This work addresses the problem of the accurate task space control subject to finite-time convergence. Dynamic equations of a rigid robotic manipulator are assumed to be uncertain. Moreover, globally unbounded disturbances are allowed to act on the manipulator when tracking the trajectory by the end-effector. Based on suitably defined task space non-singular terminal sliding vector variable and the Lyapunov stability theory, we derive a class of absolutely continuous Jacobian transpose robust controllers, which seem to be effective in counteracting uncertain dynamics, unbounded disturbances and (possible) kinematic and/or algorithmic singularities met on the end-effector trajectory. The numerical simulations carried out for a robotic manipulator of a SCARA type consisting of two revolute kinematic pairs and operating in a two-dimensional task space, illustrate performance of the proposed controllers.. (C) 2016 Elsevier Ltd. All rights reserved.