Multistage fall trajectory optimization for a generalized biped robot

Abstract

The falling process of a generalized biped robot falling backward, sidewards and to the front is investigated as a free final-time optimal control problem. The aim is to minimize a set of performance parameters to reduce the fall damage to the robot. The back fall and side fall are modeled using a single inverted pendulum. For the fall to the front a three-stage approach was chosen. For the first stage (standing upright until the knees are touching the floor) a quadruple pendulum was used, shifting in second stage (knees-to-floor until hands-to-floor) to a triple pendulum coupled to a single pendulum and in the third stage to a single pendulum with an external force exerted by the arms. The tool is written in MATLAB, where, after putting the robot parameters in and setting the optimization goals, one can find optimal joint torques, joint angles and/or joint velocities for the involved joints to implement them as an open-loop control to a real robot. This implementation is then applied in two exemplary ways: One to generate trajectories for a robot without any torque restrictions to the joint driving motors to find the general principle. Secondly to analyze a real robot including torque limitations. The torque limitations were implemented using a simplified DC motor model.