An approach to nonlinear feedback control with applications to robotics

A control problem involving a mechanical system with generalized coordinates <i>q</i>∈<i>R</i><sup>m</sup> is considered. The error in tracking a desired input <i>y</i><sup>d</sup>∈<i>R</i><sup>p</sup> is <i>e</i>=<i>E</i>(q,y<sup>d</sup>)∈<i>R</i><sup>m</sup>. If <i>E</i> satisfies simple conditions, it leads to a nonlinear control law that assures <i>e</i>(t)→0 as <i>t</i>→∞. The law is robust in that small changes in it do not produce large steady-state errors or loss of stability. In this theory a unified framework is presented for treating a number of problems in the control of mechanical manipulators.