Analysis and controller design methods abound in the literature for planar (also known as 2-D) bipedal models. This paper takes one of them developed for underactuated bipeds and documents the process of designing a family of controllers on the basis of a planar model and achieving stable walking on a physical 3-D robot, both indoors and outdoors, with walking speed varying smoothly from 0 to 0.8 m/s. The longest walk in a single experiment is 260 m over terrain with ±7 • of slope variation. Advantages and disadvantages of the design approach are discussed.INDEX TERMS 3D walking, underactuated bipedal robot, optimal control.

Abstract-Wireless magnetic resonant power transfer is an emerging technology that has many advantages over other wireless power transfer methods due to its safety, lack of interference, and efficiency at medium ranges. In this paper, we develop a wireless magnetic resonant power transfer system that enables unmanned aerial vehicles (UAVs) to provide power to, and recharge batteries of wireless sensors and other electronics far removed from the electric grid. We address the difficulties of implementing and outfitting this system on a UAV with limited payload capabilities and develop a controller that maximizes the received power as the UAV moves into and out of range. We experimentally demonstrate our prototype wireless power transfer system by using a UAV to transfer nearly 5W of power to a ground sensor.

A key challenge in robotic bipedal locomotion is the design of feedback controllers that function well in the presence of uncertainty, in both the robot and its environment. This paper addresses the design of feedback controllers and periodic gaits that function well in the presence of modest terrain variation, without over-reliance on perception and a priori knowledge of the environment. Model-based design methods are introduced and subsequently validated in simulation and experiment on MARLO, an underactuated three-dimensional bipedal robot that is of roughly human size and is equipped with an inertial measurement unit and joint encoders. Innovations include an optimization method that accounts for multiple types of disturbances and a feedback control design that enables continuous velocity-based posture regulation via nonholonomic virtual constraints. Using a single continuously defined controller taken directly from optimization, MARLO traverses sloped sidewalks and parking lots, terrain covered with randomly thrown boards, and grass fields, all while maintaining average walking speeds between 0.9 and 0.98 m/s and setting a new precedent for walking efficiency in realistic environments.

No abstract

We investigate the design of periodic gaits that will also function well in the presence of modestly uneven terrain. We use parameter optimization and, inspired by recent work of Dai and Tedrake, augment a cost function with terms that account for perturbations arising from a finite set of terrain height changes. Trajectory and control deviations are related to a nominal periodic orbit via a mechanical phase variable, which is more natural than comparing solutions on the basis of time. The mechanical phase variable is also used to penalize more heavily deviations that persist "late" into the gait. The method is illustrated both in simulation and in experiments on a planar bipedal robot.