Research on Time-Optimal Falling Trajectory of a Free-Falling Cat Robot
LIANG Xingcan1,2, XU Linsen2, LI Lu2, ZHOU Bo1,2, ZHAO Jiaxuan1,2
1. University of Science and Technology of China, Hefei 230026, China;
2. Institute of Advanced Manufacturing Technology, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Changzhou 213164, China
Abstract:A robot may be at the risk of falling from a high place when it works in an unknown complex environment, so the attitude control ability of the robot in the air should be considered to reduce the damage caused by wrong landing attitudes. When a cat drops from a high space, it can always right itself and land safely. Inspired by this biological phenomenon, the optimal falling trajectory of a free-falling cat robot is studied in a time-optimal manner for the first time, through investigating the first stage of safe landing of a cat, namely the attitude adjustment stage. Firstly, a mathematical model of the robot is formulated based on an axisymmetric dual rigid-body model. Owing to the non-integrable angular velocity, the attitude control problem of the falling cat robot is transformed into a nonholonomic motion planning problem. Considering that the time consumption of attitude adjustment is an important factor to determine the adjustment result, a time-optimal function is built with the virtual torque input instead of the real angular velocity input, and a method to solve this function is set up also. Then, a particle swarm optimization algorithm is proposed to obtain the solution of objective function with the least time consumption of attitude adjustment. Finally, using the optimal solution data, the virtual prototype experiment is carried out in the virtual physical environment, and the righting movement in the air for a falling cat robot is realized. The results show that the time consumption of attitude adjustment is effectively reduced for the free-falling robot by the proposed method.
[1] 魏鲜明,徐林森,曹凯,等.足式水上行走机器人智能控制方法设计 [J].机器人,2014,36(1):49-56.Wei X M, Xu L S, Cao K, et al. Intelligent control method design of foot robot walking on water[J]. Robot, 2014, 36(1): 49-56.
[2] 徐林森,魏鲜明,曹凯,等.仿生双足水上行走机器人优化设计及控制方法 [J].机械工程学报,2014,50(15):12-18.Xu L S, Wei X M, Cao K, et al. Optimization design and control method of biped robot running on water[J]. Journal of Mechanical Engineering, 2014, 50(15): 12-18.
[3] Xu L S, Mei T, Wei X M, et al. A bio-inspired biped water running robot incorporating the Watt-I planar linkage mechanism[J]. Journal of Bionic Engineering, 2013, 10(4): 415-422.
[4] Xu F Y, Wang X S, Jiang G P. Experimental study on the dynamic performance of a cable-robot detecting system[J]. Transactions of the Institute of Measurement and Control, 2016, 38(3): 338-347.
[5] Xu F Y, Shen J J, Hu J L, et al. A rough concrete wall climbing robot based on grasping claws: Mechanical design, analysis and laboratory experiments[J]. International Journal of Advanced Robotic Systems, 2016, 13(5): 1-10.
[6] Ge X S, Guo Z X. Nonholonomic motion planning for a free-falling cat using spline approximation[J]. Science China: Physics, Mechanics and Astronomy, 2012, 55(11): 2100-2105.
[7] Kane T R, Scher M P. A dynamical explanation of the falling cat phenomenon[J]. International Journal of Solids and Structures, 1969, 5(7): 663-670.
[8] Weng Z, Nishimura H. Final-state control of a two-link cat robot[J]. Advanced Robotics, 2002, 16(4): 325-343.
[9] Ge X S, Zhao W J, Liu Y Z. Nonholonomic motion planning for a free-falling cat using quasi-Newton method[J]. Technische Mechanik, 2011, 31(1): 42-49.
[10] Takahashi K. Remarks on motion control of nonholonomic system (falling cat) by using a quantum neural controller[C]//12th International Conference on Intelligent Systems Design and Applications. Piscataway, USA: IEEE, 2012: 961-966.
[11] Nakano D, Maeda S, Ishii S. Control of a free-falling cat by policy-based reinforcement learning[C]//Artificial Neural Networks and Machine Learning. Berlin, Germany: Springer-Verlag, 2012: 116-123.
[12] Liang X C, Xu L S, Li L. Research on trajectory planning of a robot inspired by free-falling cat based on modified quasi-Newton algorithm[C]//IEEE International Conference on Mechatronics and Automation. Piscataway, USA: IEEE, 2016: 552-557.
[13] Liang X C, Xu L S, Li L, et al. Research on trajectory planning of a robot inspired by free-falling cat based on numerical approximation[C]//IEEE International Conference on Robotics and Biomimetics. Piscataway, USA: IEEE, 2016: 631-636.
[14] Montgomery R. Isoholonomic problems and some applications\lk [J]. Communications in Mathematical Physics, 1990, 128(3): 565-592.
[15] Montgomery R. Gauge theory of the falling cat[J]. Fields Institute Communications, 1993(1): 193-218.
[16] Fernandes C, Gurvits L, Li Z, et al. Near-optimal nonholonomic motion planning for a system of coupled rigid bodies[J]. IEEE Transactions on Automatic Control, 1994, 39(3): 450-463.
[17] Neimark I, Fufaev N. Dynamics of nonholonomic systems[M]. Providence, USA: American Mathematical Society, 1972: 5-15.
[18] Goldstein H. Classical mechanics[M]. 2nd ed. Mineola, USA: Dover Publications, 1980: 78-83.
[19] Wen J T. Control of nonholonomic systems[M]//Levine W S. The Control Handbook. Boca Raton, USA: CRC Press, 1996: 1359-1368.
[20] Poli R, Kennedy J, Blackwell T. Particle swarm optimization[J]. Swarm Intelligence, 2007, 1(1): 33-57.
[21] Clerc M. Particle swarm optimization[M]. New York, USA: John Wiley & Sons, 2010: 3-58.
[22] 龚纯,王正林.精通 MATLAB 最优化计算 [M].2 版.北京:电子工业出版社,2012:270-271.Gong C, Wang Z L. Proficient in Matlab optimization calculation[M]. 2nd ed. Beijing: Publishing House of Electronics Industry, 2012: 270-271.