Trajectory tracking of mechanical systems with unilateral constraints: Experimental results of a recently introduced hybrid PD feedback controller

Abstract

Abstract-The problem of tracking a time-varying reference trajectory of a mechanical system with unilateral position constraints is addressed in this paper. We present for the first time simulation and experimental results of a recently introduced trajectory tracking controller for hybrid systems with state jumps. The controller is applied to (locally) stabilize a time-varying trajectory of a 1-DOF robotic arm impacting and bouncing off an aluminum rod. The arm is modeled as a rigid link with viscous and Coulomb friction. The impact phenomenon is assumed to instantaneously reset the velocity in accordance with the classical Newton's law of restitution. Kinematic and dynamic identified parameter values are reported. The employed controller, hereafter called "hybrid PD controller with acceleration feedforward", requires the real time detection on each impact in order to properly define the error signal. To this end, a force sensor and a triggering logic based on a force threshold are employed.

Tracking control via switched Integral Sliding Mode with application to robot manipulators

“…The latter use Trapezoidal Velocity Profiles as reference signals for each joint. The initial conditions of the robot are equal to q(0) = [π/15, 0, π/2] rad, while the sampling time is T =5 × 10 −5 s. It is assumed that the joint velocityq is measurable or estimated 350 using a Levant's differentiator [14], as successfully shown in [29].…”

Integral Sliding Mode Based Switched Structure Control Scheme for Robot Manipulators

“…The initial conditions of the robot are q(0) = [π/15, 0, π/2] rad, while the sampling time is T =5 × 10 −5 s. Note that, we assume that the joint velocityq is measurable. If this is not the case, one can use an estimate ofq, for instance, by using a Levant's differentiator [9], as successfully shown in [22].…”

Reference Spreading: Tracking Performance for Impact Trajectories of a 1DoF Setup

“…Whereas different theoretical frameworks exist for the trajectory tracking of mechanical systems performing impacting motions, the experimental validation of these control methods is somewhat lacking (see [2] and [5] for experimental examples of robots performing impacting motions). This brief aims to fill that gap for RS and builds upon a previous analysis [25] in which the preliminary experimental results using RS were presented. In [25], limitations of the setup such as dominant (unmodeled) flexural dynamics and limited stroke, appeared to undermine the controller's performance preventing the authors to execute a thorough performance analysis.…”

“…This brief aims to fill that gap for RS and builds upon a previous analysis [25] in which the preliminary experimental results using RS were presented. In [25], limitations of the setup such as dominant (unmodeled) flexural dynamics and limited stroke, appeared to undermine the controller's performance preventing the authors to execute a thorough performance analysis. In this brief, instead, we consider an experimental one-degree-of-freedom (1DoF) test-bench that has been specifically designed for performing trajectories with partially elastic impacts (see Fig.…”

“…The technique known as jump aware (JA) filtering [26] is employed for estimating position and velocity as well as for detecting impacts. On the other hand, the goal of [25] was to provide an experimental proof of principle, the objective of this brief is to analyze the control strategy from a performance and robustness perspective. We introduce three quantitative measures for assessing performance.…”