Modeling and Dynamic Performance Evaluation of Target Capture in Robotic Systems

Abstract

In this paper, a dynamic system consisting of a robot manipulator and a target is analyzed. The target is considered in a general way as a dynamic subsystem having finite mass and moments of inertia (e.g., a rigid body or a second robot). The situation investigated is when the robot establishes interaction with the target in such a way that it intercepts and captures a reference element of the target. The analysis of target capture is divided into three phases in terms of time: the precapture, "free" motion (finite motion); the transition from free to constrained motion in the vicinity of interception and capture (impulsive motion); and the postcapture, constrained motion (finite motion). The greatest attention is paid to the analysis of the phase of transition, the impulsive motion, and dynamics of the system. Based on the use of impulsive constraints and the Jourdainian formulation of analytical dynamics, a novel approach is proposed for the dynamic modeling of target capture by a robot manipulator. The proposed approach is suitable to handle both finite and impulsive motions in a common analytical framework. Based on the dynamic model developed and using a geometric representation of the system's dynamics, a detailed analysis and a performance evaluation framework are presented for the phase of transition. Both rigid and structurally flexible models of robots are considered. For the performance evaluation analyses, two main concepts are proposed and corresponding performance measures are derived. These tools may be used in the analysis, design, and control of time-varying robotic systems. The dynamic system of a three-link robot arm capturing a rigid body is used to illustrate the material presented.