The concept of dasiaLimit Cycle Walkingpsila in bipedal robots removes the constraint of dynamic balance at every instance during gait. We hypothesize that this is crucial for the development of increasingly versatile and energy-effective humanoid robots. It allows the application of a wide range of gaits and it allows a robot to utilize its natural dynamics in order to reduce energy use. This paper presents the design and experimental results of our latest walking robot dasiaFlamepsila and the design of our next robot in line dasiaTUlippsila. The focus is on the mechanical implementation of series elastic actuation, which is ideal for Limit Cycle Walkers since it offers high controllability without having the actuator dominating the system dynamics. Walking experiments show the potential of our robots, showing good walking performance, though using simple control.

Limit cycle walkers are bipeds that exhibit a stable cyclic gait without requiring local controllability at all times during gait. A well-known example of limit cycle walking is McGeer's ldquopassive dynamic walking,rdquo but the concept expands to actuated bipeds as involved in this study. One of the stabilizing effects in limit cycle walkers is the dissipation of energy that occurs when the swing foot hits the ground. We hypothesize that this effect can be enhanced with a negative relation between the step length and step time. This relation is implemented through an open-loop strategy called swing-leg retraction; a predefined time trajectory for the swing leg makes the swing leg move backwards just prior to foot impact. In this paper, we study the effect of swing-leg retraction through three bipeds; a simple point mass simulation model, a realistic simulation model, and a physical prototype. Their stability is analyzed using Floquet multipliers, followed by an evaluation of how well disturbances are handled using the Gait Sensitivity Norm. We find that mild swing-leg retraction is optimal for the disturbance rejection of a limit cycle walker, as it results in a system response that is close to critically damped, rejecting the disturbance in the fewest steps. Slower retraction results in an overdamped response, characterized by a positive dominant Floquet multiplier. Likewise, faster retraction results in an underdamped response, characterized by a negative Floquet multiplier.

The construction of more capable bipedal robots highly depends on the ability to measure their performance. This performance is often measured in terms of speed or energy efficiency, but these properties are secondary to the robot's ability to prevent falling given the inevitable presence of disturbances, i.e., its disturbance rejection. Existing disturbance rejection measures (zero moment point, basin of attraction, Floquet multipliers) are unsatisfactory due to conservative assumptions, long computation times, or bad correlation to actual disturbance rejection. This paper introduces a new measure called the Gait Sensitivity Norm that combines a short calculation time with good correlation to actual disturbance rejection. It is especially suitable for implementation on limit cycle walkers, a class of bipeds that currently excels in terms of energy efficiency, but still has limited disturbance rejection capabilities. The paper contains an explanation of the Gait Sensitivity Norm and a validation of its value on a simple walking model as well as on a real bipedal robot. The disturbance rejection of the simple model is studied for variations of floor slope, foot radius, and hip spring stiffness. We show that the calculation speed is as fast as the standard Floquet multiplier analysis, while the actual disturbance rejection is correctly predicted with 93% correlation on average.

Passive dynamic walking is a promising idea for the development of simple and efficient two-legged walking robots. One of the difficulties with this concept is the addition of a stable upper body; on the one hand, a passive swing leg motion must be possible, whereas on the other hand, the upper body (an inverted pendulum) must be stabilized via the stance leg. This paper presents a solution to the problem in the form of a bisecting hip mechanism. The mechanism is studied with a simulation model and a prototype based on the concept of passive dynamic walking. The successful walking results of the prototype show that the bisecting hip mechanism forms a powerful ingredient for stable, simple, and efficient bipeds

Biped robots based on the concept of (passive) dynamic walking are far simpler than the traditional fullyI controlled walking robots, while achieving a more natural gait and consuming less energy. However, lightly actuated dynamic walking robots, which rely on the natural limit cycle of their mechanical structure, are very sensitive to ground disturbances. Already a very small step down can cause the robot to lose stability. In this paper, we investigate the use of reinforcement learning to make a dynamic walking robot more robust against ground disturbances. The learning controller is applied to a simulated two-link biped which is an abstraction of a mechanical prototype developed at the Delft Biorobotics Laboratory. The learning controller has been designed such that it can be applied as a straightforward extension of the proportionalI-derivative (PD) controller currently used to drive the robot's pneumatic actuators. The learning controller is therefore suitable for the future implementation in the robot hardware. Simulation results demonstrate that the biped quickly learns to overcome step-down disturbances on the floor up to 10% of the leg length, without compromising the natural walking style provided by the PD controller, which was optimized for walking on an even surface.