Modeling and optimal control of dual stage cable suspended robot considering the cables’ elasticity using State Dependent Riccati Equation (SDRE) approach

In this paper, the modeling of a new two-stage cable robot is developed, while the flexibility of the cables is also considered. The performance of this robot is controlled using a strong nonlinear optimal control based on state dependent Riccati equation (SDRE) approach. The superiority of this controller is that it is able to control the end-effector of a nonlinear robot in an optimal way which is extremely important to find the optimal path of a wide workspace robot such as this studied dual case. Dual stage cable robots are useful controllable tower cranes by which the rotational workspace of the end-effector is increased thanks to its second platform. However, due to the fact that the cables used are inevitably elastic, there is an unwanted deviation in the path tracing. By modeling this uncertainty as well as controlling it using the optimal SDRE controller, not only can the precision tracking performance be enhanced, but also its DLCC criteria can be effectively improved. Here, the kinematics and kinetics of this robot in the presence of cable elasticity are developed and SDRE controller is implemented on this system to neutralize the uncertainty effects. It is shown by the aid of the simulation test that existence of elasticity of cables can deviate the end-effector from its desired tracking path and this error can be compensated by the aid of designed controller. Thus, the robot is able to carry heavier loads successfully within bigger rotational workspace.