Energy based Control Barrier functions for Robotic Manipulators with Large Safety Constraints

In this paper, we show how to realize robust safety-critical control laws for robotic manipulators with a large number of inequality constraints (>100). In particular, we use control barrier functions (CBFs) formulated via the kinetic energy terms to represent constraints like joint position and velocity limits, both in configuration and task space. By using the kinetic energy terms, we can realize model-free constraints in a quadratic program (QP), which can be solved in real-time, thereby demonstrating fast computation time despite the presence of large constraints. We will consider two types of CBFs, the reciprocal and the zeroing type, and integrate with Control Lyapunov Function (CLF) based constraints to yield a multi-objective QP. Further, we will provide feasibility and continuity guarantees, thereby yielding a continuous, robust and a safe control law for a broad class of robotic systems. Towards the end, we will demonstrate two types of QP formulations in a 6-DOF manipulator; one uses 109 constraints through the reciprocal type, and the other uses 61 constraints using the zeroing type of CBFs.