Asymptotically optimal kinematic design of robots using motion planning

In highly constrained settings, e.g., a tentacle-like medical robot maneuvering through narrow cavities in the body for minimally invasive surgery, it may be difficult or impossible for a robot with a generic kinematic design to reach all desirable targets while avoiding obstacles. We introduce a design optimization method to compute kinematic design parameters that enable a single robot to reach as many desirable goal regions as possible while avoiding obstacles in an environment. Our method appropriately integrates sampling-based motion planning in configuration space into stochastic optimization in design space so that, over time, our evaluation of a design's ability to reach goals increases in accuracy and our selected designs approach global optimality. We prove the asymptotic optimality of our method and demonstrate performance in simulation for (1) a serial manipulator and (2) a concentric tube robot, a tentacle-like medical robot that can bend around anatomical obstacles to safely reach clinically-relevant goal regions.