Optimal trajectory generation for a biped robot walking a staircase based on genetic algorithms

In this paper, we propose optimal trajectories of biped robots to move a staircase up and down using genetic algorithms and computed-torque controller to be dynamically stable. Firstly, in order to minimize the total energy efficiency, the real-coded genetic algorithm (RCGA) which of operators are composed of the reproduction, crossover and mutation is used. Constraints are divided into equalities and inequalities: equality constraints consist of position conditions at the start and end of stride period and repeatability conditions related to each joint angle and angular velocity. Next, inequality constraints include the collision avoidance conditions of swing leg at the face and edge of a stair, the knee joint conditions with respect to the singular avoidance, and the zero moment point condition with respect to the stability into the going direction. Finally, in order to approximate the walking gait, each joint angle trajectory is defined as a 4th order polynomial of which coefficients are chromosomes. In the computer simulation used 6 degree of freedom biped robot model that consists of seven links, we analyze the energy efficiency of proposed optimal trajectories about the following cases: walking on ground, ascending stairs, and descending stairs.