A Nonlinear Optimal Control Approach for Dual-Arm Robotic Manipulators

Dual-arm robotic manipulators are used in industry and for assisting humans since they enable dexterous handling of objects and more agile and secure execution of pick-and-place, grasping or assembling tasks. In this paper, a nonlinear optimal control approach is proposed for the dynamic model of a dual robotic arm. In the considered application, the dual-arm robotic system has to transfer an object under synchronized motion of its two end-effectors so as to achieve precise positioning and to compensate for contact forces. The dynamic model of this robotic system is formulated while it is proven that the state-space description of the robot’s dynamics is differentially flat. Next, to solve the associated nonlinear optimal control problem, the dynamic model of the dual-arm robot undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the dual-arm robot, a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution to the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The proposed nonlinear optimal control approach achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs.