Dual-Loop Optimal Control of a Robot Manipulator and Its Application in Warehouse Automation

Abstract

The goal of this work is to develop the next generation of coordinated optimal planning and control schemes for real-world robotic applications, with cost-effective intelligent robots that can safely and robustly perform the tasks at hand. This article presents a dual-loop optimal hierarchical control scheme for robotic manipulators consisting of outer and inner loops. The outer kinematic control loop in the operational space provides a joint velocity reference signal to the inner one. The kinematic control is formulated as a closed-loop optimal control approach to trajectory generation where the desired target (possibly time-varying) is obtained by acting upon the feedback from the actual state of the robot. The kinematic control is obtained using a closed-form analytic solution of the Hamilton–Jacobi–Bellman (HJB) equation. The proposed methodology defines the task in terms of the integral cost function, which results in a global optimal solution. The inner dynamic control loop consists of a neural network (NN)-based adaptive critic (AC) optimal tracking control scheme. The online NN approximator-based dynamic controller learns the infinite-horizon cost function related to inner loop error dynamics in continuous time and calculates the corresponding optimal control input to minimize the cost function forward in time. The stability and the performance of the proposed control scheme are shown theoretically via the Lyapunov approach and also verified experimentally using a 7-DOF Barrett WAM robot manipulator. The warehousing applications of the proposed dual-loop control scheme have been demonstrated experimentally in an exact warehouse setting. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This article was motivated by our previous experiences in the Amazon Robotics Challenge (ARC) competitions as a participant. Although the major lessons from those events revealed many important issues toward warehouse automation both from robotic vision and grasping aspects, the application aspects of control engineering to solution for these real-world problems could significantly benefit the today’s highly automated society. The intention of this article is to address this situation by designing a cost-effective robot manipulator control scheme by optimizing robot manipulation trajectories in the outer loop along with the actuator input in the inner loop. Therefore, we propose a dual-loop optimal control scheme for robotic manipulations under a cost-optimal framework with guaranteed stability proof via the Lyapunov approach. This results in smoother trajectories with cost-effective control actuator inputs than the state-of-the-art methods. We believe that this work can be beneficial for academic and industrial research to design more advanced and optimized solutions in this domain.