  Model Predictive Control (MPC) has shown the great performance of target
optimization and constraint satisfaction. However, the heavy computation of the
Optimal Control Problem (OCP) at each triggering instant brings the serious
delay from state sampling to the control signals, which limits the applications
of MPC in resource-limited robot manipulator systems over complicated tasks. In
this paper, we propose a novel robust tube-based smooth-MPC strategy for
nonlinear robot manipulator planning systems with disturbances and constraints.
Based on piecewise linearization and state prediction, our control strategy
improves the smoothness and optimizes the delay of the control process. By
deducing the deviation of the real system states and the nominal system states,
we can predict the next real state set at the current instant. And by using
this state set as the initial condition, we can solve the next OCP ahead and
store the optimal controls based on the nominal system states, which eliminates
the delay. Furthermore, we linearize the nonlinear system with a given upper
bound of error, reducing the complexity of the OCP and improving the response
speed. Based on the theoretical framework of tube MPC, we prove that the
control strategy is recursively feasible and closed-loop stable with the
constraints and disturbances. Numerical simulations have verified the efficacy
of the designed approach compared with the conventional MPC.
