Jon M. Selig

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In this lecture the group of rigid body motions is introduced via its representation on standard three dimensional Euclidian space. The relevance for robotics is that the links of a robot are usually modelled as rigid bodies. Moreover the payload of a robot is also usually a rigid body and hence much of robotics is concerned with understanding rigid(More)
A line symmetric motion is the motion obtained by reflecting a rigid body in the successive generator lines of a ruled surface. In this work we review the dual quaternion approach to rigid body displacements, in particular the representation of the group SE(3) by the Study quadric. Then some classical work on reflections in lines or half-turns is reviewed.(More)
In this work we construct a simple dynamical model for vibratory bowl feeders. The symmetrical arrangement of the springs supporting the bowl allow us to predict a simple structure for the stiffness matrix of the system. The cylindrical symmetry of the bowl itself then means that the linearized rigid body dynamics of the system can be simplified to a(More)
The Cayley map for the rotation group SO(3) is extended to a map from the Lie algebra of the group of rigid body motions SE(3) to the group itself. This is done in several inequivalent ways. A close connection between these maps and linear line complexes associated with a finite screw motions is found.
A small but interesting result of Brockett is extended to the Euclidean group SE(3) and is illustrated by several examples. The result concerns the explicit solution of an optimal control problem on Lie groups, where the control belongs to a Lie triple system in the Lie algebra. The extension allows for an objective function based on an indefinite quadratic(More)