Mixing neural networks and the Newton method for the kinematics of simple cable-driven parallel robots with sagging cables

摘要

Cable-driven parallel robots (CDPR) use cables to move a platform. These cables can be coiled/uncoiled by winches and are all attached to the platform. We are considering here a specific class of CDPR, called N-1 which has <tex>$N$</tex> cables that are all attached to the platform at the same point <tex>$B$</tex>. With 2 cables we get a planar 2-dof robot while with <tex>$N\geq$</tex> 3 we get a robot with 3 translational dof. We assume that the cables have elasticity and a mass so that sagging exists. In that case the inverse and direct kinematics (IK, DK) are difficult to solve. As kinematics plays an important role for the robot analysis it is necessary to design fast but exact kinematics procedures. In this paper we consider the 2&#x2013;1 and 3&#x2013;1 cases which have a single solution for the kinematic and addresses the use of neural network (NN) to solve the IK and DK. We show that NN provide very approximate results but also that it is possible to design a solving strategy mixing NN and the Newton method to get the exact result in a low computation time. We cannot formally prove that this approach will always work but extensive numerical tests have shown no failure.