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.

Planar underactuated manipulators are widely used in aerospace and deep-sea exploration. Due to their passive joints without actuation, it is difficult to perform trajectory planning and direct control. In this paper, an angular velocity trajectory planning method is proposed, aiming to calculate the velocity trajectory by using a superposition of basis functions and transforming the planning problem into an optimization problem by using a metaheuristic algorithm. According to the underactuated constraint relationship, the planning trajectory of the passive joint is obtained, which ensures that the passive joint can be indirectly controlled to reach the target angle while tracking the trajectory of the active joint. For the tracking control problem, a sliding mode controller with an exponential convergence rate is used to track the trajectory. Lastly, three sets of simulations are run to demonstrate the efficacy of the suggested approach.