From template to anchor: A novel control strategy for spring-mass running of bipedal robots

In this paper, we present a novel control strategy for running of bipedal robots with compliant legs. To achieve this goal and to take advantage of the characteristics of the template, we match the dynamics of the full multibody model of a real biped robot with the dynamics of a well-known running template called spring loaded inverted pendulum (SLIP) model. This can be viewed as a template and anchor approach. Because the SLIP model is theoretically conservative, it always operates at a constant energy level. However, real robots operate at various energy levels due to the positive and/or negative work done by the motors, inherent damping/friction of the components and more importantly, the regular ground impact that occurs during the running process. As a case study the proposed controller was implemented on a simulation of the bipedal robot called ATRIAS. The full dynamic equations for running of the ATRIAS robot are derived using the Lagrangian approach. To make our multibody biped robot run with a steady and stable gait that tracks the SLIP model dynamics, a two-level controller is proposed. The upper level controller in stance phase is designed with feedback linearization to make the active SLIP model follow the SLIP model trajectory. The lower level controller in stance phase is designed for the multibody model to track the toe force profile of the active SLIP model. Two active SLIP architectures are proposed for locked and unlocked torso cases of the robot. Simulation results demonstrate stable running based on this strategy for both cases of the ATRIAS model with locked and unlocked torso angle. Matching the SLIP dynamics on running biped robots not designed for spring-mass gaits is impossible due to actuator limitations, or, at best, inefficient.