  Underactuated manipulators reduce the number of bulky motors, thereby
enabling compact and mechanically robust designs. However, fewer actuators than
joints means that the manipulator can only access a specific manifold within
the joint space, which is particular to a given hardware configuration and can
be low-dimensional and/or discontinuous. Determining an appropriate set of
hardware parameters for this class of mechanisms, therefore, is difficult -
even for traditional task-based co-optimization methods. In this paper, our
goal is to implement a task-based design and policy co-optimization method for
underactuated, tendon-driven manipulators. We first formulate a general model
for an underactuated, tendon-driven transmission. We then use this model to
co-optimize a three-link, two-actuator kinematic chain using reinforcement
learning. We demonstrate that our optimized tendon transmission and control
policy can be transferred reliably to physical hardware with real-world
reaching experiments.
