2022/03/23 by William R. Clark, Clark, William, Dora Kassabova +1
Engineering · Physics and Astronomy · #Dynamical Systems (math.DS) #Experimental and Theoretical Physics Studies #FOS: Mathematics #Optimization and Control (math.OC) #Robotic Locomotion and Control #Sports Dynamics and Biomechanics
paper · pdf · doi:10.48550/arxiv.2203.12688
openalex publication_date 2022/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.