Constraints on Nonlinear Finite Dimensional Flat Systems

TL;DR

This paper introduces a method to incorporate input, state, and output constraints into trajectory planning for differentially flat systems by representing flat outputs as Bezier curves, enabling explicit control over feasible trajectories.

Contribution

It specializes flat outputs as Bezier curves and derives explicit expressions for control points, allowing unified constraint embedding in trajectory design for flat systems.

Findings

Explicit control point expressions for inputs and states.

Feasible regions for output trajectories are characterized.

Unified approach to constraints in flat system trajectory planning.

Abstract

This chapter presents an approach to embed the input/state/output constraints in a unified manner into the trajectory design for differentially flat systems. To that purpose, we specialize the flat outputs (or the reference trajectories) as Bezier curves. Using the flatness property, the system's inputs/states can be expressed as a combination of Bezier curved flat outputs and their derivatives. Consequently, we explicitly obtain the expressions of the control points of the inputs/states Bezier curves as a combination of the control points of the flat outputs. By applying desired constraints to the latter control points, we find the feasible regions for the output Bezier control points i.e. a set of feasible reference trajectories.