Consensus in Operational Space for Robotic Manipulators with Task and Input Constraints.

This paper presents a real-time control framework for consensus in operational space for robotic manipulators while satisfying task and input constraints. Consensus in operational space, as compared to joint space, enables heterogeneous robotic manipulators to achieve consensus. However, traditional frameworks tend to ignore task and input constraints while achieving consensus in operational space. We address this problem by defining safe sets in operational space and then ensure task constraint by designing Control Barrier Functions (CBF) in operational space. Control barrier functions guarantees to provide collision-free behavior for the robotic manipulator by modifying the nominal controller in a minimally invasive manner such that the trajectory of the manipulator remains in the safe set. The Quadratic Programming (QP) formulation also ensures that the nominal controller is only modified when the constraints are active, and the resulting controller is optimal in a min-norm setting. Our approach contrasts the traditional potential field method, which continues to influence the nominal controller because of its attractive and repulsive field design, and is therefore unsuitable for consensus problems. We also incorporate the input constraint in our QP formulation to ensure that the resulting controller complies with the task and input constraints. We show the efficacy of the proposed approach on 7 Degree of Freedom (DoF) KUKA LBR iiwa, 6 DoF KUKA KR5 R650 and 7 DoF Flexiv Rizon robotic manipulators, each with different dynamical and kinematic models using Dynamic Animation and Robotics Toolkit (DART) physics engine.