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

摘要

This work presents a method of finding near global optima to minimum-time trajectory generation problems for Systems that would be linear if it were not for the presence of Coulomb friction. The required final state of the system 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 acceleration during finite time intervals of zero velocity (the role of static friction) can always be assumed by the input. Other than the previous work for generating minimum-time trajectories for robotic manipulators for which the path in joint space is already specified, this work represents, to the best of our knowledge, the first approach for generating near global optima for minimum-time problems involving a non-linear class of dynamic systems. The reason the optima generated are near global optima instead of exactly global optima is due to a discrete-time approximation of the system (which is usually used anyway to simulate such a system numerically). The method closely resembles previous methods for generating minimum-time trajectories for linear 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 problem.