Dynamic modeling and optimal control of stone-carving robotic manipulators

The stone-carving robotic manipulators (SCRM) find a broad range of applications due to their high efficiency, wide range of processing and strong flexibility. However, the features of strong disturbance, uncertainty and variation in the parameters make the design of SCRM control systems more complicated. This paper introduced the inverse linear quadratic (ILQ) theory into the SCRM control system. First, we deduced the dynamic equation and state-space equation of the SCRM system with the Lagrange method. Then, the ILQ theory was used to achieve the desired closed-loop poles assignment of the system. To simplify the design process and meet the requirement of practical use, the state feedback optimal control law was determined by an improved ILQ design method. The proposed control scheme has the explicit capacity to achieve the desired joint angle and joint torque control performances, with fewer external disturbances and no sensitivity to changing model parameters. The effectiveness of the proposed control scheme compared with the traditional control strategies is shown in the simulation results. Thus, the vibration of the joint torque during the manufacturing process can be greatly reduced.