摘要
研究猫在自由下落时姿态运动规划问题.自由落体的猫在空中转体运动由于角速度不可积,姿态运动方程呈现为非完整形式.当系统角动量为0时,导出由两个对称刚体组成的自由下落猫的非完整姿态运动方程.利用该非完整方程系统的控制问题可转化为无漂移系统的非完整运动规划问题.基于Ritz近似理论,给出自由落体猫姿态运动规划的Gauss-Newton算法.最后对自由落体猫作了数值仿真实验,仿真结果验证了该算法的有效性.
The nonholonomic motion planning of a free-falling cat is investigated. Nonholonomicity arises in a free-falling cat subject to nonintegrable angle velocity constramts or nonintegrable conseration 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 moron planning for a falling cat, Based on Ritz approximation theory, the Gauss Newton method for moron planning by a falling cat is proposed. The effectiveness of the numerical algorithm is demonstrated through simulation on model of a free- falling cat.
出处
《应用数学和力学》
EI
CSCD
北大核心
2007年第5期539-545,共7页
Applied Mathematics and Mechanics
基金
国家自然科学基金资助项目(10372014)
北京市自然科学基金资助项目(1072008)
关键词
猫自由落体
非完整约束
运动规划
最优控制
free-falling cat
nonholonomic constraint
motion planning
optimal control
