标题： 用于使用纯脉冲输入的魔鬼棒螺旋桨运动的离散VHCs 显示英文标题

标题： Discrete VHCs for Propeller Motion of a Devil-Stick using purely Impulsive Inputs

摘要： 在垂直平面内，使用作用于杆件法线方向的脉冲力实现魔鬼棒螺旋运动的控制问题被考虑。 这个问题是欠驱动机器人抛接的一个例子，并且在文献中之前未被考虑过。 受虚拟完整约束的启发，首次引入了离散虚拟完整约束（DVHC）来解决这个轨道稳定问题。 在施加脉冲输入的离散时刻，魔鬼棒的质心位置是根据其方位角来指定的。 这产生了离散零动态（DZD），它提供了稳定螺旋运动的条件。 在极限情况下，当连续施加脉冲输入之间的旋转角度被选为任意小时，问题简化为在连续激励下的螺旋运动问题。 提出了一种强制执行DVHC的控制器，以及基于脉冲控制庞加莱映射方法的轨道稳定控制器。 通过仿真验证了该方法在轨迹设计和稳定方面的有效性。 显示英文摘要

摘要： The control problem of realizing propeller motion of a devil-stick in the vertical plane using impulsive forces applied normal to the stick is considered. This problem is an example of underactuated robotic juggling and has not been considered in the literature before. Inspired by virtual holonomic constraints, the concept of discrete virtual holonomic constraints (DVHC) is introduced for the first time to solve this orbital stabilization problem. At the discrete instants when impulsive inputs are applied, the location of the center-of-mass of the devil-stick is specified in terms of its orientation angle. This yields the discrete zero dynamics (DZD), which provides conditions for stable propeller motion. In the limiting case, when the rotation angle between successive applications of impulsive inputs is chosen to be arbitrarily small, the problem reduces to that of propeller motion under continuous forcing. A controller that enforces the DVHC, and an orbit stabilizing controller based on the impulse controlled Poincar\'e map approach are presented. The efficacy of the approach to trajectory design and stabilization is validated through simulations.