Date of Award


Embargo Period


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Robotics Institute


Christopher G. Atkeson


Walking is a core task for humanoid robots. Most existing walking controllers fall into one of two categories. One category plans ahead and walks precisely; they can place the feet in desired locations to avoid obstacles but react poorly to unexpected disturbances. The other category is more reactive; they can respond to unexpected disturbances but can not place the feet in specific locations. In this thesis, we present a walking controller that has many of the strengths of each category: it can place the feet to avoid obstacles as well as respond successfully to unexpected disturbances.

Dynamic programming is a powerful algorithm that generates policies for a large region of state space, but is limited by the “Curse of Dimensionality” to low dimensional state spaces. We extend dynamic programming to higher dimensions by introducing a framework for optimally coordinating multiple low-dimensional policies to form a policy for a single higher-dimensional system. This framework can be applied to a class of systems, which we call Instantaneously Coupled Systems, where the full dynamics can be broken into multiple subsystems that only interact at specific instants. The subsystems are augmented by coordination variables, then solved individually. The augmented systems can then be coordinated optimally by using the value functions to manage tradeoffs of the coordination variables.

We apply this framework to walking on both the Sarcos hydraulic humanoid robot and a simulation of it. We use the framework to control the linear inverted pendulum model, a commonly used simple model of walking. We then use inverse dynamics to generate joint torques based on the desired simple model behavior, which are then applied directly to either the simulation or the Sarcos robot. We discuss the differences between the hardware and the simulation as well as the controller modifications necessary to cope with them, including higher order policies and the inclusion of inverse kinematics.

Our controller produces stable walking at up to 1.05 m/s in simulation and at up to 0.22 m/s on the Sarcos robot. We also demonstrate the robustness of this method to disturbances with experiments including pushes (both impulsive and continuous), trips, ground elevation changes, slopes, regions where it is prohibited from stepping, and other obstacles.



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