Applied Mathematics and Mechanics

, Volume 28, Issue 5, pp 601–607

Optimal control of nonholonomic motion planning for a free-falling cat

  • Ge Xin-sheng  (戈新生)
  • Chen Li-qun  (陈立群)

DOI: 10.1007/s10483-007-0505-z

Cite this article as:
Ge, X. & Chen, L. Appl Math Mech (2007) 28: 601. doi:10.1007/s10483-007-0505-z


The nonholonomic motion planning of a free-falling cat is investigated. Nonholonomicity arises in a free-falling cat subject to nonintegrable angle velocity constraints or nonintegrable conservation laws. When the total angular momentum is zero, the motion equation of a free-falling cat is established based on the model of two symmetric rigid bodies and conservation of angular momentum. The control of system can be converted to the problem of nonholonomic motion planning for a free-falling cat. Based on Ritz approximation theory, the Gauss-Newton method for motion planning by a falling cat is proposed. The effectiveness of the numerical algorithm is demonstrated through simulation on model of a free-falling cat.

Key words

free-falling cat nonholonomic constraint motion planning optimal control 

Chinese Library Classification


2000 Mathematics Subject Classification

49M15 70E55 70F25 

Copyright information

© Editorial Committee of Appl. Math. Mech. 2007

Authors and Affiliations

  • Ge Xin-sheng  (戈新生)
    • 1
  • Chen Li-qun  (陈立群)
    • 2
  1. 1.Mechanical Engineering DepartmentBeijing Institute of MachineryBeijingP. R. China
  2. 2.Shanghai Institute of Applied Mathematics and MechanicsShanghai UniversityShanghaiP. R. China

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