Control strategy based on differential evolution algorithm for planar second-order nonholonomic manipulator

Abstract

This paper presents a two-stage position control strategy based on the differential evolution (DE) algorithm for a planar second-order nonholonomic manipulator, which has one passive joint and this passive joint is not the first joint (planar $\mathrm{A}^{\mathrm{m}}\mathrm{PA}^{\mathrm{n}}$ manipulator for short, where $m\geq 1, n\geq 0$ ). An offline DE algorithm is used to calculate all link target angles corresponding to the target position. According to these target angles, a Lyapunov function is constructed to design the controllers A for the control stage 1, which are used to control all active links to their target angles. According to the constraint equation of the planar $\mathrm{A}^{\mathrm{m}}\mathrm{PA}^{\mathrm{n}}$ manipulator, an oscillatory trajectory is planned for the first active link based on the online DE algorithm. When the first active link tracks the oscillatory trajectory, it will back to its target angle eventually. Meantime, the passive link will be jointly controlled to its target angle eventually. Then, the other Lyapunov function is constructed to design the controllers B for the control stage 2, which are used to control the first active link tracks the target trajectory and control the remaining $m+n-1$ active links maintain in their target angles. Simulation results of a planar AAPA manipulator demonstrate the effectiveness of the proposed control strategy.