  Soft robot serial chain manipulators with the capability for growth,
stiffness control, and discrete joints have the potential to approach the
dexterity of traditional robot arms, while improving safety, lowering cost, and
providing an increased workspace, with potential application in home
environments. This paper presents an approach for design optimization of such
robots to reach specified targets while minimizing the number of discrete
joints and thus construction and actuation costs. We define a maximum number of
allowable joints, as well as hardware constraints imposed by the materials and
actuation available for soft growing robots, and we formulate and solve an
optimization problem to output a planar robot design, i.e., the total number of
potential joints and their locations along the robot body, which reaches all
the desired targets, avoids known obstacles, and maximizes the workspace. We
demonstrate a process to rapidly construct the resulting soft growing robot
design. Finally, we use our algorithm to evaluate the ability of this design to
reach new targets and demonstrate the algorithm's utility as a design tool to
explore robot capabilities given various constraints and objectives.
