  This paper is concerned with the optimal kinematic control of a robot
manipulator where the robot end effector position follows a task space
trajectory. The joints are actuated with the desired velocity profile to
achieve this task. This problem has been solved using a single network adaptive
critic (SNAC) by expressing the forward kinematics as input affine system.
Usually in SNAC, the critic weights are updated using back propagation
algorithm while little attention is given to convergence to the optimal cost.
In this paper, we propose a critic weight update law that ensures convergence
to the desired optimal cost while guaranteeing the stability of the closed loop
kinematic control. In kinematic control, the robot is required to reach a
specific target position. This has been solved as an optimal regulation problem
in the context of SNAC based kinematic control. When the robot is required to
follow a time varying task space trajectory, then the kinematic control has
been framed as an optimal tracking problem. For tracking, an augmented system
consisting of tracking error and reference trajectory is constructed and the
optimal control policy is derived using SNAC framework. The stability and
performance of the system under the proposed novel weight tuning law is
guaranteed using Lyapunov approach. The proposed kinematic control scheme has
been validated in simulations and experimentally executed using a real six
degrees of freedom (DOF) Universal Robot (UR) 10 manipulator.
