Full Dynamics LQR Control With Multi Contact Phases For Bipedal Walking

Humanoid robots are expected to both locomote and interact with objects within unstructured environments. A key component to realizing this goal is the ability for our algorithms to handle multiple contact switching scenarios within a whole-body control framework. To complement the many advances in trajectory optimization we must recognize which tools work best to robustly track these trajectories while providing a well-defined disturbance rejection behavior. Over recent years, optimal control strategies have showed very promising results in simulation and on real systems for torque controlled humanoids that use operational-space techniques to achieve whole-body manipulation and locomotion. Previous work, [5], [12], [1], [11], [2], has utilized Quadratic Programs (QPs) that optimize over a variety of constraints (e.g. dynamic consistency, joint tracking, friction cones, etc.) in order to compute joint torques. Trajectories are often planned using operational-space techniques and then converted to joint torques using QPs, achieving whole-body manipulation. QPs can further be organized into hierarchies to solve whole-body optimal control problems such that there is a set priority in goals that the robot should achieve and tasks of higher priorities will always be achieved first [4]. Unfortunately, coupled with the growing flexibility of these methods there is also the added computational overhead, complexity in tuning, and a lack of theoretical disturbance rejection metrics, such as the gain and phase margin seen in classical control, that prevent these algorithms from being compared with one another. Currently, it remains unclear what level of complexity in controllers is needed on real systems. Real systems have problems such as model error, sensor noise, actuator saturations, backlash, stiction, and imperfect state estimation. Because of theses issues, the advances seen by algorithms in simulation do not always transfer to real systems. To address this unknown, we propose testing simpler optimal control strategies that still offer whole-body control and can handle multiple contact constraints. We are interested in studying to what extent contact-consistent linearized dynamic models can be used for the control of whole-body behaviors on real robots. In particular, we are interested in understanding how the performance compares with more advanced operationalspace control approaches on real robots. Previously in [7], Fig. 1. Balancing experiment conducted on the hydraulic torque controlled Sarcos humanoid. The weighted torso tracked a sine trajectory while the lower body balanced using a LQR controller with multiple foot constraints.