Speed optimization of transport motion of a portal robot

Journal article, 1992

An algorithm for calculating piecewise-constant control with modulo-limited components is proposed for a nonlinear model of a three-degree portal robot; this control contains two switching points and drives the dynamical system from an arbitrary given initial state to an arbitrary given final phase state in a finite time. Underlying the algorithm is a solution of the speed problem for controlled motion of a mass point in n-dimensional Euclidean space with modulo-limited components of the control vector. It is demonstrated that this solution is nontrivial for non-zero phase velocities at the beginning and end of the control process. The algorithm for solving a nonlinear problem yields a practical speed-optimized control in this simple class of control actions while, in certain cases, where the initial and final conditions are given, it also yields a control in a class of arbitrary piecewise­ continuous controls. The effectiveness of the algorithm is confirmed by numerical examples.