Gait Generation and Stabilization for Nearly Passive Dynamic Walking Using Auto‐distributed Impulses

Abstract

We propose a state feedback control design via linearization for flexible walking on flat ground. First, we generate nearly passive limit cycles, being stable or not, using impulsive toe‐off actuations. The term ‘nearly passive’ means that the dynamics is completely passive almost everywhere except at the toe‐off moment. A feature of our gait generation method is that walking gaits are characterized only by amounts of supplied energy, and we observe that other variables, including input torques, are auto‐balanced via our method. After gait generation, we design a feedback controller considering robustness and input saturation. As a result, each limit cycle can be matched with its respective controller classified only by energy levels. We have verified that walking speeds monotonically increase by adding more energy, and the ankle joint plays a significant role in compass‐gait walking. Finally, instead of applying impulsive torques, we discuss a practical issue regarding realistic control inputs that ensure stable gait transitions as energy levels are elevated.

Impulsive torque control of biped gait with power packets

“…[19,32,33]), as well as a fully actuated one (e.g. [12,13,22]). For example, the robot discussed in [32] exhibits a stable gait only with the ankle joint powered.…”

“…4.1 Results with (n 1 , n 2 ) = (6, 4) and (2,6) This subsection shows an example of the successful gait generation with two specific setups of (n 1 , n 2 ). According to the literature on the purely impulsive gait generation [22,23], it is expected that a periodic gait is obtained under an appropriate selection of (n 1 , n 2 ). Here we introduce a discrete map F called a step-to-step map [3].…”

“…a virtual gravity based strategy by Asano et al [12], an energy shaping based strategy by Spong et al [13], Sinnet and Ames [14], de-León-Gómez et al [15], and Yeatman et al [16]. Apart from the energy based ones, there have recently been many proposals of active control strategies from various perspectives, including a bio-mimetic approach by Fu et al [17,18], an OGY-based feedback control by Gritli et al [19,20], and impulsive input strategies by Kuo [21], Moon et al [22], and Mochiyama and Hikihara [23].…”

“…Among the various strategies, we focus on an impulsive excitation [21][22][23], where an impulsive torque is applied only at the toe-off instance. The point is that the natural dynamics of the mechanical configuration is kept in almost all of the gait period.…”

Analysis of period-1 passive limit cycles for flexible walking of a biped with knees and point feet

“…We chose a maximum value of 12 • for the slope because we are interested in walking speeds less than 1.00 m/s. According to Moon et al, 25 a compass-gait walker, standing 1.0 m tall and weighing 20 kg, required control torques up to 87.2 Nm when walking at 0.64 m/s in a simulation. The robot, currently being built by our research group, has actuators with a maximum torque of only 20.0 Nm.…”