A robot's dynamics -- especially the degree and location of compliance -- can significantly affect performance and control complexity. Passive dynamics can be designed with good regions of attraction or limit cycles for a specific task, but achieving flexibility on a range of tasks requires co-design of control. This paper takes an information perspective: the robot dynamics should reduce the amount of information required for a controller to achieve a threshold of performance in a range of tasks. Towards this goal, an iterative method is proposed to minimize the directed information from state to control on discrete-time nonlinear systems. iLQG is used to find a controller and value of information, then the design parameters of the dynamics (e.g. stiffness of end-effector or joint) are optimized to reduce directed information while maintaining a minimum bound on performance. The approach is validated in simulation, on a two-mass system in contact with an uncertain wall position and a high-DOF door opening task, and shown to improve noise robustness and reduce time variance of control gains.
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