Designing Energy-Minimizing Rigid Body Motions in the Presence of Obstacles

We present a solution for variational motion design of a rigid body in the presence of rigid obstacles of arbitrary shape that fully employs the available degrees of freedom in the design process. This question remained open in our paper on energy- minimizing splines in manifolds (Hofer and Pottmann, 2004). The main idea is to reduce the problem to a curve design task on a suitable barrier surface embedded in an appropriate kinematic image space.