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The presence of joint velocity and acceleration limits must be taken into account by the inverse kinematics of robot manipulators, so as to avoid incorrect task execution when these are violated. To solve this problem, a novel algorithmic approach to kinematic control is presented in this paper, which guarantees that the joint variables do not overtake their limits. The proposed technique is based on a new second-order inverse kinematics algorithm, which enables the handling of velocity and acceleration constraints while tracking the desired end-effector path. The goal is achieved by suitably slowing down the task-space trajectory via a time warp when joints limits are encountered. The proposed method is designed for on-line applications, i.e., the desired trajectory is not known in advance, and requires a light computational burden. The application of the proposed approach is finally illustrated in experiments implemented on a six-degree-of-freedom industrial robot manipulator.

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This paper proposes an approach to the design of control laws for underwater vehicles that takes into account the hydrodynamic effects affecting the tracking performance. To this aim, a suitable adaptive action based on appropriate kinematic transformations between the earth-fixed frame and the vehicle-fixed frame is developed. The proposed control law adopts quaternions to represent attitude errors, thus avoiding representation singularities that occur when using instead Euler angles. The stability of the designed control law is demonstrated by means of a Lyapunov-based argument. In view of practical implementation, a simplified version of the developed control law is also proposed that compensates only the persistent hydrodynamic terms, namely, the restoring generalized forces and the ocean current. Finally, the tracking performance of the proposed control law is analyzed in comparison to that of other existing control laws available in the literature. The obtained simulation results confirm the effectiveness of the proposed technique

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