Robust Ballistic Catching: A Hybrid System Stabilization Problem

Abstract

This paper addresses a remaining gap between today's academic catching robots and their future in industrial applications: reliable task execution. A novel parameterization is derived to reduce the three-dimensional (3-D) catching problem to 1-D on the ballistic flight path. Vice versa, an efficient dynamical system formulation allows reconstruction of solutions from 1-D to 3-D. Hence, the body of the work in hybrid dynamical systems theory, in particular on the 1-D bouncing ball problem, becomes available for robotic catching. Uniform Zeno asymptotic stability from bouncing ball literature is adapted, as an example, and extended to fit the catching problem. A quantitative stability measure and the importance of the initial relative state between the object and end-effector are discussed. As a result, constrained dynamic optimization maximizes convergence speed while satisfying all kinematic and dynamic limits. Thus, for the first time, a quantitative success-oriented comparison of catching motions becomes available. The feasible and optimal solution is then validated on two symmetric robots autonomously playing throw and catch.

Tracking and grasping of moving target based on accelerated geometric particle filter on colored image

“…Pierluigi et al [13,14] used linear and nonlinear optimization to obtain the interception point on the visually tracked object's moving trajectory. The aforementioned methods to a large extent depend on the tracking and estimating of the target's motion trajectory, and then move the robot to proper pose to intercepts the target's flying path at the right moment [15].…”

“…As for the grasping strategy, with interception strategy alone is not suitable for randomly moved object since the interception point is hard to predict. Also, purely interception may result in failure due to the impact forces and rebound which may cause the object to bounce off the gripper [15]. To cope with this problem, Billard et al [17] proposed a tracking-interception strategy which have the robot moves with the object for a short period of time before intercepting.…”

A Separated Adaptive Control Strategy for Different Conditions Based on Flexible Dynamics Equation of Robot Manipulator

“…These methods can be roughly divided into classic control and modern control. The modern control approaches are extended from classic ones to further address the nonlinearity and uncertainty of the robot [11,12].…”

Stochastic exponential stabilization of hybrid systems with time‐varying delays via adaptive control

“…Introduction: Over recent years there have been increasing interests in the field of hybrid dynamical systems. The asymptotic behaviour of such systems, the stability in particular, has been widely investigated, for example, see [1][2][3] and the references therein. This is mainly because the application of hybrid systems depends heavily on their stability.…”

“…They are usually closely related to physics, electric accessory and machinery systems. Stabilized hybrid systems have been widely applied in manufacturing and engineering [1,2]. For unstable systems, there is a need for being stabilized by feedback controller before wide applications.…”