A force limiting adaptive controller for a robotic system undergoing a non-contact to contact transition

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 non-contact 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 of hyperbolic tangent functions as a means to limit the impact forces resulting from large initial conditions as the robot transitions from a non-contact to contact state. New control development, closed- loop error systems, and Lyapunov-based stability analysis arguments are used to conclude the result.