论文标题
平面对称的魔鬼杂耍
Planar Symmetric Juggling of a Devil-Stick
论文作者
论文摘要
杂乱无章的魔鬼可以描述为非骚扰的问题。假设魔鬼粘性仍然局限于垂直平面，则考虑了在两个对称配置之间杂耍棍子的问题。冲动力间歇性地应用于棍子，并将力的冲动及其应用点建模为对系统的控制输入。由于冲动力和重力引起的魔鬼刺激性的动力学用两个庞加罗截面之间的半回归图来描述。对称配置是这些部分的固定点。坐标转换用于将杂耍问题转换为固定点之一的稳定问题。在动态模型中包含坐标转换会导致非线性离散时间系统。其中一个输入的Dead-Beat设计简化了控制问题，并导致了线性时间不变的离散时间系统。标准控制技术用于表明可以从任意初始条件中实现对称杂耍。
Juggling a devil-stick can be described as a problem of non-prehensile manipulation. Assuming that the devil-stick remains confined to the vertical plane, the problem of juggling the stick between two symmetric configurations is considered. Impulsive forces are applied to the stick intermittently and the impulse of the force and its point of application are modeled as control inputs to the system. The dynamics of the devil-stick due to the impulsive forces and gravity is described by half-return maps between two Poincare sections; the symmetric configurations are fixed points of these sections. A coordinate transformation is used to convert the juggling problem to that of stabilization of one of the fixed points. Inclusion of the coordinate transformation in the dynamic model results in a nonlinear discrete-time system. A dead-beat design for one of the inputs simplifies the control problem and results in a linear time-invariant discrete-time system. Standard control techniques are used to show that symmetric juggling can be achieved from arbitrary initial conditions.
