Martijn Wisse

A Three-Dimensional Passive-Dynamic Walking Robot with Two Legs and Knees

The authors have built the first three-dimensional, kneed, two-legged, passive-dynamic walking machine. Since the work of Tad McGeer in the late 1980s, the concept of passive dynamics has added insight into animal locomotion and the design of anthropomorphic robots. Various analyses and machines that demonstrate efficient human-like walking have been developed using this strategy. Human-like passive machines, however, have only operated in two dimensions (i.e., within the fore-aft or sagittal plane). Three-dimensional passive walking devices, mostly toys, have not had human-like motions but instead a stiff legged waddle. In the present three-dimensional device, the authors preserve features of McGeer’s two-dimensional models, including mechanical simplicity, human-like knee flexure, and passive gravitational power from descending a shallow slope. They then add specially curved feet, a compliant heel, and mechanically constrained arms to achieve a harmonious and stable gait. The device stands 85 cm tall. It weighs 4.8 kg, walks at about 0.51 m/s down a 3.1-degree slope, and consumes 1.3 W. This robot further implicates passive dynamics in human walking and may help point the way toward simple and efficient robots with human-like motions.

Design and Construction of MIKE; a 2-D Autonomous Biped Based on Passive Dynamic Walking

For research into bipedal walking machines, autonomous operation is an important issue. The key engineering problem is to keep the weight of the actuation system small enough. For our 2D prototype MIKE, we solve this problem by applying pneumatic McKibben actuators on a passive dynamic biped design. In this paper we present the design and construction of MIKE and elaborate on the most crucial subsystem, the pneumatic system. The result is a fully autonomous biped that can walk on a level floor with the same energy efficiency as a human being. We encourage the reader to view the movies of the walking results at http://dbl.tudelft.nl/.

A Disturbance Rejection Measure for Limit Cycle Walkers: The Gait Sensitivity Norm

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 robots 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 model with upper body

This paper presents the simplest walking model with an upper body. The model is a passive dynamic walker, i.e. it walks down a slope without motor input or control. The upper body is confined to the midway angle of the two legs. With this kinematic constraint, the model has only two degrees of freedom. The model achieves surprisingly successful walking results: it can handle disturbances of 8% of the initial conditions and it has a specific resistance of only 0.0725(−).

Adding an Upper Body to Passive Dynamic Walking Robots by Means of a Bisecting Hip Mechanism

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

Three additions to passive dynamic walking; actuation, an upper body, and 3D stability

One of the main challenges in the design of human-like walking robots (useful for service or entertainment applications as well as the study of human locomotion) is to obtain dynamic locomotion, as opposed to the static form of locomotion demonstrated by most of the current prototypes. A promising concept is the idea of passive dynamic walking; even completely unactuated and uncontrolled mechanisms can perform a stable gait when walking down a shallow slope. This concept enables the construction of dynamically walking prototypes that are simpler yet more natural in their motions than the static bipeds. This paper presents three additions to the concept of passive dynamic walking. First, hip actuation is added to increase the fore-aft stability and to provide power to the system, removing the need for a downhill floor. Second, a reciprocating hip mechanism is introduced to allow the addition of a passive upper body without compromising the simplicity, efficiency and naturalness of the concept of passive dynamic walking. Third, skate board-like ankle joints are implemented to provide 3D stability. These ankles couple the unstable sideways lean motion to yaw (steering), a kinematic coupling which provides sideways stability when walking with sufficient forward velocity. The three additions are investigated both with elementary simulation models and with prototype experiments. All three prototypes demonstrate an uncannily natural and stable gait while requiring only two foot switches and three on/off actuators.

System overview of bipedal robots Flame and TUlip: Tailor-made for Limit Cycle Walking

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.

Ankle Actuation for Limit Cycle Walkers

Limit Cycle Walkers are bipeds that exhibit a stable cyclic gait without requiring local controllability at all times during gait. Well-known example are McGeers “Passive Dynamic Walkers”, but the concept expands to actuated bipeds as involved in this study. Current state-of-the-art Limit Cycle Walkers excel in being very energy efficient, but their ability to handle disturbances (i.e. disturbance rejection) is still limited. A way to improve this ability while maintaining low energy consumption is the use of ankle actuation, which has so far seen few applications in this type of walker. In this paper we study the effect of (1) applying (passive) stiffness in the ankle joint, (2) applying control in the stance ankle based only on local sensor information and (3) modulating ankle push-off. For all three strategies the paper shows how they influence energy use and disturbance rejection of a simple point mass walking model, a more realistic model and a physical prototype. We find that applying a passive ankle spring that results in premature heel rise is energetically optimal and gives an actuation pattern that largely resembles that of humans. Local stance ankle control and ankle push-off modulation can improve the disturbance rejection of a Limit Cycle Walker by at least 60%, without increasing its energy use. These findings are substantiated by showing that our prototype is able to handle large disturbances such as a step-down of 5% of its leg length, while walking efficiently at a mechanical cost of transport of 0.09.

Controlling the Walking Speed in Limit Cycle Walking

“Limit Cycle Walking” is a relatively new paradigm for the design and control of two-legged walking robots. It states that achieving stable periodic gait is possible without locally stabilizing the walking trajectory at every instant in time, as is traditionally done in most walking robots. Well-known examples of Limit Cycle Walkers are the Passive Dynamic Walkers, but recently there are also many actuated Limit Cycle Walkers. Limit Cycle Walkers generally use less energy than other existing bipeds, but thus far they have not been as versatile. This paper focuses on one aspect of versatility: walking speed. We study how walking speed can be varied, which way is energetically beneficial and how walking speed affects a walkers ability to handle disturbances (that is, disturbance rejection). The study is performed using one prototype and one simulation model. The speed of these two walkers is adapted by changing three parameters: the amount of ankle push-off, upper body pitch and step length. The study has resulted in four conclusions. (1) Steady-state speeds between 0.24 and 0.68 m s -1 (for a 0.6 m leg length) were obtained, with loss of stability determining the lower limit and actuation limits determining the upper limit. This result shows the applicability of Limit Cycle Walking for versatile walking machines. (2) For any speed, powering the gait by leaning the body forward costs less energy than using ankle push-off. (3) In contrast to the apparent tradeoff between speed and stability in traditional walking robots, in Limit Cycle Walking we find that increasing the walking speed, independent of how this is done, automatically results in an increasing disturbance rejection. (4) A combination of feedforward actuation adjustment and step-to-step feedback from walking speed shows that it is possible to change walking speed in only a few steps and maintain a desired speed when performing tasks such as carrying loads and walking on slopes. In particular, this fourth conclusion underlines the applicability of the concept of Limit Cycle Walking for versatile two-legged walking machines.

Swing-Leg Retraction for Limit Cycle Walkers Improves Disturbance Rejection

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 McGeers 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.