Reachable Configurations of a Two-Link Manipulator under Time-Optimal Control with Angular Velocity Constraints

This paper considers the problem of constructing reachable domains for a planar two-link manipulator with a statically balanced second link under time-optimal control of its motion with angular velocity constraints for the links. The optimal controls belong to the class of relay regimes and contain the minimum total number of switchings sufficient to satisfy the boundary conditions: the system is at rest at the initial and final time instants. A method is developed to find reachable domains in the manipulator’s configuration plane under the proposed controls with angular velocity constraints.