End-effector control for bipedal locomotion

Biped locomotion can be formulated as goal-directed tasks in the low-dimensional end-effector space, with the upper body and the two feet as end effectors. Based on this observation and the neuroscience hypothesis about hierarchical control in human for tasks such as arm reaching and handwriting, I design a framework for the automatic synthesis of hierarchical controllers for biped locomotion. The controller consists of two components: a per-footstep end-effector path planner at the higher level, and a per-timestep generalized-force solver at the lower level. At the start of each footstep, the planner performs short-term planning in the space of end-effector trajectories. These trajectories at run-time adapt to the interactive task goals and the features of the surrounding uneven terrain in the virtual environment. Using the per-footstep plan, the generalized-force solver takes ground contacts into consideration and solves a quadratic program at each simulation timestep to obtain joint torques that drive the biped. The framework solves for the parameters of the planner and the generalized-force solver for different tasks in offline optimizations. I demonstrate the capabilities of the controllers in navigation tasks where they perform gradual and sharp turns and transition between moving forwards, backwards, and sideways on uneven terrain according to the interactive task goals. I show that the resulting controllers are capable of handling certain morphology changes to the character. To verify that such hierarchical end-effector controllers can potentially be used in real-world mechanical systems, I also show that the controllers are robust to disturbances such as actuator and sensor noise, and changes in the friction coefficient. Because human locomotion is routinely subject to these disturbances, robustness against these disturbances also suggests that the hierarchical control hypothesis about human arm reaching and handwriting control may be a good candidate hypothesis for human locomotion control as well.