Design of a Passively-adaptive Three Degree-of-freedom Multi- Legged Robot with Underactuated Legs

This paper discusses the design of a three degree-of-freedom (3-DOF) non-redundant walking robot with decoupled stance and propulsion locomotion phases that is exactly constrained in stance and utilizes adaptive underactuation to robustly traverse terrain of varying ground height. Legged robots with a large number of actuated degrees of freedom can actively adapt to rough terrain but often end up being kinematically overconstrained in stance, requiring complex redundant control schemes for effective locomotion. Those with fewer actuators generally use passive compliance to enhance their dynamic behavior at the cost of postural control and reliable ground clearance, and often inextricably link control of the propulsion of the robot with control of its posture. In this paper we show that the use of adaptive underactuation techniques with constraint-based design synthesis tools allows for lighter and simpler lower mobility legged robots that can adapt to the terrain below them during the swing phase yet remain stable during stance and that the decoupling of stance and propulsion can greatly simplify their control. Simulation results of the swing phase behavior of the proposed 3-DOF decoupled adaptive legged robot as well as proof-of-concept experiments with a prototype of its corresponding stance platform are presented and validate the suggested design framework. INTRODUCTION When dealing with the problems of robotic locomotion, legged robots can offer significant advantages over wheeled robots when dealing with rough terrain, including obstacles present in human environments. By utilizing discrete contact points with the ground and the ability to lift their legs over obstacles and other discontinuities in the terrain, legged robots generate stance configurations that are used to propel the body forward and stabilize it while walking. Many multi-legged walking robots, e.g. those relying on statically-stable gaits to remain upright, have been designed with legs of high kinematic complexity that have a large number of actuators to allow for complete control over the motion of the feet relative to the body (e.g.[1]). However, such designs tend to suffer from actuator redundancy in the stance phase, with more control inputs required than independently controllable degrees of freedom in the stance platform. Indeed, any legged robot with greater than six actuators engaged during stance is necessarily redundant, and this limit can be lower depending on the specific design in question. Moreover, in the absence of additional internal freedoms, such robots are also kinematically over-constrained in stance, potentially leading to destabilizing forces acting on the robot or the violation of the contact constraints. While over-constraint is not necessarily a problem, it does make effective control of a robot difficult due to the overdetermined nature of the system. Some control techniques developed to deal with this issue include the avoidance of overconstrained motions [2] and impendence control [3]. While these and other control laws have been shown to work under specific conditions, they generally rely on either lowimpendence actuators or high-fidelity output sensing, both of which are difficult to accomplish in practice. Additionally, the presence of redundant actuators in stance lead to heavier and