Effector Shape and Motion Optimization

Abstract

In this thesis, methods are proposed for co-optimizing the shape and motion of robotic effectors for planar tasks. An effector is a device, typically at the end of a robotic arm, used to interact with the environment. While planning object and robot-object contact trajectories is extensively studied, designing an effector that can execute the planned trajectories receives less attention. As such, this thesis includes a framework that synthesizes an object trajectory and object-effector contact trajectory into an effector trajectory and shape that (a) does not penetrate the object, (b) makes contact with the object as specified, and (c) optimizes a user-specified objective. This simplifies manipulator control by encoding task-specific contact information in the effector's geometry. The key insight is posing these requirements as constraints in the effector's reference frame, preventing the need for explicit parameterization of the effector shape. This prevents artificial restrictions on the shape design space. Importantly, it also facilitates posing the shape and motion design problem as a tractable nonlinear program. This method is particularly useful for problems where the shape of the effector surface must be precisely chosen to achieve a task. This work is then extended to parallel-jaw grasping problems, in which grasp stability is considered while optimizing over contact locations, effector shape, and grasp configuration. This provides a path forward for future work in which effectors with multiple internal degrees of freedom are co-optimized with motion. Methods are demonstrated on example problems, including jar-opening, picking up objects in constrained spaces, and stably grasping sets of nonconvex objects. The algorithms' results and computational cost are evaluated. A physical experiment demonstrates a robotic arm picking up a screwdriver from a table using a tool that was designed using the proposed framework and manufactured to the derived shape.