Robots

Proceedings of the 2003 IEEE International Conference on Robotics,Intelligent Systems and Signal Processing Changsha, China - October 2003

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Dynamic Model and Motion Control Analysis of Three-link Gymnastic Robot on Horizontal Bar
Xie Jian, Li Zushu
Institute of Intelligent Automation, Chongqing University, 400044 Institute of Artificial Intelligence System, Chongqing Institute ofThechnology, 400050 Xjane7441@sina.com, zushuli@vip.sina.com

Abstract
Based on the observation of gymnast’s swing-up movement, a simplified three-link horizontal bar robot is designed. With corresponding mathematic model developed, its dynamic characteristics are analyzed and simulation results are presented. From a general control perspective, an effective approach, that combines Humansimulated intelligent control method with Schema theory, and its feasibility are pointed out to obtain the planning motion control. torque cooperation from the coxa, this predetermined motion can be finished accurately. Certainly, on the point of bionics, human joints have no ability to drive a free 360degree rotation, which are under the limits of strength and angle. Therefore, all these limitingfactors should be represented in the gymnastic robot for obtaining more accurate physical model. In this paper, horizontal bar gymnastic robot, with three links, including two active joints and a passive joint, is presented, and its mathematic model is derived in details, further, two kinds of typical motion behaviors, free move and forced move, are simulated in the section II. Considering conditionsof torque strength and angular limits, in section III, we demonstrate a set of complete trajectory parameters analysis based on the gymnast swingup and handstand on the horizontal bar. Finally, a control method with integration of Human-Simulated Intelligent Control method and Schema Theory of Cognitive Science is proposed.

1 Introduction
Through training and repeated practice, a gymnast cancomplete some complicated and skillful motions on gymnastic appliances such as body’s curling, giant swing, swing-up and handstand, etc. Meanwhile, magnitude and direction of forces generated by body joints are harmonized and controlled with very high skills and sensory-motor intelligence. Therefore, study and understand their body movement and related joint’s action are very helpful to develop theintelligent control theory for autonomous robots motion control. As a major mechanism for studying such kind of motion that simulating human on the gymnastic apparatus, gymnastic robots, including rings [1] and horizontal bar gymnastic robots, have been proposed for many years, and some significant results can be found. Acrobot, a twodegree-of-freedom planar robot with a single actuator at itscoxa, but no actuator at the wrist is discussed in [2~5], in which fuzzy control, heuristic control, partial feedback linearization and control method based on energy are applied respectively to finish planning trajectories of swing-up and inverted equilibrium. According to the analysis of gymnast’s skills and sensorymotor intelligence, however, the gymnastic robot model with only two joints is notenough to demonstrate human movement on the horizontal bar because it is apparent that athlete’s shoulder joints play a very important role in controlling trunk’s action. Briefly, in the process of body swing-up and being inverted, the shoulder can bend so that certain angle is formed between arms and trunk, and with
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2 Three-link gymnastic robot dynamicsFig. 1 shows the two-dimensional coordinates map for the horizontal bar gymnastic robot, in which the model consists of three links and three joints. Shoulder and coxa are active limited joints with rotation range of –5~225 degrees for the angle between arm and trunk, and –5~180 degrees for the angle between leg and trunk; the pivot connecting hand and bar is passive joint, which has 0~360 degrees...