Minimum-time control of systems with Coulomb friction: near global optima via mixed integer linear programming

This work presents a method of finding near global optima to minimum-time t rajectory generation problems for systems that would be linear if it were n ot for the presence of Coulomb friction. The required final state of the sy stem is assumed to be maintainable by the system, and the input bounds are assumed to be large enough so that the role of maintaining zero acceleratio n during finite time intervals of zero velocity (the role of static frictio n) can always be assumed by the input. Other than the previous work for gen erating minimum-time trajectories for robotic manipulators for which the pa th in joint space is already specified, this work represents, to the best o f our knowledge, the first approach for generating near global optima for m inimum-time problems involving a non-linear class of dynamic systems. The r eason the optima generated are near global optima instead of exactly global optima is due to a discrete-time approximation of the system (which is usu ally used anyway to simulate such a system numerically). The method closely resembles previous methods for generating minimum-time trajectories for li near systems, where the core operation is the solution of a Phase I linear programming problem. For the non-linear systems considered herein. the core operation is instead the solution of a mixed integer linear programming pr oblem. Copyright (C) 2001 John Wiley & Sons, Ltd.