text: Whole-body control (WBC) is a generic task-oriented control method for feedback control of loco-manipulation behaviors in humanoid robots. The combination of WBC and model-based walking controllers has been widely utilized in various humanoid robots. However, to date, the WBC method has not been employed for unsupported passive-ankle dynamic locomotion. As such, in this paper, we devise a new WBC, dubbed whole-body locomotion controller (WBLC), that can achieve experimental dynamic walking on unsupported passive-ankle biped robots. A key aspect of WBLC is the relaxation of contact constraints such that the control commands produce reduced jerk when switching foot contacts. To achieve robust dynamic locomotion, we conduct an in-depth analysis of uncertainty for our dynamic walking algorithm called time-to-velocity-reversal (TVR) planner. The uncertainty study is fundamental as it allows us to improve the control algorithms and mechanical structure of our robot to fulfill the tolerated uncertainty. In addition, we conduct extensive experimentation for: 1) unsupported dynamic balancing (i.e. in-place stepping) with a six degree-of-freedom (DoF) biped, Mercury; 2) unsupported directional walking with Mercury; 3) walking over an irregular and slippery terrain with Mercury; and 4) in-place walking with our newly designed ten-DoF viscoelastic liquid-cooled biped, DRACO. Overall, the main contributions of this work are on: a) achieving various modalities of unsupported dynamic locomotion of passive-ankle bipeds using a WBLC controller and a TVR planner, b) conducting an uncertainty analysis to improve the mechanical structure and the controllers of Mercury, and c) devising a whole-body control strategy that reduces movement jerk during walking.
  @cite_30: In order to explore the balance in legged locomotion, we are studying systems that hop and run on one springy leg. Pre vious work has shown that relatively simple algorithms can achieve balance on one leg for the special case of a system that is constrained mechanically to operate in a plane (Rai bert, in press; Raibert and Brown, in press). Here we general ize the approach to a three-dimensional (3D) one-legged machine that runs and balances on an open floor without physical support. We decompose control of the machine into three separate parts: one part that controls forward running velocity, one part that controls attitude of the body, and a third part that controls hopping height. Experiments with a physical 3D one-legged hopping machine showed that this control scheme, while simple to implement, is powerful enough to permit hopping in place, running at a desired rate, and travel along a simple path. These algorithms that control locomotion in 3D are direct generalizations of those in 2D, with surpris...
  @cite_26: Passive-dynamic walkers are simple mechanical devices, composed of solid parts connected by joints, that walk stably down a slope. They have no motors or controllers, yet can have remarkably humanlike motions. This suggests that these machines are useful models of human locomotion; however, they cannot walk on level ground. Here we present three robots based on passive-dynamics, with small active power sources substituted for gravity, which can walk on level ground. These robots use less control and less energy than other powered robots, yet walk more naturally, further suggesting the importance of passive-dynamics in human locomotion.
  @cite_21: This report documents our work in exploring active balance for dynamic legged systems for the period from September 1985 through September 1989. The purpose of this research is to build a foundation of knowledge that can lead both to the construction of useful legged vehicles and to a better understanding of animal locomotion. In this report we focus on the control of biped locomotion, the use of terrain footholds, running at high speed, biped gymnastics, symmetry in running, and the mechanical design of articulated legs.
  @cite_23: 
  @cite_10: There exists a class of two-legged machines for which walking is a natural dynamic mode. Once started on a shallow slope, a machine of this class will settle into a steady gait quite comparable to human walking, without active control or en ergy input. Interpretation and analysis of the physics are straightforward; the walking cycle, its stability, and its sensi tivity to parameter variations are easily calculated. Experi ments with a test machine verify that the passive walking effect can be readily exploited in practice. The dynamics are most clearly demonstrated by a machine powered only by gravity, but they can be combined easily with active energy input to produce efficient and dextrous walking over a broad range of terrain.
summary: Passive walking robots @cite_10 @cite_26 fall in the dynamic locomotion category too. These studies shed light on the important aspects of biped locomotion, but do not provide direct application for feedback control related to our methods. On the other hand, the progress made in actuated planar biped locomotion is impressive. @cite_21 @cite_23 show biped robots running and their capability to recover from disturbances on irregular terrains. However, there is an obvious gap between supported (or constrained) locomotion and unsupported walking. @cite_30 shows unsupported single leg hopping, which is a remarkable accomplishment. Besides the strong contribution in dynamic locomotion of that work, the study omitted several important aspects of unsupported biped locomotion such as body posture control, continuous interaction of the stance leg through the ground contact phases, and disturbances from the other limbs' motion, which are a focus of our paper.