Orientation Control of the Bouncing Ball

TL;DR

This paper investigates controlling the orientation of a bouncing ball by manipulating impact locations, emphasizing discrete control through external variables to influence internal variables during impacts.

Contribution

It introduces a novel approach to hybrid system control by focusing on guard location manipulation to control internal variables during impacts.

Findings

Demonstrates control of ball orientation via impact position adjustments

Highlights the role of external variables in hybrid system control

Provides a theoretical framework for discrete impact control

Abstract

Control of a hybrid dynamical system can manifest in one of two main ways: either through the continuous or the discrete dynamics. An example of controls influencing the continuous dynamics is legged locomotion, where the joints are actuated but the location and nature of the impacts are uncontrolled. In contrast, an example of discrete control would be in tennis; the player can only influence the trajectory of the ball through striking it. This work examines the latter case with two key emphases. The first is that controls manifest through changing the location of the guard (as opposed to changing only the reset). The second is that the location of the guard is described by "external variables" while the goal is to control "internal variables." As a simple test of this theory, orientation control of a bouncing ball is explored; the ball is only controlled during impacts which are exclusively position-dependent.