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

Abstract

Abstract-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.

Tracking and parameter identification for model reference adaptive control

“…x pr is the reference trajectory for (5) and the reference input r. Then the system error dynamics is given by using (9), (10), and (12), and has the forṁ…”

“…While usually dependent on some structural properties of the system, adaptive control is valuable because of its ability to solve tracking problems for a wide range of possible values of the unknown model parameters including higher‐order systems. One area where adaptive control is important is in aerospace problems . In basic adaptive control for some classes of control systems (such as linear systems), one can often use nonstrict (or weak) Lyapunov functions to ensure that tracking objectives are realized, and then achieve parameter identification (ie, convergence of the parameter estimates to the true parameter values) provided that a persistency of excitation (PE) condition is also satisfied.…”

“…One area where adaptive control is important is in aerospace problems. [5][6][7][8][9][10][11][12][13][14][15][16] In basic adaptive control for some classes of control systems (such as linear systems), one can often use nonstrict (or weak) Lyapunov functions to ensure that tracking objectives are realized, and then achieve parameter identification (ie, convergence of the parameter estimates to the true parameter values) provided that a persistency of excitation (PE) condition is also satisfied.…”

Control of a robot interacting with an uncertain viscoelastic environment with adjustable force bounds

“…Capturing the phenomenon at contact in a physically consistent contact model [11]- [13] is a first step to designing an efficient controller to deal with the problem of destabilizing impact forces in an uncertain environment. In our previous works [7], [8], [14], we investigated the problem of controlling the robot contact transition with stiff environments and developed continuous controllers with guaranteed stability. The developed controllers obviated the need for force or acceleration measurements, which can be noisy and have been shown to cause contact instability [15].…”

Neural Network Control of a Robot Interacting With an Uncertain Hunt-Crossley Viscoelastic Environment

“…In our previous efforts [16], [23], a linear spring contact model was used to develop a controller for robot contact transition with a stiff environment. The contribution of the work was the development of a single continuous controller for both the non-contact and contact states of the robot.…”