Time Optimal Control for Quadruped Walking Robots

Abstract

Time optimal control method for quadruped walking robots are developed and installed into a practical robot system. Each leg is modeled as a two link manipulator whose time optimal control theory has already been established by Bobrow. However, in legged robot systems, each leg supports their body weight, and the reaction forces from its ground must be inside of their friction corn. Moreover, the ZMP (zero moment point) of the robot is constrained for stable walk. Therefore, time optimal control inputs are designed considering these constraints for a trot walk. First, motion control commands for supporting legs are derived with a tentative initial condition in order to achieve a trot walk, then those for swinging legs are calculated by using the initial and terminal conditions obtained from the results of supporting legs. If the desired torque commands for the swinging legs exceed the maximum torques of motors of swinging legs, motion commands for supporting legs are re-designed by modifying the initial condition. By iterating the above operations, time optimal control commands are obtained. SONY ERS-7 is used as a quadruped walking robot and a fundamental experiment is done. From the experimental results, the effectiveness of the developed control algorithm is verified.