Biped Locomotion with Arm Swing, Based on Truncated Fourier Series and Bees Algorithm Optimizer

Bipedal walking is a difficult task due to its intrinsic instability and developing successful controller architectures for this mode of locomotion has proved substantially more difficult than for other types of walking (Beer et al. 1998). This type of walking has been tackled from different directions that all of them have been divided to two major approaches of static walking (Kato et al. 1974) and dynamic walking (Takanishi et al. 1982). Static walking assumes that the robot is statically stable. This means that, at any time, if all motion is stopped the robot will stay indefinitely in a stable position. It is necessary that the projection of the center of gravity of the robot on the ground must be contained within the foot support area. This approach was abandoned because only slow walking speeds could be achieved, and only on flat surfaces. Biped dynamic walking allows the center of gravity to be outside the support region for limited amounts of time. There is no absolute criterion that determines whether the dynamic walking is stable or not. Indeed a walker can be designed to recover from different kinds of instabilities(Hodgins and Raibert 1990). However, if the robot has active ankle joints and always keeps at least one foot flat on the ground then the Zero Momentum Point (ZMP) can be used as a stability criterion. There are two major approaches, model-based and model-free, in Dynamic walking researches. In model-based approaches, controller of robot is dependent on model of robot and from one robot to another everything in controller should be changed. Two well-known methods in this approach are “Zero Moment Point” (Zhang et al. 1999; Vukobratovic et al. 2001) (ZMP) and “Inverted Pendulum” (Kajita et al. 2001). ZMP specifies the point with respect to which dynamic reaction