In this article, we propose a robust high-order control barrier functions (HoCBFs)-based optimal control method for nonlinear systems with state constraints to achieve safety-stability perspectives. First, a kind of HoCBFs is presented for constrained nonlinear systems to address state constraints with high relative degrees. Second, the robustness property of the HoCBFs is analyzed based on the asymptotic stability of the forward invariant set. Specifically, a robust HoCBFs-based Lyapunov function is constructed to prove the uniform asymptotic stability of the set associated with the HoCBFs. In this way, a new sufficient condition is obtained for the stability analysis of the forward invariant set by using the inequalities of high-order derivatives of Lyapunov function. Third, a robust HoCBFs-based optimal control scheme is proposed for the constrained nonlinear system to achieve the safety-stability perspectives of constraints satisfaction and system stabilization, where the robust HoCBFs are combined with control Lyapunov functions (CLFs) to satisfy the small control property (SCP) in solving a quadratic program (QP). Furthermore, the proposed optimal control scheme is shown to be Lipschitz continuous and has no initial condition restrictions. Finally, two examples are presented to demonstrate the control performance of the proposed scheme. Note to Practitioners —The motivation of this article is that constraints exist widely in actual control systems, and the lack of constraint satisfaction in control systems may inevitably lead to safety defects, which usually degrade the control performances or even damage the entire system. In this article, a robust HoCBFs-based optimal control scheme is proposed for constrained nonlinear systems. The theoretical derivation demonstrates that the proposed control scheme can achieve safety-stability perspectives, which ensure system stabilization and task-oriented performance without violating the state constraints. The satisfactory control performances of the simulation on a constrained robotic manipulator show the potential practical application on a real robotic system.

This article presents an event-triggered adaptive neural impedance control (ETANIC) scheme for robotic systems, where the combination of impedance control (IC) and event-triggered mechanism can significantly reduce the computational burden and the communication cost under the premise of ensuring the stability and tracking performances of the robotic systems. The IC is used to achieve the compliant behavior of the robotic systems in response to the environment. The uncertainties of the robotic systems are estimated by the radial basis function neural network (RBFNN), and the update laws for RBFNN are derived from the designed Lyapunov function. The stability of the whole closed-loop control system is analyzed by the Lyapunov theory, and the event-triggered conditions are designed to avoid the Zeno behavior. The numerical simulation and experimental tests demonstrate that the proposed ETANIC scheme can achieve better efficiency for controlling the robotic systems to perform the interaction tasks with the environment in comparison to the adaptive neural IC (ANIC).

By mapping the performances of the task requirement and the inherent physical characteristics of the robotic systems to the hybrid constraints, this article proposes a task-oriented adaptive position/force control (TOAPFC) scheme for the robotic systems to ensure the execution of the predefined tasks and the safety of robotic manipulators and humans in the task workspace. In the proposed scheme, a reference trajectory generation strategy and admittance model are regarded as the outer loop of TOAPFC to obtain and shape the robotic system's task trajectory that guarantees the safety of the interaction system. An admittance-based adaptive position/force control scheme unifying the position and force into a control law is used as the inner loop of TOAPFC to track the shaped task trajectory, where a barrier Lyapunov function is utilized to constrain the tracking errors within permitted ranges. Moreover, the system uncertainties and lumped disturbances are compensated by the radial basis function neural network and robust compensator, respectively. Meanwhile, the stability of the proposed admittance-based adaptive position/force control scheme is analyzed by using the Lyapunov stability theory. Finally, the effectiveness of the proposed scheme is verified by experiments on a real robotic system.