Spring-mass Walking with Atrias in 3d: Robust Gait Control Spanning Zero to 4.3 Kph on a Heavily Underactuated Bipedal Robot

We present a reduced-order approach for robust, dynamic, and efficient bipedal locomotion control, culminating in 3D balancing and walking with ATRIAS, a heavily underactuated legged robot. These results are a development toward solving a number of enduring challenges in bipedal locomotion: achieving robust 3D gaits at various speeds and transitioning between them, all while minimally draining on-board energy supplies. Our reduced-order control methodology works by extracting and exploiting general dynamical behaviors from the spring-mass model of bipedal walking. When implemented on a robot with spring-mass passive dynamics, e.g. ATRIAS, this controller is sufficiently robust to balance while subjected to pushes, kicks, and successive dodgeball strikes. The controller further allowed smooth transitions between stepping in place and walking at a variety of speeds (up to 1.2 m/s). The resulting gait dynamics also match qualitatively to the reduced-order model, and additionally, measurements of human walking. We argue that the presented locomotion performance is compelling evidence of the effectiveness of the presented approach; both the control concepts and the practice of building robots with passive dynamics to accommodate them. INTRODUCTION We present 3D bipedal walking control for the dynamic bipedal robot, ATRIAS (Fig. 1), by building controllers on a foundation of insights from a reduced-order “spring-mass” math model. This work is aimed at tackling an enduring set of challenges in bipedal robotics: fast 3D locomotion that is efficient and robust to disturbances. Further, we want the ability to transition between gaits of different speeds, including slowing to and starting from zero velocity. This set of demands is challenging from a generalized formal control approach because of various inconvenient mathematical properties; legged systems are typically cast as nonlinear, hybrid-dynamical, and nonholonomic systems, which at the same time, because of the very nature of walking, require highly robust control algorithms. Bipedal robots are also increasingly becoming underactuated, i.e. a system with fewer actuators than degrees of freedom [1]. Underactuation is problematic for nonlinear control methods; as degrees of underactuation increase, handy techniques like feedback-linearization decline in the scope of their utility. 1 Copyright c © 2015 by ASME FIGURE 1: ATRIAS, A HUMAN-SCALE BIPEDAL “SPRINGMASS” ROBOT DESIGNED TO WALK AND RUN IN THREE DIMENSIONS. Whenever a robot does not have an actuated foot planted on rigid ground, it is effectively underactuated. As a result, the faster legged robots move and the rougher the terrain they encounter, it becomes increasingly impractical to avoid these underactuated domains. Further, there are compelling reasons, both mechanical and dynamical, for removing actuators from certain degrees of freedom (see more in the robot design section). With these facts in mind, our robotic platform is built to embody an underactuated and compliant “spring-mass” model (Fig. 2A), and our control reckons with the severe underactuation that results. ATRIAS has twelve degrees of freedom when walking, but just six actuators. However, by numerically analyzing the spring-mass model, we identify important targets and structures of control that can be regulated on the full-order robot which approximates it. We organize the remainder of this paper as follows. We begin by surveying existing control methods for 3D, underactuated, and spring-mass locomotion. 2) The design philosophy of our spring-mass robot, ATRIAS, and its implementation are briefly described. 3) We then build a controller incrementally from a 1D idealized model, to a 3D model, to the full 12-degree-of-freedom robot. 4) We show that this controller can regulate speeds ranging from 0 m/s to 1.2 m/s and transition between them. 5) With a set of perturbation experiments, we demonstrate the robustness of the controller and 6) argue in our conclusions for the thoughtful cooperation between the tasks of robot design and control. (A) (B) Virtual leg Vi rtu al leg dir ec tio n spring-mass k m FIGURE 2: THE DESIGN PHILOSOPHY OF ATRIAS, WHICH MAXIMALLY EMBODIES THE “SPRING-MASS” MODEL OF WALKING AND RUNNING. A) THE SPRING MASS MODEL WITH A POINT MASS BODY AND MASSLESS LEG SPRING. B) ATRIAS WITH A VIRTUAL LEG SPRING OVERLAID.