Inverse dynamics of flexible manipulators with Coulomb friction or backlash and non-zero initial conditions
For nonlinear control systems, of the form \[ \begin{cases} M\ddot x+ C\dot x+ Kx= Bu+ e(x,\dot x,u,t),\\ y= Gx,\end{cases} \] with \(x\), \(u\), \(y\) denoting respectively the state, input and output vectors, \(u\) and \(y\) being of equal dimensionality, and with constant matrices \(M\), \(C\), \(K\), \(G\), iterative, approximate algorithms of direct and inverse dynamics are presented. We recall that the direct dynamics consist in computing an output trajectory \(y(t)\) for given control \(u(t)\) and an initial state \(x_0\), while the inverse dynamics algorithm finds out a control action generating a desirable output trajectory (i.e. perform the system inversion). As an illustration of the inverse dynamics algorithm, a mathematical model of a flexible link robotic manipulator with a single link is examined; it includes viscous damping, Coulomb friction and backslash. Computer simulations demonstrate the performance of the algorithm.
scientific article; zbMATH DE number 1295121