An Incremental Fuzzy Algorithm for the Balance of Humanoid Robots

Humanoid robots base their appearance on the human body (Goddard et al., 1992; Kanehira et al., 2002; Konno et al., 2000). Minimalist constructions have at least a torso with a head, arms or legs, while more elaborated ones include devices that assemble, for example, human face parts, such as eyes, mouth, and nose, or even include materials similar to skin. Humanoid robots are systems with a very high complexity, because they aim to look like humans and to behave as they do. Mechanical control, sensing, and adaptive behaviour are the constituting logical parts of the robot that allow it to “behave” like a human being. Normally, researchers study these components by modelling only a mechanical part of the humanoid robot. For example, artificial intelligence and cognitive science researches consider the robot from the waist up, because its visual sensing is located in its head, and its behavior with gestures normally uses its face or arms. Some engineers are mostly interested in the autonomy of the robot and consider it from the waist down. They develop mathematical models that control the balance of the robot and the movement of its legs (Miller, 1994; Yamaguchi et al., 1999; Taga et al., 1991), allowing the robot to walk, one of the fundamental behaviours that characterizes human beings. Examples of such mathematical models are static and dynamic walking. The static walking model controls the robot to maintain its center of gravity (COG) inside a stable support region, while the dynamic walking model maintains the zero moment point (ZMP) inside the support region. Kajita et al. (1992) designed and developed an almost ideal 2-D model of a biped robot. He supposed, for simplicity, that the robot's COG moves horizontally and he developed a control law for initiation, continuation and termination of the walking process. Zhen and Shen (1990) proposed a scheme to enable robot climbing on inclined surfaces. Force sensors placed in the robot's feet detect transitions of the terrain type, and motor movements correspondingly compensate the inclination of robot. The models mentioned above can be, however, computationally very expensive, and prohibitive for its implementation in microcontrollers. Control algorithms for a stable walking must be sufficiently robust and smooth, to accomplish a balance correction without putting in risk the mechanical stability of the robot. This could be resolved by using a controller that modifies its parameters according to a