Robotic Manipulators and Vehicles

Abstract

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Nonlinear optimal control for a five-link parallel robotic manipulator

“…Parallel robots of closed-kinematic chain are frequently used in industrial and humans assisting tasks (Rigatos and Busawon, 2018; Chang et al, 2011; Ouyang et al, 2004). Such robotic mechanisms are met in applications where high stiffness, high lift force, and high velocity/acceleration of the end-effector and joints have to be developed (Ghorbel et al, 2000; Muller and Hufnagel, 2012; Shang and Cong, 2020; Shang et al, 2011; Shang and Cong, 2014).…”

“…This controller achieves the solution of the nonlinear optimal control problem for the robotic manipulator under model uncertainty and external perturbations. Actually, this controller represents a min-max differential game taking place between (i) the control inputs which try to minimize a cost function that contains a quadratic term of the state vector’s tracking error and (ii) the disturbance and model uncertainty inputs which try to maximize this cost function (Rigatos and Busawon, 2018). To select the feedback gains of the H-infinity controller, an algebraic Riccati equation is repetitively solved at each time-step of the control algorithm (Rigatos, 2011; Rigatos, 2015).…”

“…The global stability properties of the control method are proven through Lyapunov analysis. First, it is shown that the control scheme satisfies the H-infinity racking performance criterion which signifies elevated robustness against model uncertainty and external perturbations (Rigatos and Busawon, 2018; Toussaint et al, 2000). Next, under moderate conditions, it is also shown that the control loop is globally asymptotically stable.…”

“…The proposed control method retains the advantages of linear optimal control, that is, fast and accurate tracking of reference setpoints under moderate variations of the control inputs. Finally, to perform state estimation-based control without the need to measure the entire state vector of the robotic system, the H-infinity Kalman filter is used as a robust state estimator (Rigatos and Busawon, 2018).…”

“…Control and estimation for the nonlinear dynamics of parallel robotic manipulators remains a challenging research topic (Rigatos and Busawon, 2018). The present article provides a novel solution to the nonlinear optimal control problem of the five-link parallel robotic system which is of proven global stability while also remaining computationally efficient.…”