Study on the exponential path tracking control of robot manipulators via direct adaptive methods

Abstract

In this paper the expoiieiitial-transforinna.tion is a l lplied t o obtain transformed robot dynamics. Tliis is used t o derive several adaptive control algorithms that achieve exponential path tracking. In contrast to the existing composite adaptive coli t 1.01 method , where both the tracking error and the p r~l i c t i o n error are used and persistent excitation (p.e.) i s required, t,lv proposed strategy requires only t h r I racking error. 'rhis makes the control structure much simpler and easier t o implement. T h e main contribution of this paper is the complete removal of the p.e. requirement (as opposed t o relaxing it t o seini-p.e. as was done in a recent work [ 5 ] ) . T h e fundamental idea introduced for exponential stability ailalysis is conceptually simple and global results are obtained. Robotics has enticed system coirlrol researchers for many years and considerable work has been reported recently [l-61. As can be seen, the study of the path tracking control problem of robots has matured to a stage where asymptotic tracking result8s have been well established. What we are encouraged to study is tlie investigation of the transieiit, performance, as remarked in [4]. It has been shown that exponeiitially stable systems possess desirable properties such as an exponential convergence rate a.nd robust,ness to bounded disturbances a.nd iiniiiodeled dynamics. However, results along this line are limited. Recently, a so-called composite adaptive control scheme, which ensures exponential path tracking under t,he conclition of persistent excitation (p.e.) was proposed in [7]. Tlie implementation of this method uses the prediction error [ 3 ] , which has to be calculated on-line by a coiiiput,atioiiall!. expensive filt,eriiig t,echnicluc. Furt,lierniore, it, is desirable t o remove the p.e. requirement since the pli1,sical meaning of such a requirement is not esplicit,ly clear. At, tlie very least. it. increases the coinplesity of path planning, and in turn actually restricts tlie applicafion of the proposed control method. In other words, the exponential coiivergence is guaraiiteed only for those desired pat,lis that satisfy the p.c condition. Furthermore this coiiditioii must be satisfied relative t o the structure of t,lie robot t o be controlled. A recent effort by [5] introduces another exponential control scheme that relaxes the p.e. assurnption to semi-p.e., and presents a local exponential result.T h e purpose of this paper is t o introduce recent, results on tlie exponential path tracking control of roliot manipul;rr ors. Adaptive control lams are presented t,liat ensii i r~ globally exponential path tracking wit,liout t,he I 1 iluireinent of p.e. This obviously facilihtes path plaii iiing, and enlarges the applicat,ion region of the coiirrol method. It is shown t h a t , icitli these strategies, the convergence rat,e of t8he tracking error is a t least e -X t or (A > 0, a > e ) , which can be arbitrarily specified. Furthecmore, since the control strategies depend only on the tracking error and ri...

The use of adaptive multiple models for predefined exponential stability of control systems of uncertain discrete‐time nonlinear objects

“…By selecting appropriate parameters 𝜂 i and 𝜇 j (i = 1, 2, … , n, j = 2, 3, … , n), it can guarantee that the equality 0 < C n < 1 holds. Then, using ( 17), ( 25) and ( 29), (35) can be updated as:…”

“…In this context, the speed transformation function was employed to ensure that the original system dynamics is proved to be accelerated stability 34 . In addition, the assigned convergence rate has been realized and further it was extended to robotic systems 35 . It is notable that the proposed method 34 must require a suitable rate function.…”

“…34 In addition, the assigned convergence rate has been realized and further it was extended to robotic systems. 35 It is notable that the proposed method 34 must require a suitable rate function. In order to cope with this problem, the adaptive controller based on the use of the time varying exponential transformation method was established.…”

Adaptive Control of Redundant Multiple Robots in Cooperative Motion

“…The second property deals with the linearity of M, N2 and GI with respect to the load parameter vector Po, Ma, +N2vO +GI =YoPo (18) where a, E R6 and vo E R6 are the "reference acceleration of the load and the "reference velocity of the load," respectively. We will denote by Po E RS" the vector of so load parameters which are constants for a given load.…”

“…We will start by defining a few variables needed for the development. The weighted reference velocity error for the ith robot is defined as, The scalar weighting function w, will be chosen as, w, = e b , where b is a positive constant (see [18] for the use of weighting functions in the adaptive control of single rigid robots). We will group the p,, (i=l,.…”