Contril of rigid‐link, flexible‐joint robots:a survey of backstepping approaches

Abstract

The purpose of this article is to show how the design procedure commonly referred to as integrator backstepping can be used to design globally stable trajectory tracking controllers for Rigid‐Link Flexible‐Joint (RLFJ) robot manipulators. Three different types of controllers are developed: (1) an exact model knowledge‐based controller, (2) an adaptive controller that compensates for parametric uncertainty, and (3) a robust controller that compensates for parametric uncertainty and unknown bounded disturbances. All three controllers are based on previously published work but are presented here in a unifying framework. © 1995 John Wiley & Sons, Inc.

Global Adaptive Output Feedback Tracking Control of an Unmanned Aerial Vehicle

“…Property 2: The function in (24) denotes a normal projection algorithm, which ensures that the following inequality is satisfied (for further details, see [32]- [35]): (26) where , denote known, constant lower and upper bounds, respectively, of . After substituting the time derivative of (22) into (20), the closed-loop error system can be determined as (27) where denotes the parameter estimation error defined as (28) 2 Since the measurable regression matrix Y (1) contains only the reference trajectories x and _ x , the expression in (24) can be integrated by parts to prove that the adaptive estimate (t) can be generated using only measurements of e (t) (i.e., no r (t) measurements, and hence, no _ x(t) measurements are required).…”

“…. (29) where the auxiliary signals and , and the individual elements are defined as (30) , where the subscript denotes the th element of the corresponding vector, and is defined as (31) It can be shown that the following inequalities can be developed [8], [31]: (32) where is defined in (9), and are known positive bounding constants. Note that only depends on the diagonal elements to of due to the strictly upper triangular nature of .…”

“…After using (30) and (31), the time derivative of can be expressed as (33) where (34) (35) After utilizing Property 1, (24), and (26), the following inequalities can be developed: (36) where are known positive bounding constants. Based on (29), the closed-loop error system can be expressed as (37) where (38) Based on (19), (32), and (38), the following inequalities can be developed: (39) where are known positive bounding constants, and , , and are introduced in (19) and (36).…”

Tracking Control of Robot Manipulators with Bounded Torque Inputs

“…Remark 2 By exploiting Properties 1, 4, and 5 of the robot dynamics, the first inequality of (12) and the definition of (13) (8), and the control gain matrix ␣ defined in (13).…”

A Survey on the Control of Flexible Joint Robots

“…Hundreds of papers have been published on the subject of this survey paper. Among those papers, only three of them were found to be survey papers, of which two of them are specialized in two narrow categories [11,12] and only one wide survey [13] was published in 1990. After more than a decade of advancement in this area, this paper intends to summarize the new advancements and to provide an assessment for future developments.…”