configuration spaces affect the modeling of mechanical systems and the reader will be able to derive the dynamics of complex mechanical systems with different configuration spaces, both Euclidean and non-Euclidean. Emphasis is put on obtaining well-defined and singularity-free dynamic equations by using the results from differential geometry and Lie theory presented in the previous chapters.
KeywordsMultibody System Velocity Variable Configuration Space Robotic Manipulator Inertia Matrix
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