辽宁科技大学本科生毕业设计 第 10 页Learning Control of Robot ManipulatorsROBERTO HOROWITZDepartment of Mechanical EngineeringUniversity of California at BerkeleyBerkeley，CA 94720,U.S.APhone:（510）642-4675e-mail:horowitzcanaima.berkeley.eduAbstractLearning control encompasses a class of control algorithms for programmable machines such as robots which attain, through an interactive process, the motor dexterity that enables the machine to execute complex tasks. In this paper we discuss the use of function identification and adaptive control algorithms in learning controllers for robot manipulators. In particular, we discuss the similarities and differences between betterment learning schemes, repetitive controllers and adaptive learning schemes based on integral transforms. The stability and convergence properties of adaptive learning algorithms based on integral transforms are highlighted and experimental results illustrating some of these properties are presented.Key words: Learning control, adaptive control, repetitive control, roboticsIntroductionThe emulation of human learning has long been among the most sought after and elusive goals in robotics and artificial intelligence. Many aspects of human learning are still not well understood. However, much progress has been achieved in robotics motion control toward emulating how humans develop the necessary motor skills to execute complex motions. In this paper we will refer to learning controllers as the class of control systems that generate a control action in an interactive manner using a function adaptation algorithm, in order to execute a prescribed action. In typical learning control applications the machine under control repeatedly attempts to execute a prescribed task while the adaptation algorithm successively improves the control systems performance from one trial to the next by updating the control input based on the error signals from previous trials.The term learning control in the robot motion control context was perhaps first used by Arimoto and his colleagues(c,f(Arimoto et al.,1984;Arimoto et al.,1988).Arimoto defined learning control as the class of control algorithms that achieve asymptotic zero error tracking by an interactive betterment process ,which Arimoto called learning. In this process a single finite horizon tracking task is repeatedly performed by the robot, starting always from the same initial condition. The control action at each trial is equal to the control action of the previous trial plus terms proportional to the tracking error and its time derivative respectively.Parallel to the development of the learning and betterment control schemes, a significant amount of research has been directed toward the application of repetitive control algorithms for robot trajectory tracking and other motion control problems (c.f.(Hara et al.,1988;Tomizuka et al.,1989;Tomizuka,1992). The basic objective in repetitive control is to cancel an unknown periodic disturbance or to track an unknown periodic reference trajectory. In its simplest form, the periodic signal generator of many repetitive control algorithm closely resembles the betterment learning laws in (Arimoto et al., 1984; Arimoto et al.,1988).However, while the learning betterment controller acts during a finite time horizon, the repetitive controller acts continuously as regulator. Moreover, in the learning betterment approach, it is assumed that, at every learning trial, the robot starts executing the task from the same initial condition. This is not the case in the repetitive control approach.My interest in learning and repetitive control arouse in 1987, as a consequence of studying the stability of a class of adaptive and repetitive controllers for robot manipulators with my former student and colleague Nader Sadegh. My colleague and friend Masayoshi Tomizuka had been working very actively in the area of repetitive control and he introduced me to this problem. At that time there was much activity in the robotics and control communities toward finding adaptive control algorithms for robot manipulators which were rigorously proven to be asymptotically stable. The problem had been recently solved using passivity by Slotine and Li (1986), Sadegh and Horowitz (1987) and Wen and Baynard (1988). In contrast, most of the stability results in learning and repetitive control of that period relied on several unrealistic assumptions: either the dynamics of the robot was assumed linear, or it was assumed that it could be at least partially linearized with feedback control. Moreover, it was assumed in most works that the actual response of the robot was periodic or repeatable, even during the learning transient, and that joint accelerations could be directly measured. Nader and I had recently overcome some of these problems in our adaptive control research, and concluded that learning controllers could be synthes