On one generic choice of transverse coordinates for a trajectory of a controlled mechanical system subject to non-holonomic constraints

Abstract:

Analysis of dynamics of mechanical systems with non-integrable constraints is fundamental for qualitative and quantitative characterization of agile motions of various mobile platforms and robots. Given a nominal motion of a system, general tools that would allow efficient verification of important properties of dynamics in a vicinity of its trajectory (such as orbital stability and instability; sensitivities to parametric uncertainties in the model and coefficients of feedback controller if proposed; estimates for tubing region of attraction; etc) are of common interest.

As known, transverse coordinates as well as an associated moving Poincare section introduced in a vicinity of the motion’s orbit are appropriate concepts for investigating such questions. However, these quantities are often found only numerically. In this work we propose new arguments and constructive analytical steps for defining one set of transverse coordinates that have several distinctive features. In particular, this set of transverse coordinates admits analytical linearization along the motion, where parametric uncertainties in the nonlinear model become uncertainties in the linear one prior any feedback controller design step is done. The method is illustrated by series of examples.

Slides