MIMO Feedback Linearization of Redundant Robotic Systems using Task-Priority Operational Space Control

Abstract

Redundant robotic systems are designed to accomplish multiple tasks simultaneously. Task-priority control schemes exploit system redundancy by arranging tasks in priority and ensuring strict prioritization between tasks at different priority levels. This paper investigates the relationship between task-priority operational space control and feedback linearization of multiple-input-multiple-output (MIMO) systems. We derive sufficient conditions for input-output feedback linearization and input-to-state feedback linearization of a redundant robotic system influenced by a task-priority operational space pre-feedback control law. Moreover, we analyze the effect of incompatible tasks and provide sufficient conditions for input-output and input-to-state feedback linearizability of the controllable dimensions of incompatible lower-priority tasks. These conditions can be employed when designing the operational space tasks in order to guarantee both task space and joint space stability.