In this paper, we propose a new optimal trajectory planning method for the manipulator to optimize its operating efficiency and ensure the smoothness of the motion process. The position sequences in joint space corresponding to a specified trajectory in task space are obtained by using the inverse kinematic algorithm, and the seventh-degree B-spline curve interpolation method is used to construct the joint trajectory with controllable start–stop kinematic parameters, and continuous velocity, acceleration and jerk. The kinematic constraints of the manipulator are transformed into the control point constraints of the B-spline curve, the sequential quadratic programming method is used to solve the optimal motion time node, and then the time-optimal continuous jerk trajectory satisfying the nonlinear kinematic constraints is planned. Simulation results show that the proposed trajectory planning method provides the ideal trajectory for the joint controller, ensuring the manipulator can smoothly track any specified trajectory in the task space in the shortest time.

This article proposes a comprehensive stable control strategy for the planar multi-link underactuated manipulator (PMLUM), considering several uncertainties. According to the nilpotent approximation property, the control procedure is split into two stages. In the first stage of control, we postulate the idea of model degradation, reducing the PMLUM to a planar virtual Pendubot (PVP). This occurs by controlling the active link (AL) to a specific desired position and the passive link (PL) moves along with it. When the AL moves to the desired position, the second phase of control is entered. Meanwhile, all ALs are regarded as a whole, so the PMLUM can be regarded as a mechanical arm with 2-DOF. In the second stage of control, due to the nilpotent approximation feature of the PVP, the PVP is guided to the desired angle using the iterative steering technique. Simulation experiments are carried out on active–active–passive (AAP) and active–active–active–passive (AAAP) systems under major uncertainties, which contain initial velocity and torque disturbances. The final results validate the effectiveness of the method proposed.