A Force Limiting Adaptive Controller for a Robotic System Undergoing a Noncontact-to-Contact Transition

The problem of prescribing, reducing, or controlling the interaction forces between a robot and the environment during a noncontact-to-contact transition is intriguing because large interaction forces can damage both the robot and/or the environment or lead to degraded performance or instabilities. In this paper, we consider a two-link planar robotic arm that transitions from free motion to contact with an unactuated mass-spring system. The objective is to control a robot from a noncontact initial condition to a desired (in-contact) position so that the mass-spring system is regulated to a desired compressed state. The feedback elements for the controller in this paper are contained inside hyperbolic tangent functions as a means to limit the impact forces resulting from large initial conditions as the robot transitions from a noncontact to contact state. The main challenge of this work is that the use of saturated feedback does not allow some coupling terms to be canceled in the stability analysis, resulting in the need to develop state-dependent upper bounds that reduce the stability to a semiglobal result. New control development, closed-loop error systems, and Lyapunov-based stability analysis arguments are used to conclude the result. It is interesting to note that only the position and velocity terms are required for the proposed controller (i.e., the controller does not depend on measuring the impact force and the acceleration terms). Experimental results that successfully demonstrate the control objective are provided.