Modelling of Parameter and Bound Estimation Laws for Adaptive-Robust Control of Mechanical Manipulators Using Variable Function Approach

Two different approaches have been actively studied to maintain performance in the presence of parametric uncertainties: adaptive control and robust control. The basic philosophy of adaptive controller is that incorporates some sort of parameter estimation and adaptive controller can learn from experiences in the sense that parameters are changed. Some of the adaptive control laws introduced by Craig et al.(1987), Middleton&Goodwin (1988), Spong&Ortega (1990) require the acceleration measurements and/or the computation of the inverse of the inertia matrix containing estimated parameters. Later, Slotine&Li (1987, 1988) Spong et.al (1990), Egeland&Godhavn (1994) have derived adaptive control algorithms without using the joint accelerations and the inverse of inertia matrix. Other adaptive control laws are proposed in references (Carelli et al 1995, Kelly et al 1989, Burkan&Uzmay 2005, Burkan 2005, Burkan, 2006). Comparative studies of adaptive control laws are given in references (Ortega&Spong 1989, Colbaugh at al 1996). On the other hand, robust control has been successfully used to design controller with disturbance, unmodelled dynamics and other sources of uncertainty. The papers about application these techniques for the background of robotic application are given in survey papers (Abdullah at al 1991, Sage at al 1999). Based on the approach of Corless-Leitmann (1981), Spong (1992) developed a new robust control law. In this approach (Spong 1992), the Leitmann (1981) or Corless-Leitmann (1981) approach was used to design a robust controller. Different extension of the scheme by Spong (1992) has been developed by Liu&Goldenberg (1996a, 1997), Yaz (1993), Candudas de Wit et al. (1996). An adaptive scheme of uncertainty bound is given in the papers (Koo&Kim 1994, Burkan and Uzmay 2003b, Burkan and Uzmay 2005). Similar algorithms have proposed by Dawson at. al. (1993) and Zenieh&Corless (1997). Comparative studies of robust controllers are given in the references (Liu & Goldenberg 1996b, Jaritz & Spong (1996).