Position Control for a Planar Underactuated Manipulator Based on Model Reduction and Energy Attenuation

Planar Active-Active-Passive-Active (AAPA) underactuated manipulator is a four-link mechanical system with a passive third joint, which moves in the horizontal plane. In this paper, a stable control strategy is proposed based on model reduction and energy attenuation to realize the position control for the planar AAPA manipulator. First, the dynamics model of the system is built, and the control process is divided into two stages to realize the control objective. In stage 1, the first two links move to the target angles which can ensure the target position is in the reachable area of the system. Meanwhile, based on the energy attenuation, the third link converges to an intermediate attitude angle. Then, the differential evolution (DE) algorithm is employed to optimize the target angles for last two links, which satisfy the angle constraint. In stage 2, the angles of the first and second links remain unchanged, that is the system is reduced to a virtual planar Acrobot, and then the third and fourth links move to the target value to realize the control objective. Finally, the validity of the control strategy is demonstrated via the simulations.