Nontumbling Gait for Multilegged Robots and Its Directional Normalized Energy Stability Margin

This paper discusses the importance of a nontumbling gait, a gait that allows preventing complete tumbling of the robot. Nontumbling gait is made possible by the effect of the swing leg which may contact the ground even when the robot is affected by an external disturbance. Such an effect is present in both static walking and dynamic walking. Stability criterion required to maintain the nontumbling gait is then considered and proposed through generalized directional normalized energy stability margin. The validity of the introduced criterion is evaluated by a tumbling experiment with a simplified walking robot model. The concept is also applied to the gait control of the newly developed walking robot TITAN-XIII. 1. Introduction Over the past few years the development of various multilegged robots has gained significant traction. However, most of the advances have been made in the direction of mechanical design and high-level control systems. There has been little discussion about such important subject as stability of multi-legged locomotion, and most of the scholars continue to rely on normalized energy stability margin, or NESM [1]. In one of our previous works we proposed a directional normalized energy stability Margin [2], or , which allowed us to estimate robot’s stability at any given direction. In this paper, we will further investigate the properties and possible applications of DNESM . We will do so through the discussion about the effect that swinging leg may have on the stability of a multi-legged robot during its motion. 2. Nontumbling Gait When a multi-legged robot cannot maintain a planned stable walking or running due to some disturbance, for example, wind, its movement can be described by one of the two tumbling states: complete tumbling, and partial tumbling (it should be noted that under tumbling we understand a disruption of a planned walking sequence under the influence of external disturbance). Complete tumbling is a state when robot tumbles until its body hits the ground, whereas partial tumbling is a state when robot inclines, but does not overturn due to the effect of the swing legs which hit the ground and help to maintain standing posture. Figures 1 and 2 illustrate partial tumbling in detail. Figure 1: Crawling gait and subsequent rotation after the application of external disturbing energy. Figure 2: Trotting gait and possible subsequent rotations in case of application of external disturbing energy. Let us assume that the robot is performing a statically stable crawling gait and maintaining stability by forming a supporting