This paper deals with the problem of controlling a robotic system whose joints have bounded position, velocity and acceleration/torque. Assuming a discrete-time acceleration control, we compute tight bounds on the current joint accelerations that ensure the existence of a feasible trajectory in the future. Despite the clear practical importance of this issue, no complete and exact solution has been proposed yet, and all existing control architectures rely on hand-tuned heuristics. We also extend this methodology to torque-controlled robots, for which joint accelerations are only indirectly bounded by the torque limits. Numerical simulations are presented to validate the proposed method, which is computationally efficient and hence suitable for high-frequency control.