On null-space control of kinematically redundant robot manipulators

Abstract

In this study, we consider the null-space control problem of redundant robot manipulators. Specifically for robot manipulators with kinematically redundancy where at least one extra degree of freedom is present, we introduce a subtask controller that will ensure the use of the extra degrees of freedom for possible control purposes while still ensuring the main objective. The stability of the main (end-effector tracking) and sub-task objectives are obtained via Lyapunov based arguments. Extension to adaptive controller formulation for robotic devices with uncertain system dynamics is also presented. Numerical studies for the adaptive controller are presented to illustrate the liability of the proposed method.

An Extended Jacobian-Based Formulation for Operational Space Control of Kinematically Redundant Robot Manipulators With Multiple Subtask Objectives: An Adaptive Control Approach

“…As opposed by the operational space controller along with the pseudo-inverse of Jacobian-based null-space controller in Refs. [11,12], and [16], our extended Jacobian-based controller (20) allows us to carry out a combined stability analysis for both operational space tracking and subtask objectives without requiring to design an external null-space controller. In addition, the other advantage of the proposed controller ( 20) is able to apply to hyper redundant robot manipulators without requiring a separate stability analysis for multiple subtask objectives while still ensuring the operational space control objective.…”

“…For the same problem with dynamical uncertainties, adaptive control methods were presented for kinematically redundant robot manipulators in Refs. [8]- [16]. To compensate unstructured uncertainties in robot dynamics, robust control methods were presented in Refs.…”

“…Later, the proposed methodology of Ref. [16] ensured a combined stability analysis for both operational space tracking and subtask objectives. However, in Ref.…”

“…However, in Ref. [16], only one subtask objective can be performed since the proposed methodology was applicable for one redundant DOF (i.e., n À m ¼ 1). One of our motivations in this study arises from the requirement of multiple subtask objectives for highly redundant robot manipulators (i.e., n À m > 1).…”

Cable-driven Parallel Robot to Simulate the Underwater Environment in Humanoids

“…The more tension configurations are allowed for a specific pose, the further the system is from a configuration with sagging cables as well as the more control possibilities it has. The size of the space that holds these different tension configurations is measured with the null-space of the structure matrix of the system (Cetin et al, 2016), as analyzed in detail in previous chapters. The tension configuration of the system considering the freedom that redundancy provides can be expressed as:…”