Numerical method for attitude motion planning of one-legged hopping robot

Numerical method for attitude motion planning of one-legged hopping robot

Lili Yang

Zibo Vocational Institute Zibo 255314, China

Corresponding Author Email:
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31 December 2017
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The attitude motion planning for one-legged hopping robot with nonholonomic constraint is studied. Firstly, the dynamic model of the robot is established by using the nonholonomic constraint characteristic. Secondly, the energy consumption of the robot is used as the optimization objective function. Lastly, a numerical algorithm is designed by combining curve fitting method and particle swarm optimization algorithm, which is used to realize the optimal trail of robot’s attitude motion by optimizing the objective function. The designed algorithm makes use of curve fitting to approach the motion trail of the robot’s drivable leg, and the coefficients of the fitting polynomial are taken as the optimization parameters which can be obtained by particle swarm optimization algorithm. The main advantage of this method lies in that the initial value and the final value of the optimal control input are all zero, which solves the problem that the initial value and the final value of the control input are not zero in the traditional method, making it convenient to control the motion of the drivable leg by the motor in engineering application. At the end of the study, the effectiveness of this method is proved by the results of the numerical simulation.


one-legged hopping robot, nonholonomic constraint, attitude motion planning, optimization

1. Introduction
2. Robot model
3. Optimal control of attitude motion based on curve fitting method
4. Particle swarm optimization for attitude motion planning of system
5. Example simulation
6. Conclusions

This work was supported by Zibo science and technology development plan (2016kj010057).


Bingül Z., Karahan O. (2011). Dynamic identification of staubli rx-60 robot using pso and ls methods. Expert Systems with Applications, Vol. 38, No. 4, pp. 4136-4149.

Chen L. B., Zheng Y. Q. (2012). Study on curve fitting based on least square method. Journal of Wuxi Institute of Technology, Vol. 11, No. 5, pp. 52-55.

Hyon S. H., Emura T., Mita T. (2003). Dynamics-based control of a one-legged hopping robot. Proceedings of the Institution of Mechanical Engineers Part I Journal of Systems & Control Engineering, Vol. 217, No. 2, pp. 83-98.

Janiak M., Tchoń K. (2011). Constrained motion planning of nonholonomic systems. Systems & Control Letters, Vol. 60, No. 8, pp. 625-631.

Liu M., Zhong X., Wang X., Chen F., Zha F., Guo W. (2016). Motion control for a single-legged robot. International Conference on Advanced Robotics and Mechatronics, pp. 336-341.

Naik K. G., Mehrandezh M., Barden J.M. (2006). Control of a One-legged hopping robot using a hybrid neuro-PD controller. Canadian Conference on Electrical and Computer Engineering, pp. 1530-1533.

Poli R., Kennedy J., Blackwell T. (2007). Particle swarm optimization. Swarm Intelligence, Vol. 1, No. 1, pp. 33-57.

Raibert M. H., Tello E. R. (2007). Legged robots that balance. IEEE Expert, Vol. 1, No. 4, pp. 89-89.

Shabestari S. S., Emami M. R. (2016). Gait planning for a hopping robot. Robotica, Vol. 34, No. 8, pp. 1822-1840.

Su P., He G. P., Xu M. (2012). Research on motion simulation of hopping robot based on minimum energy-loss principle. Machinery Design & Manufacture, No. 4, pp. 171-173.

Venter G., Sobieszczanski-Sobieski J. (2003). Particle swarm optimization. AIAA Journal, Vol. 41, No. 8, pp. 1583-1589.

Wu J. W., Shi S., Liu H., Cai H. (2011). Spacecraft attitude disturbance optimization of space robot in target capturing process. Robot, Vol. 33, No. 1, pp. 16-21.

Yang L. L. (2013). The numerical method to nonholonomic motion planning of a hopping robot. Manufacturing Automation, Vol. 35, No. 13, pp. 86-89.