Asymptotically Optimal Design of Piecewise Cylindrical 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. We focus on the kinematic design of piecewise cylindrical robots, robotic manipulators whose shape can be modeled via cylindrical components. 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 (i) a serial manipulator and (ii) a concentric tube robot, a tentacle-like medical robot that can bend around anatomical obstacles to safely reach clinically-relevant goal regions.