The calculation of the optimal trajectory of the stepped top-down robot was made using a genetic algorithm and a computational torque controller. First, the total energy efficiency was minimized using the Red-Cold Generic Algorithm (RCGA) consisting of reproductive, cross, and mutation. The reproducibility condition related to the position assembly of the start and end of the stride and the joints, angles, and angular velocities are linear constraints. Next, the unequal constraint accompanies the condition for preventing the collision of the swing leg at the corner with the outer surface of the stairs, the condition of the knee joint for preventing kinematic peculiarity, and the condition of no moment in safety in the traveling direction. Finally, the angular trajectory of each joint is defined by fourth-order polynomial whose coefficient is to approximate chromosomes. This is to approximate walking. In this study, the energy efficiency of the optimal trajectory was analyzed by computer simulation through a biped robot with seven degrees of freedom composed of seven links.

Walking method based zero moment position algorithms that can guarantee the stability of the biped walking robot while walking, but it moves the legs for the stability of the walking in a way that is not related to energy conservation. Walking method using ZMP can cause low battery efficiency and load on leg joints. The walking method using the passive walking, which is a natural and efficient method of walking, can reduce the load on the joints of the robot by using the method without using the inertia that occurs when walking and reduced control elements and efficient use of battery. In this paper, a biped robot with an actuator based on the principle of passive dynamic walker mechanism is applied to a passive walking algorithm. In order to solve the problem of stabilization of the posture during walking, the posture was stabilized by using the swing motion of the arm. and the walking movement of the robot was observed using the AHRS sensor applied to the robot .It was confirmed that the posture can be stabilized based on measured values using AHRS.

Generating motion of center of mass for biped robots is a challenging issue since biped robots can easily lose balance due to limited contact area between foot and ground. In this paper, we propose force control method to generate high-speed motion of the center of mass for horizontal direction without losing balancing condition. Contact consistent multi-body dynamics of the robot is used to calculate force for horizontal direction of the center of mass considering balance. The calculated force is applied for acceleration or deceleration of the center of mass to generate high speed motion. The linear inverted pendulum model is used to estimate motion of the center of mass and the estimated motion is used to select either maximum or minimum force to stop at goal position. The proposed method is verified by experiments using 12-DOF torque controlled human sized legged robot.

Humanoid robot is the most intimate robot platform suitable for human interaction and services. Biped walking is its basic locomotion method, which is performed with combination of joint actuator’s rotations in the lower extremity. The present work employs humanoid robot simulator and numerical optimization method to generate optimal joint trajectories for biped walking. The simulator is developed with Matlab based on the robot structure constructed with the Denavit-Hartenberg (DH) convention. Particle swarm optimization method minimizes the cost function for biped walking associated with performance index such as altitude trajectory of clearance foot and stability index concerning zero moment point (ZMP) trajectory. In this paper, instead of checking whether ZMP’s position is inside the stable region or not, reference ZMP trajectory is approximately configured with feature points by which piece-wise linear trajectory can be drawn, and difference of reference ZMP and actual one at each sampling time is added to the cost function. The optimized joint trajectories realize three phases of stable gait including initial, periodic, and final steps. For validation of the proposed approach, a small-sized humanoid robot named DARwIn-OP is commanded to walk with the optimized joint trajectories, and the walking result is successful.

Based on the stability criteria of ZMP (Zero Moment Point), this paper proposes an adjusting algorithm that modifies walking trajectory of a bipedal robot for stable walking by analyzing ZMP trajectory of it. In order to maintain walking balance of the bipedal robot, ZMP should be located within a supporting polygon that is determined by the foot supporting area with stability margin. Initially tilting imposed to the trajectory of the upper body is proposed to transfer ZMP of the given walking trajectory into the stable region for the minimum stability. A neural network method is also proposed for the stable walking trajectory of the biped robot. It uses backpropagation learning with angles and angular velocities of all joints with tilting to get the improved walking trajectory. By applying the optimized walking trajectory that is obtained with the neural network model, the ZMP trajectory of the bipedal robot is certainly located within a stable area of the supporting polygon. Experimental results show that the optimally learned trajectory with neural network gives more stability even though the tilting of the pelvic joint has a great role for walking stability.