Strict stealth walking gait generation for 3-link underactuated biped robots

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ORIGINAL ARTICLE

Strict stealth walking gait generation for 3‑link underactuated biped robots Hiroki Shibata1 · Fumihiko Asano1 Received: 20 May 2020 / Accepted: 14 September 2020 © International Society of Artificial Life and Robotics (ISAROB) 2020

Abstract In this paper, we propose a method for generating a stable stealth gait on frictionless road surface without including the double-limb support phase for biped robots. First, we introduce a model of a biped robot with an upper body, and derive the conditions to maintain the horizontal ground reaction force at zero. Second, we derive an approximate analytical solution for the target initial state using the linearized equation of motion. Third, to generate a stealth walking gait of the nonlinear model, we propose a numerical method to identify the target initial state based on the result of the linearized model, and evaluate the mathematical results obtained through numerical simulations. Furthermore, we discuss the effect of semicircular feet on the improvement of energy efficiency. Keywords  Stealth walking · Gait generation · Bipedal robots · Frictionless road surface

1 Introduction Adaptation to irregular terrain is one of the important issues in walking robots. In particular, the foot should be landed carefully on the road surface where the scaffolding is unstable, such as rubble. For this problem, Asano proposed the method of stealth walking [1], which is a form of legged locomotion that avoids kinetic-energy loss at impact of the legs with the ground [2, 3]. With the aim of adapting to low friction surfaces [4, 5], Asano further extended this to the method to strict stealth walking (SSW) [6]. For achieving SSW, the horizontal ground reaction force should be maintained at zero, and the target condition to be met then becomes that the third-order derivative of the robot’s total angular momentum around the stance foot with respect to time is maintained at zero during motion. This control This work was presented in part at the 3rd International Symposium on Swarm Behavior and Bio-Inspired Robotics (Okinawa, Japan, November 20–22, 2019). * Fumihiko Asano [email protected] Hiroki Shibata [email protected] 1



Graduate School of Advanced Science and Technology, Japan Advanced Institute of Science and Technology, 1‑1 Asahidai, Nomi, Ishikawa 923‑1292, Japan

is referred to as angular momentum constraint control (AMCC). In addition, for achieving high-speed and energyefficient walking, reducing the long period of double-limb support phases is indispensable [1], and an appropriate initial state must be identified with high accuracy. Finding the initial state accurately is therefore one of the basic problems in generation of a SSW gait, and the solution to this problem has already been investigated with rimless wheel models [6, 7]. Extension to biped robots, however, has been left unsolved. In our previous works, on the assumption that the ground contact point of the supporting leg does not slip, an approach to generate a stealth gait in which the motions of