Iterative learning of energy-efficient dynamic walking gaits

Felix Kong, Sydney University


Iterative Learning Control (ILC) is a method to learn the control signal to track a reference trajectory over several attempts, with the potential for fast convergence and robustness to modelling errors. Terminal ILC (TILC), a variant of ILC, allows other performance objectives to be addressed by ignoring parts of the reference, blending trajectory optimization and motion control. However, ILC and TILC assume a fixed time duration for each attempt; for some tasks, the time duration is not known in advance. For example, the time duration of a footstep of an underactuated walking robot, or the time duration of a rocket's flight between planets changes significantly based on the control input applied to it, resulting in a problem with a ``free final time''. To address this, we introduce Phase-indexed ILC/TILC, where a phase variable in which the problem is periodic is used in place of time as an index variable for ILC/TILC. Using phase-indexed TILC, we construct such a phase variable, use it to optimize the walking gait of an underactuated dynamic walking robot, and discuss the advantages and disadvantages of this formulation compared to other trajectory optimization methods.