Unified control of n-link underactuated manipulator with single passive joint: A reduced order approach

This paper addresses the motion control problem of an n-link planar underactuated manipulator with any one of its joints being passive. A reduced order approach is proposed to achieve a swing-up control and a balancing control. The presented approach involves two stages. In Stage 1, (n− 2) control laws are first designed to force both the angles and angular velocities of (n− 2) actuated links to converge to zero, which guarantees that the n-link manipulator is reduced to like a 2-link one. Then the control law of the rest actuated link is temporarily set to constant to simplify the design of the control laws. In Stage 2, the states of the reduced system are guaranteed by maintaining the (n− 2) control laws designed in Stage 1. Meanwʹhile, a swing-up control law and a balancing control law are designed for the rest actuated link. Integrated with the (n− 2) nonlinear control laws designed in Stage 1, the n-link underactuated manipulator is swung up quickly and balanced at the straight-up unstable equilibrium position effectively. Simulation results on a 4-link underactuated manipulator with different passive joint positions demonstrate the effectiveness of the proposed control approach.