Limit Cycle Walking

This chapter introduces the paradigm `Limit Cycle Walking'. This paradigm for the design and control of two-legged walking robots can lead to unprecedented performance in terms of speed, efficiency, disturbance rejection and versatility. This is possible because this paradigm imposes fewer artificial constraints to the robot's walking motion compared to other existing paradigms. The application of artificial constraints is a commonly adopted and successful approach to bipedal robotic gait synthesis. The approach is similar to the successful development of factory robots, which depend on their constrained, structured environment. For robotic walking, the artificial constraints are useful to alleviate the difficult problem of stabilizing the complex dynamic walking motion. Using artificial stability constraints enables the creation of robotic gait, but at the same time inherently limits the performance of the gait that can be obtained. The more restrictive the constraints are, the less freedom is left for optimizing performance. The oldest and most constrained paradigm for robot walking is that of `static stability', used in the first successful creation of bipedal robots in the early 70's. Static stability means that the vertical projection of the Center of Mass stays within the support polygon formed by the feet. It is straightforward to ensure walking stability this way, but it drastically limits the speed of the walking motions that can be obtained. Therefore, currently most humanoid robots use the more advanced `Zero Moment Point' (ZMP) paradigm (Vukobratovic et al., 1970). The stability is ensured with the ZMP-criterion which constrains the stance foot to remain in flat contact with the floor at all times. This constraint is less restrictive than static walking because the Center of Mass may travel beyond the support polygon. Nevertheless, these robots are still under-achieving in terms of efficiency, disturbance handling, and natural appearance compared to human walking (Collins et al., 2005). The solution to increase the performance is to release the constraints even more, which will require a new way of measuring and ensuring stability. This is the core of `Limit Cycle Walking'; a new stability paradigm with fewer artificial constraints and thus more freedom for finding more efficient, natural, fast and robust walking motions. Although this is the first time we propose and define the term `Limit Cycle Walking', the method has been in use for a while now. The core of the method is to analyze the walking motion as a limit cycle, as first proposed by Hurmuzlu (Hurmuzlu and Moskowitz, 1986). Most of the research on `Passive Dynamic Walking' initiated by McGeer (McGeer, 1990a) follows this stability method. But also various actuated bipedal robots that have been built around the world fall in the category of `Limit Cycle Walkers'.