Iterative learning control for spatial path tracking

Abstract

Iterative learning control (ILC) is a high performance method for systems operating in a repetitive manner, which aims to improve tracking performance by learning from previous trial information. In recent years research interest has focused on generalizing the task description in order to achieve greater performance and flexibility. In particular, researchers have addressed the ease of tracking only at a single, or a collection of time instants. However, there still remain substantial open problems, such as the choice of the time instants, the need for system constraint handling, and the ability to release explicit dependence on time. A number of ILC methods have tackled the latter problem, loosely termed spatial ILC, but are all application specific and limited in scope.

The aim of this thesis is to unlock this potential, and the specific contributions are as follows: first a mechanism to optimize the time instants at the critical tracking positions within point-to-point tracking is developed. This is achieved by embedding an additional cost function and deriving a ‘Two Stage’ design framework to yield an iterative algorithm which minimizes control effort as well as guaranteeing high performance tracking. This approach is based on norm optimal ILC and gradient minimization. Then the task description is further generalized by expanding the formulation to embed via-point constraint and linear planar constraints. This embeds the incorporation of various design objectives including spatial path tracking in a general class of systems, and a mixed form of system constraints are added into this framework. An algorithmic ILC solution is derived using the successive projection method to achieve high performance tracking of the design objectives. Finally, the Two Stage design framework and the generalized ILC framework are combined together to yield the first spatial ILC algorithm capable of optimizing an additional cost function whilst completing the spatial path tracking objective for a general class of systems. All proposed algorithms are verified experimentally on a gantry robot platform, whose experimental results demonstrate their practical efficacy and ability to substantially widen the scope of the current ILC framework.

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