Control of Mechanical Systems with Variable Degrees of Freedom

Many mechanical systems can change dimension. r θ l k/2 k/2 y v u v m φ Body 2 1 m v v θ Rake x l θ We are primarily concerned with the problem of determining controllability and the motion planning problem. Slide 1 This motivational slide is intended to illustrate two main points: • Changing dimensions is common, and • There is a natural kinematic/dynamic dichotomy in such problems, which will be reflected in this talk. The changing dimensionality for the kinematic systems comes, at least for legged robot examples, from intermittent contact with some physical boundary. Dynamical problems could also have this feature, but additionally they can have intermittent nonholonomic constraints, as illustrated by the shimmying wheel.