Some Applications of Classical Algebraic Geometry in Robotics

Some Applications of Classical Algebraic Geometry in Robotics

Historically the development of Algebraic Geometry in the late nineteenth century was greatly influenced by problems in the theory of mechanisms and machines. In this talk I will briefly look at the Study quadric, as six dimensional variety whose point (minus a single 3-plane) correspond to rigid-body displacements.  In particular I will look at some modern applications to serial robots and parallel manipulators. I will then discuss some connections between classical line geometry and screw theory.  The applications here will include some recent work on the line geometry associated to the inertia matrix of a rigid body.