A stable control for second-order nonholonomic planar underactuated mechanical system: energy attenuation approach

A stable control strategy is proposed via energy attenuation to realise the position control for a second-order nonholonomic planar four-link active-passive-active-active (APAA) underactuated mechanical system. Since a first-order nonholonomic planar passive-active-active (PAA) system can be stabilised at the target position, we control the first link based on the principle of energy attenuation to target value and the planar APAA system is reduced to be a first-order nonholonomic PAA system, where the target value is selected to ensure the target position comes within the reachable area of the PAA system. Meanwhile, we divide the control of the reduced-order PAA system into two stages based on the holonomic characteristic of planar acrobot, and the target angles of which are obtained according to the target position by using the simulated annealing algorithm. Each stage controllers of the reduced-order system are designed according to its control target. Finally, the validity of the control strategy is demonstrated via the simulations.