Nonholonomic Motion Planning for a Free-Falling Cat Using Quasi-Newton Method

  • Xin-Sheng Ge
  • Wei-Jia Zhao
  • Yan-Zhu Liu


The motion planning problem of a free-falling cat is investigated. Nonholonomicity arises in a free-falling cat subject to nonintegrable velocity constraints or nonintegrable conservation laws. When the total angular momentum is zero, the rotational motion of the cat subjects to nonholonomic constraints. The equation of dynamics of a free-falling cat is obtained by using the model of two symmetric rigid bodies. The control of system can be converted to the motion planning problem for a driftless system. Based on the input parameterization, the continuous optimal control problem is transformed into the discrete one. The quasi-Newton method of motion planning for nonholonomic multibody system is proposed. The effectiveness of the numerical algorithm is demonstrated by numerical simulation.