Momentum Estimation, Planning and Control for Force-Centric Bipedal Locomotion

The stability of a humanoid robot is ensured by constraining its Center of Pressure (CoP) within its support polygon; using a simplified model such as the Linear Inverted Pendulum Model (LIPM) allows for a linear mapping between Center of Mass (CoM) and CoP motion. This enables the use of linear Model Predictive Control (MPC) methods to generate a CoM trajectory which realizes a desired CoP motion for the LIPM [1]. Traditional approaches to walking resolve the planned motion for joint trajectories and track these using stiff position control. However, the CoP is defined by interaction forces not positions. Since position control offers no direct control of force, this method relies on trajectory engineering and tuning. On a torque-controlled robot, however, one can directly track LIPM-consistent forces rather than COM motion. This allows for control of impedance, yet even this fails to work well without tuning for several reasons. First, the simplified model forces even if reproduced exactly on the robot will not generate the desired CoP motion due to model differences between the robot and the LIPM. Second, inverse dynamics solvers do not account for discrepancies between planned and measured forces due to perturbations, unobserved terrain and so on. In order to generate dynamic reactive behaviors on the real robot, we need to use descriptive simplified models which are consistent with the full dynamics and make use of endeffector force/torque (F/T) sensors for state estimation.