A control law for a rigid robotic manipulator optimizing quadratic cost functional composed of sliding surface and its derivative for fixed final time and free final state was proposed by Z. Ahmad (1995; 2000). Closed form solutions for such a control law corresponding to constant in time and specific diagonal time-varying weighting matrices are presented. These closed form solutions for the two point boundary value problem greatly reduce computational load and allow for real time implementation. Simulation results for a two degree of freedom manipulator are also provided.

Summary form only given. Previous work where estimation of the parameters of a plant was incorporated through exploratory schedules (ESs) which are reference input trajectories designed to enhance the learning of system parameters, is extended. In that work, ESs were generated offline and used in an open-loop fashion. Moreover, these ESs were used in between actual control tasks, therefore limiting the process of estimation during idle time. In this work the authors present an approach for generating ESs in a closed-loop manner. Such trajectories in general may not be the desired trajectories, since they result in larger tracking errors. However, ESs offer faster convergence to the system parameters and therefore yield smaller long-term tracking errors. The automation for the design of ESs requires online modification of the desired trajectory to enhance learning at the expense of poorer initial tracking.>

A nonalgorithmic method is presented for the solution to the inverse kinematic problem of a robot. The method is robot independent and involves a hybrid approach whereby a neural solution is augmented with an iterative procedure which provides the final solution within some specified tolerance. Essentially, the neural solution is similar to a lookup table in providing a good initial guess to a classical iterative search. It has been found that for the industrial manipulator PUMA 560, the proposed hybrid method achieves about a twofold increase in computational efficiency with better uniformity of the time required to obtain the solution to the robotic manipulator.>