Control Barrier Functions for Mechanical Systems: Theory and Application to Robotic Grasping

Abstract

Control barrier functions have been demonstrated to be a useful method of ensuring constraint satisfaction for a wide class of controllers. However, the existing results are mostly restricted to continuous-time systems. Mechanical systems, including robots, are typically second-order systems in which the control occurs at the force/torque level. These systems have actuator, velocity, and position constraints (i.e., relative degree two) that are vital for safety and/or task execution. Additionally, mechanical systems are typically controlled digitally as sampled-data systems. The contribution of this article is twofold. The first contribution is the development of novel, robust control barrier functions that ensure constraint satisfaction for sampled-data systems in the presence of model uncertainty and allows for satisfaction of actuator constraints. The second contribution is the application of the proposed method to the challenging problem of robotic grasping in which a robotic hand must ensure that an object remains inside the grasp while manipulating it to the desired reference trajectory. A grasp constraint satisfying controller is proposed that can admit the existing nominal manipulation controllers from the literature while simultaneously ensuring no slip, no overextension (e.g., singular configurations), and no rolling off of the fingertips. Simulation and experimental results validate the proposed control for the robotic hand application.