On the Computation of Rigid Body Motion
نویسنده
چکیده
We present two methods for generating trajectories and motion interpolants that minimize energy functionals on SE(3), the group of rigid body displacements. We treat SE(3) as a Lie Group and endow it with a left-invariant Riemannian metric derived from energy considerations. The first method is based on a relaxation formulation where the Euler-Lagrange equations for the minimization problem are solved. The second method offers a closed form, but approximate solution to the problem. Both methods preserve invariance. We compare the two methods in terms of computational efficiency and accuracy.
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