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.

This work deals with development of effective redundancy resolution algorithms for the motion control of manipulator. Differently from the typical kinematically redundant robots that are attached to the fixed ground, the ZMP condition should be taken into account in the manipulator motion in order to guarantee the system stability. In this paper, a new motion planning algorithm for redundant manipulator not fixed to the ground is introduced. A sequential redundancy resolution algorithm is proposed, which ensures the ZMP (Zero Moment Point) stability, the planned operational motion, and additional sub‐criteria such as joint limit index. A geometric constraint equation derived by reshaping the existing ZMP equation enables one to employ the sequential redundancy algorithm. The feasibility of the proposed algorithm is verified by simulating a redundant manipulator model.

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.