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 walker's 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.