The problem of nonprehensile manipulation of a stick in three-dimensional space using intermittent impulsive forces is considered. The objective is to juggle the stick between a sequence of configurations that are rotationally symmetric about the vertical axis. The dynamics of the stick is described by five generalized coordinates and three control inputs. Between two consecutive rotationally symmetric configurations, the dynamics is conveniently represented by a Poincar\'e map in the reference frame of the juggler. Stabilization of the orbit associated with a desired juggling motion is accomplished by stabilizing a fixed point on the Poincar\'e map. The Impulse Controlled Poincar\'e Map approach is used to stabilize the orbit, and numerical simulations are used demonstrate convergence to the desired juggling motion from an arbitrary initial configuration. In the limiting case, where consecutive rotationally symmetric configurations are chosen arbitrarily close, it is shown that the dynamics reduces to that of steady precession of the stick on a hoop.
翻译:在三维空间使用间歇性冲动力对一根棍子进行非致命操纵的问题得到了考虑。 目标是在垂直轴上旋转对称的组合序列之间拼凑杆子。 棒子的动态用五个通用坐标和三个控制输入来描述。 在两个连续旋转的对称配置中, 动态可以方便地用一个 Poincar\'e 地图在杂乱动作的参考框中代表。 稳定与所希望的杂乱动作相关的轨道的方法是通过稳定波卡勒地图上的固定点来实现的。 使用 Inmpulse Control Poincar\'e Map 方法来稳定轨道, 并使用数字模拟来显示与任意初始配置所希望的杂动趋同。 在限制的案例中, 连续旋转对称配置被任意选为近处, 这表明, 动态会降低到hoop 上粘液的稳定前期。