Trajectory Control of RLED Robot Manipulators Using a New Type of Learning Rule

Rigid Link Electrically Driven (RLED) robot manipulators are used extensively in applications. For RLED manipulators, a hybrid adaptive-learning controller, which do not utilize the velocity measurements, is designed and proved that it can be made semi-global asymptotically stable (Canbolat et al., 1996). The learning part in that work (Canbolat et al., 1996) is based on the results given in (Messner et al. 1991). However (Messner et al., 1991) neglected the electrical dynamics and the velocity measurements are available. In (Canbolat et al., 1996), the system is designed through a high pass filter which produces the surrogates of velocity. Later in another work, (Kaneko & Horowitz, 1997) designed a similar controller for a robot manipulator using a velocity observer neglecting the electrical dynamics. The system in (Canbolat et al., 1996) had not been verified through simulation and experiments. Recently, (Uguz & Canbolat, 2006) published the simulation results of the controller proposed in (Canbolat et al., 1996) for a sinusoidal desired position. However, a typical desired position for a robotic application is not generally sinusoidal. Due to this, more general position vectors should be generated. A general task requires a smooth trajectory, which starts from an initial position to a final position and repeats this over and over again. Such a desired trajectory can be generated in several ways (Fu et al., 1987). In the simulation of the system in (Canbolat et al., 1996), desired functions should satisfy the certain specifications. For this purpose, the polynomial method given in (Fu et al., 1987) is slightly modified in order to accommodate with the requirements of the controller. The modifications are necessary due to the continuous third derivative or jerk requirement in (Canbolat et al., 1996). Here, we also proposed other methods, which utilize transcendental functions. Transcendental function methods give a trajectory that can be continuously differentiable up to any order. Learning control law is usually used for repetitive tasks in which a certain task should be repeated in each cycle. Indeed, the adaptive and learning control schemes are very similar, since both strategies are based on the estimation of unknown system dynamics. However, the learning control philosophy tries to estimate the unknown time functions instead of estimating the unknown constant parameters of the system as in the adaptive control setup. The aim of the learning control is to improve the tracking performance of the manipulator at 32