Solving constrained minimum‐time robot problems using the sequential gradient restoration algorithm

Abstract

Abstract In this paper three constrained minimum‐time control problems of a two‐link manipulator are solved using the sequential gradient and restoration algorithm (SGRA). In addition to the hard bounds on the control torques commonly considered in the literature, we also consider cases with bounded output power and with a constrained shoulder arm. The inequality constraints considered are reduced via Valentine‐type transformations to non‐differential path equality constraints. The SGRA is then used to solve these transformed problems with equality constraints. The results obtained indicate that at least one of the two controls is at its limits at any instant in time. The remaining control then adjusts itself so that none of the system constraints is violated. Hence the minimum‐time control is either a pure bang–bang control or a combined bang—bang/singular control.