This paper proposes a novel optimal control scheme for constrained image based visual servoing of a robot manipulator. For a robot manipulator with an eye-on-hand configuration, visibility constraint is an essential requirement to avoid servo failure, while robot's actuator limits must also be satisfied. To ensure this, the constraints are modelled implicitly via learning the task and defining safe regions using expert human demonstrations via mixture of Dynamic Movement Primitives (DMPs). The visual servoing problem is then formulated as a closed-loop optimal control problem using these constraint model where a desired target (possibly time-varying) is obtained by acting upon the feedback from the real-time visual sensors. The visual servo control loop consists of a single network adaptive critic optimal tracking control scheme whose weights are tuned using Lyapunov stability criteria. The stability and the performance of the proposed control scheme is shown theoretically via Lyapunov approach and also verified experimentally using a seven degree of freedom (DOF) Franka Emika and six DOF Universal Robot (UR) 10 manipulator. The approach is also demonstrated on a use case scenarios in mock-up convenience store and warehouse setup.

Real-time optimal path planning for robotic manipulations in task space is a very fundamental and important problem. In this paper, the problem of generating robot trajectories in an obstacle-ridden environment is formulated under an optimal control framework using Hamilton-Jacobi-Bellman (HJB) equation. The novel contribution of this paper is that a closed form HJB control solution (a necessary and sufficient condition for global optimality of a control solution with respect to a cost function) has been achieved for generating real-time optimal trajectories for a robot manipulator. In contrast with the decoupled end-effector path planning and subsequent trajectory generation, the proposed scheme can exploit sensory input for real-time trajectory generation where the end-effector path as well as the joint trajectory is recomputed online while satisfying the real-time constraints. The stability and the performance of the proposed control framework is shown theoretically via Lyapunov approach and also verified experimentally using a 6 degrees of freedom (DOF) Universal Robot (UR) 10 robot manipulator. It is shown that a significant saving in cost metrics can be obtained over similar trajectory generation approaches from the state-of-the-art with obstacle-ridden environment and also has better performance in high speed tracking applications. Warehouse applications of the proposed scheme in case of static and dynamic targets with respect to the robot manipulator is also included.