This paper proposes an approximate-kinetic-model-based self-adaptive (AKS) control system to rapidly generate target walking speed by an underactuated compasslike bipedal walker. First, a model of the underactuated compass-like bipedal walker is built, and an open-loop system is introduced and analysed as the prototype of AKS system. Second, the control law of AKS is described in detail. The dynamic updating of trajectory is proposed and the calculation of control parameters by an approximate linearized model is analysed. Finally, simulations are conducted, and thus the capability of disturbance rejection and versatility is tested. As a conclusion, target walking speeds with 4∼6% steady-state error can be generated rapidly and steadily. Limit cycle walker can obviously improve the capability of handling disturbance and various tasks by AKS control system.

Toward stable gait generation on a steep slope, this paper discusses a method for generating a stable walking gait completing in one step for an underactuated rimless wheel. First, we introduce a model of a six-legged rimless wheel with a reaction wheel, and develop two controllers for the single-limb and double-limb support phases. For easily achieving precise control of the state variables, we apply a discrete-time output deadbeat control for each phase. We numerically analyze the fundamental properties of the generated gait, and show that the target period of the double-limb support phase must be chosen as a significantly long so that the rear and fore feet are grounded during control of the reaction wheel. The gait efficiency is also analyzed in terms of the walking speed and specific resistance through numerical simulations.

This paper proposes a novel method for generating an underactuated bipedal gait that completes in one step. First, we introduce an underactuated biped robot model that has a circular torso as a reaction wheel. Second, we consider an input-output linearization to formulate an output-following control law for achieving collisionless limit cycle walking. We then mathematically analyze the stability of the zero dynamics and investigate the fundamental gait properties through numerical simulations. Furthermore, we discuss an extension to generation of a few-steps walking motion aimed at safe and quick passage from a safety island to the next.

This paper investigates the analytical solution of target steady walking speed in 1-DOF limit cycle walking. We introduce an active combined rimless wheel (CRW) model to analyze the target steady walking state when the CRW walks on level ground. The walking speed is determined by the step period because the step length is constant. First we propose a two-period stepwise control system and the target walking period can be generated by solving the equations of boundary conditions. Second we extend this method to (n + 1)-period stepwise control system and generate a general formula for the boundary equation. At last we generate the target steady step period in the continuous control systems by calculating the approximate solution based on discretization of control input. We verify all the results through numerical simulations. If the generated walking gait is single-step-cycle, we can generate the target steady step period by our general formula in most of control systems.

This paper discusses the problem of how to achieve high speed, energy efficient, and fast convergent limit cycle walking. We newly introduce the convergence speed of the generated gait as a criterion for evaluation. Through mathematical and numerical investigations, we clarify the role and importance of deceleration effect in fast convergent gait generation. First, we generate ballistic gaits of the simplest 1-DOF active walker by applying a simple control torque, and show that the stance phase is destabilized in the case only of acceleration effect. Second, we propose another method for generating a fast convergent gait by adding deceleration effect and investigate the validity through numerical simulations. Furthermore, we extend our analysis to the cases taking joint viscosity and time delay into account and discuss the effects on the gait properties.