Shape and Motion Optimization of Rigid Planar Effectors for Contact Trajectory Satisfaction

We propose a framework for co-optimizing the shape and motion of rigid robotic effectors for planar tasks. 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, our framework 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. Our 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. Our method is particularly useful for problems where the shape of the effector surface must be precisely chosen to achieve a task. We apply our method to several such problems, including jar-opening and picking up objects in constrained spaces. We evaluate the performance and computational cost of our method, and provide a physical experiment of a robotic arm picking up a screwdriver from a table with a designed tool.