A multistage position/force control for constrained robotic systems with friction: Joint-space decomposition, linearization, and multiobjective observer/controller synthesis using LMI formalism

A historical review of constrained robot modeling and control strategies is first introduced. Next, a design of a motion/force controller for a constrained servo-robot, which is based on a commonly known modeling structure, is proposed. The contact between the end-effector and the environment is subject to frictional features. Accordingly, the control plant is based on the LuGre friction closed-loop observer. Therefore, new nonlinear position and force input transforms, which are slightly different from classical computed torques, are proposed, combined with a new change of variable. The main purpose of this paper is to establish the stability condition by using the passivity of interconnected linear and nonlinear subplants. From then on, because of this formulation, the authors succeed in designing a full-order dynamic position feedback and an integral force controller that ensure exponential stabilization within an H-infinity multiobjective optimization. These conditions are expressed in terms of linear matrix inequalities. The performances are experimentally validated on a two-degrees-of-freedom robot manipulator acting on a horizontal worktable with friction. The LuGre model estimator exhibits a richer behavior in terms of friction compensation and positioning tracking when experimentally compared to the Karnopp friction compensation. The latter form exhibits poor modeling properties at zero crossings of the velocity.