Robot visual servoing with iterative learning control

Abstract

Abstract-This paper presents an iterative learning scheme for visionguided robot trajectory tracking. At first, a stability criterion for designing iterative learning controller is proposed. It can be used for a system with initial resetting error. By using the criterion, one can convert the design problem into finding a positive definite discrete matrix kernel and a more general form of learning control can be obtained. Then, a three-dimensional (3-D) trajectory tracking system with a single static camera to realize robot movement imitation is presented based on this criterion.Index Terms-Adaptive control, iterative learning control, visual servoing.

Range and Motion Estimation of a Monocular Camera Using Static and Moving Objects

“…1, we need to introduce the orthogonal coordinate systems attached to a monocular camera denoted by F * and F C , each of which is, respectively, placed at the initial location with the initial time t 0 and the moved location via a rotation matrixR(t) ∈ SO (3) and a translational vectorx f (t) ∈ R 3×1 from the initial location. Then, the Euclidean coordinates of a feature point observed by a moving camera should be introduced as m(t) := [x 1 (t), x 2 (t), x 3 (t)] T ∈ R 3×1 in the camera frame F C .…”

“…For the further development of the nonlinear observer, we introduce the practical assumption as in [42] that ḡ(·) ≤ζ 1 , ġ (·) ≤ζ 2 , and g (·) ≤ζ 3 for known positive constantsζ 1 ,ζ 2 , andζ 3 .…”

A stochastic iterative learning control algorithm with application to an induction motor

“…However, in the past few years, applications of ILC algorithms have been used in a wider variety of systems than ever before. For example, control of: chemical reactor (Cabassud et al 2002), high precision wafer stage (Bosgra and Dijkstra 2002), robot visual servoing (Jiang and Unbehauen 2002), wafer temperature (Yang et al 2001), liquid slosh in an industrial packaging machine (Bernhardsson and Grundelius 2001), camless valve actuator (Hoffmann and Stefanopoulou 2001), batch processes , switched reluctance motors (Panda et al 2001), PM synchronous motors (Lam et al 2000), electrohydraulic injection moulding machine (Alleyne and Havlicsek 1999), impedance control (Arimoto et al 1999), VCR (Kim and Ha 1999), extruders (Pandit and Buchheit 1999), and coil-to-coil control in rolling (Garimella and Srinivasan 1998). For a general outlook of ILC algorithms, the reader is referred to Owens et al (2002).…”

Nussbaum Gain Based Iterative Learning Control for a Class of Multi-input Multi-output Nonlinear Systems

“…If let n(k) = v(k + 1) , a(t)= -Ao, y(k)=1, and G=1 in Property 2, we can obtain the following property along iterative horizon i: Property 3 [5]. For any vector n(i) and any repeatable constant vector a(t), a positive definite discrete matrix kernel F(i -q) ensures that the following accumulation along iterative horizon i is always upper bounded: In the proposed ILC (11), if F1 and F2 are selected to be A6>0 and /32>0, which are positive definite discrete matrix kernels because their z-transformations are positive real discrete transfer matrices with a pole at z=1.…”

“…Reference [4] proposed an adaptive high-gain iterative learning controller for a class of MIMO linear time-invariant systems but a priori knowledge about the control gain matrix CB is required as well, where it should be positive definite. In some cases, such as uncalibrated visual servoing [5], it is difficult to gain this kind of prior knowledge. In adaptive control, the Nussbaum gain [6][7] [8] and the correction vector method [9] were proposed to deal with this kind of control problem without prior information.…”