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On the generation of smooth three-dimensional rigid body motions. Abstract This paper addresses the problem of generating smooth trajectories between an initial and final position and orientation in space. The main idea is to define a functional depending on velocity or its derivatives that measures the smoothness of a trajectory and find trajectories that(More)
The set of rigid body motions forms the Lie group SE(3), the special Euclidean group in three dimensions. In this paper we investigate Riemannian metrics and aane connections on SE(3) that are suited for kinematic analysis and robot trajectory planning. In the rst part of the paper, we study metrics whose geodesics are screw motions. We prove that no(More)
The problem of designing optical systems that contain free-form surfaces is a challenging one, even in the case of designing a single surface. Here we present a method for the coupled design of two free-form reflective surfaces that will have a prescribed distortion. On one hand, the method can be described using traditional vectors and matrices, which we(More)
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