Input Dexterity and Output Negotiation in Feedback-Linearizable Nonlinear Systems

TL;DR

This paper develops a taxonomy for actuator inputs in nonlinear systems, enabling flexible task execution through input classification and a unified control approach that allows graceful task downgrades without transients.

Contribution

It introduces a novel taxonomy of actuator inputs in feedback-linearizable systems, defining dexterity inputs and providing a unified control framework for task flexibility.

Findings

Unified linearizing controller for full and reduced tasks

Simulations demonstrate graceful task downgrades in aerial platform

Input classification enables flexible and robust control strategies

Abstract

We introduce a task-relative taxonomy of actuator inputs for nonlinear systems within the input-output feedback-linearization framework. Given a flat output specifying the task, inputs are classified as essential, redundant, or dexterity: essential inputs are required for exact linearization, redundant inputs can be removed without effect, and dexterity inputs can be deactivated while preserving exact linearization of a reduced task. We show that a subset is dexterity if and only if, under a suitable dynamic prolongation, it can appear as additional output channels (flat-input complement) on a common validity set. Whenever a family of systems obtained by (de)activating dexterity inputs admits a common prolongation, the family can be interpreted as a single prolonged system endowed with different output selections. This enables a unified linearizing controller that negotiates between full and reduced tasks without transients on shared outputs under compatibility and dwell-time conditions. Simulations on a fully actuated aerial platform illustrate graceful task downgrades from six-dimensional pose tracking as lateral-force channels are deactivated.